Topology Seminars in Edinburgh

Upcoming Topology Seminar events

Recent Topology Seminar events

• "From chains to prime numbers" (CANCELLED)
  28th February 2018, 4:00pm to 5:00pm Room 5328, JCMB -- Show/hide abstract
  Abstract: Please note that this event has been cancelled.
• Scottish Topology Seminar
  12th January 2018, 1:30pm to 5:30pm International Centre for Mathematical Sciences (ICMS), 15 S College St, Edinburgh EH8 9AA, UK -- Show/hide abstract
  Abstract: https://www.maths.gla.ac.uk/sts/HomePage
• "Topology - the Dark Ages, 1820-1870" S.J.Patterson (Goettingen)
  21st September 2017, 4:00pm to 5:00pm Room 5323, JCMB -- Show/hide abstract
  Abstract: "Topology - the Dark Ages, 1820-1870" S.J. (Paddy) Patterson, Goettingen 4PM, Thursday, 21st September Room 5323, JCMB Abstract: In the 1850s and 1860s one finds the first arguments in mathematics and mathematical physics in which topological concepts are used. The most prominent name here is Riemann but Helmholtz and Maxwell also used such ideas. It seems fairly clear that such ideas did not spring suddenly into existence like Athene from Zeus' forehead but had long existed but were not published. At this time they seem to have become respectable and could be presented in polite company. The problem which I shall discuss in this talk is as how can one search for evidence about these early developments and to what extent can one reliably reconstruct what happened. Video of topology seminar by Paddy Patterson on 22 September 2014 "Riemann and topology in Goettingen" https://www.youtube.com/watch?v=SbtiSoCkkk0 Video of topology seminar by Patterson on 23rd March 2016 "The Riemann Hypothesis: Gold at the end of the rainbow" https://www.youtube.com/watch?v=NkLtCMg5ka0
• ICMS Workshop on braids in algebra, geometry and topology (22-26 May)
  31st March 2023, 8:46am to 8:46am International Centre for Mathematical Sciences (ICMS), 15 S College St, Edinburgh EH8 9AA, UK -- Show/hide abstract
  Abstract: http://icms.org.uk/workshop.php?id=421
• Scottish Topology Seminar #14
  30th September 2016, 10:00am to 5:30pm ICMS, University of Edinburgh, 15 S College St, Edinburgh EH8, UK -- Show/hide abstract
  Abstract: In honour of Andrew Ranicki. Speakers: Sir Michael Atiyah (Edinburgh), Tara Brendle (Glasgow), Stefan Friedl (Regensburg), Erik Pedersen (Copenhagen), Graeme Segal (Oxford)
• HODGE DAY (organized by Vanya Cheltsov)
  17th June 2016, 9:00am to 6:00pm Room 5327, JCMB -- Show/hide abstract
  Abstract: http://www.maths.ed.ac.uk/cheltsov/hodge2016/index.html
• TOPOLOGY SEMINAR (Nigel Hitchin, Oxford)
  16th June 2016, 4:00pm to 5:00pm Room 5327, JCMB -- Show/hide abstract
  Abstract: “Spinors, Higgs bundles and Lagrangians” Abstract: The talk concerns holomorphic vector bundles V on a Riemann surface which have a symplectic structure and for which there is a holomorphic section \psi of V\otimes K^{1/2} — a solution to the coupled Dirac equation. If V is associated to a principal G-bundle by a symplectic representation then the moment map defines a Higgs field and a point in the Higgs bundle moduli space for the group G. Following an approach of Gaiotto this lies on a Lagrangian subvariety. We consider these varieties, for different representations of SL(2), from the point of view of determinant divisors in the moduli space of stable bundles and the integrable system structure on the Higgs bundle moduli space. The special case of genus 2 links up with the classical geometry of the Kummer surface. Professor Hitchin was recently awarded a Shaw Prize http://www.shawprize.org/en/ He is visiting Michael Atiyah.
• TOPOLOGY SEMINAR (Matthias Nagel, CIRGET/UQAM)
  26th May 2016, 4:00pm to 5:00pm Room 6311, JCMB TBC -- Show/hide abstract
  Abstract: Title: Representation varieties and essential surfaces Abstract: We explain Culler-Shalen's construction of essential surfaces in a 3-manifold, which uses the representation variety of SL(2,C). No knowledge on 3-manifold topology is required. After generalising this construction to SL(n,C) representations, if time allows, we explain how all essential surfaces can be obtained from it. Based on joint work with Stefan Friedl and Takahiro Kitayama.
• TOPOLOGY SEMINAR (MARK POWELL, UQAM)
  17th May 2016, 4:00pm to 5:00pm Room 4312, JCMB -- Show/hide abstract
  Abstract: Topological 4-manifolds and surgery theory Without assuming any specialist knowledge, I will endeavour to describe a selection of results on the classification of topological 4-manifolds. The main tool is surgery theory, which thanks to Freedman's disc embedding theorem can be applied to 4-manifolds with certain fundamental groups. I will touch on recent (epsilon) progress on the disc embedding theorem, and consider the stable classification problem, which arises if one allows connect sum with copies of S^2 x S^2.
• TOPOLOGY SEMINAR (Bismut, Orsay) - Joint with EMPG
  4th May 2016, 4:00pm to 5:00pm ICMS, 15 South College Street, NOTE CHANGE OF VENUE AND TIME -- Show/hide abstract
  Abstract: Hypoelliptic Laplacian, index theory and the trace formula http://www.maths.ed.ac.uk/~aar/bismut.pdf
• TOPOLOGY SEMINAR (MARTIN FRANKLAND, OSNABRUCK)
  25th March 2016, 4:10pm to 5:10pm JCMB 4312 -- Show/hide abstract
  Abstract: Title: Higher Toda brackets and the Adams spectral sequence Abstract: I will review the construction of the Adams spectral sequence in a triangulated category equipped with a projective or injective class, along with examples from topology and from algebra. Then, following Cohen and Shipley, I will describe higher Toda brackets in a triangulated category. The main result expresses differentials in the Adams spectral sequence as certain higher Toda brackets, which can be viewed as higher cohomology operations. This is joint work with Dan Christensen.
• TOPOLOGY SEMINAR (S.J.PATTERSON, GOETTINGEN) Riemann and his Hypothesis - a pot of gold at the end of the rainbow?
  23rd March 2016, 4:10pm to 5:10pm Lecture Room C, JCMB -- Show/hide abstract
  Abstract: The Riemann Hypothesis is a question which has exercised considerable fascination even beyond the usual mathematical circles. It has been the subject of several popular books and of an extensive TV programme. The purpose of this talk is to experiment in, and to reflect on, the communication of the Riemann Hypothesis to non-experts. The more technical aspects can only be indicated by analogy and I shall make use of acoustics. On the historical side, documents which have recently become available illuminate the context in which was Riemann was working, and thereby his lines of thought. Riemann has often been felt to be an obscure writer, a mathematical Heraclitus. A major reason for this is that he gives very little idea of where the ideas he is using came from. It seems as if he learnt mathematical ideas without paying any heed to their provenance. In a talk given in this seminar in September, 2014 I argued that Riemann assumed topological notions from Gauss and, especially, Listing; these ideas were also taken up in different contexts by Clerk Maxwell and Tait. In this talk I shall speak about the ideas which go into Riemann's short paper on the distribution of prime numbers and how, it seems, he himself approached the question of the zeros. Later it was especially George Polya (Pólya György) who followed a similar path so that, despite the hopes of some, it seems most unlikely that a proof of the hypothesis (or even of Hardy's theorem) is lurking in his papers in Göttingen or elsewhere. http://www.maths.ed.ac.uk/~aar/papers/riemannprim.pdf (Riemann's paper) http://www.maths.ed.ac.uk/~aar/papers/riemannprimeng.pdf (English translation) http://www.claymath.org/publications/riemanns-1859-manuscript
• SCOTTISH TOPOLOGY SEMINAR (O.Randal-Williams, C.Rovi, M.Weiss)
  11th March 2016, 2:00pm to 6:00pm ICMS, South College Street -- Show/hide abstract
  Abstract: Speakers: Oscar Randal-Williams (Cambridge), Carmen Rovi (MPIM, Bonn), Michael Weiss (Muenster) 14:00 - 15:00 Michael Weiss https://wwwmath.uni-muenster.de/u/michael.weiss/ "Rational Pontryagin classes of fiber bundles with fiber a euclidean space" Abstract: The i-th Pontryagin characteristic class of a vector bundle is a class in the integral cohomology of degree 4i of the base space. If deRham cohomology is used, and the base space is a smooth manifold, and the vector bundle is a smooth vector bundle equipped with a connection, then the Pontryagin classes admit a description in terms of the curvature of that connection (Chern-Weil theory). A key step in the development of surgery theory, accomplished by Thom and Novikov, was to show that the Pontryagin classes can also be defined for a fiber bundle with fiber homeomorphic to a euclidean space (without specified vector space structures on the fibers), provided that cohomology with rational coefficients is used. Such fiber bundles arise naturally in manifold topology as tangent bundles of topological manifolds. Understanding their classifying space(s) is therefore also essential when it comes to classifying smooth structures on a topological manifold of dimension >4. The Pontryagin classes are stable characteristic classes: they do not change when a vector bundle (or fiber bundle with fiber homeomorphic to a euclidean space) is replaced by its Whitney sum with a trivial line bundle. Nevertheless a few interesting things can be said about the Pontryagin classes of vector bundles with a specified fiber dimension n. For example, the Pontryagin classes of such a vector bundle vanish in cohomology dimensions greater than 2n. If n is even and the vector bundle is oriented, then the Pontryagin class in degree 2n is the square of the Euler class in degree n. For many years I tried to show that these relations or vanishing results are also satisfied in the absence of vector space structures, i.e., in the case of fiber bundles with fiber homeomorphic to a euclidean space and their rational Pontryagin classes. Only about 3 years ago I began to understand that this is not the case. The counterexamples are based on a method from 1960s differential topology called plumbing, enhanced with more recent results from parameterized surgery and functor calculus. 15.10-16.10 Carmen Rovi http://people.mpim-bonn.mpg.de/rovi "The signature mod 8 of a fibration" Abstract: In this talk we shall be concerned with the residues modulo 4 and 8 of the signature σ(M) in Z of an oriented 4k-dimensional geometric Poincaré complex M^{4k}. The precise relation between the signature modulo 8, the Brown-Kervaire invariant was worked out by Morita some 40 years ago. We shall discuss how the relation between these invariants and the Arf invariant can be applied to the study of the signature modulo 8 of a fibration. In particular it had been proved by Meyer in 1973 that a surface bundle has signature divisible by 4. This was generalized to higher dimensions by Hambleton, Korzeniewski and Ranicki in 2007. I will explain two results from my thesis concerning the signature modulo 8 of a fibration: firstly under what conditions can we guarantee divisibility of the signature by 8 and secondly what invariant detects non-divisibility by 8 in general. 16.10-16.40 Tea 16.40-17.40 Oscar Randal-Williams https://www.dpmms.cam.ac.uk/~or257/ "Realising characteristic numbers of fibre bundles" Abstract: I will first give an introduction to my ongoing work with S. Galatius concerning the cohomology of moduli spaces of manifolds. I will then explain how this may be used to address certain realisation questions for fibre bundles: when is there a fibre bundle F -> E -> B with F, E, and B having prescribed characteristic numbers? In particular, I will show how one can deduce the existence of fibre bundles on which the signature is not multiplicative modulo 8.
• GEOMETRY CLUB: Floer Theory, to A-infinity and beyond (Tim Large, Cambridge)
  11th December 2015, 2:30pm to 3:30pm ROOM 4312, JCMB -- Show/hide abstract
  Abstract: Floer theory, to A-infinity and beyond Tim Large (Cambridge) Floer theory is a powerful tool now ubiquitous in symplectic and low-dimensional topology. In its incarnation as Lagrangian Floer cohomology, it plays a central role in various mathematical formulations of string theory, and modern formulations of mirror symmetry link it to the study of coherent sheaves on algebraic varieties. We will set up Floer cohomology in its simplest setting, on oriented (Riemann) surfaces, where the hard analysis that characterises the higher-dimensional theory disappears, and the theory becomes wonderfully visual and essentially combinatorial. However all the essential algebraic features of the theory are clear and very geometric in this formulation, including the surprising appearance of A-infinity categories: "categories" where the composition of morphisms is not strictly associative, but this failure is tightly controlled by "higher order composition" maps. Absolutely no knowledge of symplectic geometry is required- we will be starting from scratch and working entirely in an elementary setting!
• GEOMETRY/TOPOLOGY SEMINAR: Oscar Garcia Prada
  12th November 2015, 1:10pm to 2:10pm Room 6311, JCMB -- Show/hide abstract
  Abstract: Oscar Garcia-Prada (ICMAT, Madrid) Title: Higgs bundles and representations of surface groups Abstract: In this talk I will show how Higgs bundles over a compact Riemann surface can be used to study the moduli space of representations of the fundamental group of the surface in a non-compact semisimple Lie group. Special attention will be given to the case in which the symmetric space defined by the Lie group is of Hermitian type.
• TOPOLOGY SEMINAR: Thomas Huetteman (Belfast)
  30th October 2015, 4:10pm to 5:10pm Room 6311, JCMB -- Show/hide abstract
  Abstract: "On a toric criterion for finite domination of chain complexes" A chain complex of R-modules is called R-finitely dominated if it is homotopy equivalent to a bounded complex of finitely generated projective R-modules. (This notion is relevant, for example, in topology of manifolds, group theory, and - in the guise of "perfect complexes" - in algebraic geometry.) An important special case can be treated explicitly: A bounded chain complex of finitely generated free R[x,1/x]-modules is R-finitely dominated if and only if its "Novikov homology" (homology with coefficients in rings of formal Laurent series) is trivial (Ranicki 1995). In the talk I will discuss a generalisation of this homological criterion for finite domination to cover the case of Laurent polynomial rings in many indeterminates. This is joint work with David Quinn, and ultimately leads to a characterisation of finite domination in terms of projective toric varieties over non-commutative rings. More precisely I will explain how finite domination implies triviality of suitable versions of Novikov homology. The proof is inspired by a result on totalisation of double chain complexes of Bergman. I will explain how homotopy commutative cubical diagrams occur quite naturally in this context, and how these are related to the formalism of multicomplexes and their totalisations.
• TOPOLOGY SEMINAR (Paul Kirk)
  9th October 2015, 4:10pm to 5:10pm ROOM 6206, JCMB -- Show/hide abstract
  Abstract: Paul Kirk (Bloomington/MPIM Bonn) Studying knots in 3-manifolds via spaces of SU(2) representations of their fundamental group 4.10PM, Room 6206, JCMB Abstract: The most powerful invariant of a 3 manifold (such as the complement of a knotted circle in the 3-sphere) is its fundamental group. One approach to probing this group is to study the spaces of homomorphisms from the fundamental group into a Lie group such as SU(2). The topological properties of these representation spaces reflect geometric properties of the 3-manifold. I will illustrate, mostly via examples, what some of these representation spaces look like, and discuss some approaches to extract invariants of 3 manifolds and knots by studying the properties of their representation spaces.
• TOPOLOGY SEMINAR : 3 TOPOLOGY-RELATED SUMMER PROJECTS
  2nd October 2015, 4:10pm to 5:31pm JCMB ROOM 5215 -- Show/hide abstract
  Abstract: 16.10-16.30 Imogen Morris "'Untangling Celtic Knots' All around Edinburgh, on the buildings, gravestones and shop signs, you can see Celtic knots laid out in beautiful and elegant patterns. But how do you know that the complex tangle of your bike lock or headphone cable isn't also a Celtic knot? By calculating the Seifert matrix of Celtic knots we will learn how to recognise them in unexpected places. http://www.maths.ed.ac.uk/~aar/ImogenMorrisreport.pdf 16.30-16.50 Jaan-Eerik Past "Applications of Persistent Homology to Image Analysis" The ever-increasing amounts of data produced by modern science and industry demand new and more effective methods of analysis. A strong contender for the solution is topological data analysis - a young field that uses algebraic topology to find deep and unexpected structures in data. Specifically, we will explain how and why persistent homology has already been applied in areas ranging from cancer detection and movements of robots to analysing brain scans. We will also demonstrate very accessible software used for persistent homology calculations and how we used it to find a Klein bottle hidden in pictures of cities. http://www.maths.ed.ac.uk/~aar/JaanEerikPastreport.pdf 16.50 -17.10 Carl Pierer "Exploring the Topology of Scottish Ceilidh Dances" Imagine that, in a Scottish ceilidh dance, each dancer is holding a ribbon connected to a point on the ceiling. As the dance unfolds, the dancers will move around each other and create a mathematical braid in their ribbons. By examining the mathematical properties of the resulting braids, we understand the relation between mathematics and the movements in a ceilidh. Is there a trivial ceilidh? Are there two distinct, yet mathematically equivalent ceilidhs? This understanding is then applied to robot motion planning, where braids have proved useful in the design of collision-avoidance algorithms. Videos: https://www.youtube.com/playlist?list=PLNgPFIW8JiXL1mirKnt-Y0TBmVe2OvsyK
• Structure and Symmetry Symposium + Topology Seminar: C.MANOLESCU, TRIANGULATION CONJECTURE
  18th May 2015, 4:00pm to 5:00pm Room 6206, James Clerk Maxwell Building, Edinburgh, United Kingdom -- Show/hide abstract
  Abstract: VISIT SUPPORTED BY SCHEME 2 OF THE LONDON MATHEMATICAL SOCIETY
• TOPOLOGY SEMINARS: HYDRODYNAMICS AND TOPOLOGY, IN HONOUR OF H.K.MOFFATT'S 80th BIRTHDAY
  14th May 2015, 2:00pm to 6:00pm International Centre for Mathematical Sciences (ICMS), 15 South College Street, Edinburgh, Midlothian EH8 9AA, United Kingdom -- Show/hide abstract
  Abstract: Hydrodynamics and Topology: Meeting in honour of Keith Moffatt's 80th birthday 2-6PM at ICMS, 15 South College Street. 2.00-2.50 Gunnar Hornig (Dundee) Magnetic Helicity: applications and generalisations 2.55-3.45 Etienne Ghys (ENS-Lyon) Is helicity a topological invariant? 3.45-4.15 Tea 4.15-5.05 Michael Proctor (DAMTP, Cambridge) Mean-field Electrodynamics in the nonlinear regime? 5.10-6.00 Keith Moffatt (DAMTP, Cambridge) introduced by Michael Atiyah, Topological jumps in deforming soap films and in vortex dynamics
• TOPOLOGY SEMINAR (SZPIRO) The Truth, the Whole Truth, And Nothing but the Truth
  9th April 2015, 4:00pm to 5:00pm Room 6206, JCMB -- Show/hide abstract
  Abstract: The Truth, the Whole Truth, And Nothing but the Truth George Szpiro (New York/Jerusalem) In this seminar I will discuss the difficulties a journalist faces who writes about mathematics for the general reader. Mathematics is a very technical subject and, unlike other sciences, like physics, medicine or biology, cannot be easily explained to non-specialists. Nevertheless, the writer must try to communicate at least an idea of what our subject is about, strictly avoiding to ‘dumb down,’ and all the while trying to keep the reader interested.
• Scottish Topology Seminar
  19th March 2015, 1:00pm to 6:00pm International Centre for Mathematical Sciences (ICMS), 15 South College Street, Edinburgh, Midlothian EH8 9AA, United Kingdom -- Show/hide abstract
  Abstract: 1.00-3.00 Saul Schleimer (Warwick), 3.30-4.30 Jake Rasmussen (Cambridge), 4.40-5.40 Maciej Borodzik (Warsaw)
• TOPOLOGY SEMINAR, MICHELLE BUCHER-KARLSSON (GENEVA)
  18th February 2015, 4:00pm to 5:00pm Rooom 4325B, JCMB -- Show/hide abstract
  Abstract: "Characteristic numbers and volumes of hyperbolic representations"
• TOPOLOGY SEMINAR (Riemann and Topology in Goettingen, S.J.Patterson)
  22nd September 2014, 4:10pm to 5:10pm Room 6206, JCMB (tbc) -- Show/hide abstract
  Abstract: Riemann and topology in Goettingen S.J.Patterson (Goettingen)
• DOUBLE TOPOLOGY SEMINAR "Topology and Art"
  4th August 2014, 3:00pm to 5:00pm LECTURE ROOM C, JCMB -- Show/hide abstract
  Abstract: There will be a special topology seminar on Monday, 4th August, 15.00-17.00, in Lecture Room C, James Clerk Maxwell Building, featuring two speakers who are topologists actively involved both in the theory and practice of the artistic representations of spaces. 15.00 Henry Segerman (OSU) https://www.math.okstate.edu/~segerman/ "Sculpture in four-dimensions" Abstract - Humans evolved in a three-dimensional environment. As a result we are very good at visualising three-dimensional objects. But what about four-dimensional objects? The best we can do is look at their three-dimensional "shadows". Just as the shadow of a three-dimensional object squishes it into a two-dimensional plane, we can squish a four-dimensional shape into three-dimensional space. If the four-dimensional object is not too complicated, and if we choose a good way to squish it, then we can get a very good sense of what it is like. We will explore the sphere in four-dimensional space, the four-dimensional polytopes (which are the four-dimensional versions of the three-dimensional polyhedra - the shapes of dice), and various sculptures and puzzles that have come from thinking about these things. See also: http://www.segerman.org/ https://www.math.okstate.edu/~segerman/#art_exhibitions https://www.shapeways.com/shops/henryseg https://www.youtube.com/user/henryseg http://www.thingiverse.com/henryseg/designs 16.00 Saul Schleimer (Warwick) http://homepages.warwick.ac.uk/~masgar/ "Minimal and Seifert surfaces" Abstract - "Surfaces" are interfaces; boundaries between this and that. The peel of an orange, the crust of a bagel, the skin of a person, the bark of a tree: all are examples of surfaces. These are studied mathematically using the tools of geometry and topology. Important examples arise in geometry in the guise of "minimal surfaces": the soap films pondered by child and professor alike. In topology Seifert surfaces serve as an interface between knots, one-dimensional loops, and knot complements, three-manifolds of startling beauty. I will describe these objects via many two-dimensional pictures and three-dimensional prints. Most are constructed in the three-sphere and then stereographically projected into our three-dimensional space.
• TOPOLOGY SEMINAR (CARL McTAGUE)
  9th June 2014, 4:15pm to 5:15pm Room 6301, JCMB "New applications of differential geometry to big data" -- Show/hide abstract
  Abstract: "New applications of differential geometry to big data"
• TOPOLOGY SEMINAR (David Epstein)
  12th May 2014, 4:10pm to 5:10pm Room 6311, James Clerk Maxwell Building, Edinburgh, United Kingdom -- Show/hide abstract
  Abstract: Machine learning and topology
• TOPOLOGY SEMINAR (LUECK)
  29th April 2014, 2:30pm to 5:10pm Room 6301, JCMB -- Show/hide abstract
  Abstract: Tuesday, 29th April Wolfgang Lueck (HIM, Bonn) Room 6301, JCMB. 2.30-3.30PM "Introduction to $L^2$-invariants" Abstract: We give an introduction to $L^2$-invariants such as $L^2$-Betti numbers and $L^2$-torsion which generalize the classical notions of Betti numbers and Reidemeister and Ray-Singer torsion. We discuss the large variety of applications to problems in geometry, topology, group theory and spectral theory. Tuesday, 29th April Wolfgang Lueck (HIM, Bonn) Room 6301, JCMB. 4.10-5.10PM "On the possible values of the $L^2$-invariants" Abstract: In this talk we address the question what the possible values of $L^2$-Betti numbers of closed manifolds are. On one hand it is possible that they are irrational but on the other hand the variant of a question of Atiyah, whether they are always integers for an aspherical manifold $M$ is still open, and we give some evidence for it.
• JOINT GEOMETRY/TOPOLOGY SEMINAR (ETIENNE GHYS)
  21st March 2014, 3:00pm to 4:00pm David Hume Tower,Edinburgh, Faculty Room North
• TOPOLOGY: A CHAOTIC AFTERNOON WITH ETIENNE GHYS
  20th March 2014, 1:00pm to 5:30pm International Centre for Mathematical Sciences (ICMS), South College Street, Edinburgh, United Kingdom -- Show/hide abstract
  Abstract: Scottish Topology Seminar. Book tickets with Eventbrite http://www.eventbrite.co.uk/e/a-chaotic-afternoon-with-etienne-ghys-part-1-tickets-9566089431?aff=es2&rank=2&sid=f8701d11958311e3a61212313b049561 http://www.eventbrite.co.uk/e/a-chaotic-afternoon-with-etienne-ghys-part-2-tickets-10588631883?aff=es2&rank=1&sid=f8701d11958311e3a61212313b049561
• TOPOLOGY SEMINAR (3 INFORMAL TALKS ON KNOT THEORY)
  18th February 2014, 2:00pm to 5:00pm International Centre for Mathematical Sciences (ICMS), 15 South College Street, Edinburgh, United Kingdom -- Show/hide abstract
  Abstract: Three informal talks on knot theory. Gunnar Hornig (Dundee), 2.00-2.45PM, TBA Brendan Owens (Glasgow) Searching for slice disks 3.00-3.45PM, Andrew Ranicki (Edinburgh) Surgery and braids 4.15-5.00PM, Abstracts on http://hodge.maths.ed.ac.uk/tiki/Topology+seminar
• TOPOLOGY SEMINAR. Topology of Neural Systems (Ran Levi, Aberdeen)
  24th January 2014, 3:00pm to 4:00pm Faculty Room North, David Hume Tower -- Show/hide abstract
  Abstract: This talk is a report on an ongoing project that aims to contribute to the understanding of certain aspects of brain activity. The project is carried out jointly with Kathryn Hess, and Sophie Raynor, in collaboration with the Blue Brain Project in EPFL, and as a part of the Human Brain Project https://www.humanbrainproject.eu/en_GB. The brain, or possibly any part of it, can be viewed as a graph in several ways, the simplest of which is by regarding the neurons as vertices with an edge between two vertices if they are connected to each other by a synapse. One naturally regards this graph as oriented, as the connections in a neural system are directional, but for some purposes ignoring orientation is also interesting. Experimental data will impose restrictions on the nature of such a graph, for instance on the number and strength of connections between any given vertex and other vertices. Once a graphical description is the basic concept one deals with, a variety of mathematical structures that may be biologically relevant emerge. In this talk I will discuss a number of ideas that we have been investigating, ranging from the application of basic techniques of algebraic topology to the study of state of the art simulated neural systems, to a category theoretic model of neural systems which encodes not only their structure, but also the activity within them and their ever changing states.
• TOPOLOGY SEMINAR (ATIYAH, GRABOWSKI)
  17th January 2014, 3:00pm to 5:30pm Room 6206, JCMB -- Show/hide abstract
  Abstract: 3.00-4.00 Atiyah "Discrete groups, von Neumann algebras and L^2 Betti numbers" (Edinburgh) 4.30-5.30 Grabowski (Warwick) "On Turing dynamical systems and the Atiyah problem" For further details see http://hodge.maths.ed.ac.uk/tiki/Topology+seminar
• SCOTTISH TOPOLOGY SEMINAR IN EDINBURGH (GRAY, BARROW-GREEN, COLLINS)
  19th December 2013, 1:00pm to 6:00pm EDINBURGH, ICMS, 14 South College Street -- Show/hide abstract
  Abstract: Book your free ticket here http://www.eventbrite.co.uk/e/afternoon-lectures-from-the-history-of-topology-tickets-9565926945?aff=efblike Four lectures on the history of topology + 13.00-13.55 Jeremy Gray (Open) "Poincaré and the study of surfaces"The study of surfaces was one of Henri Poincaré’s lifelong interests. He began in the early 1880s with the study of flows on surfaces, which he partly regarded as a preliminary to the study of celestial mechanics, and then switched to the study of complex differential equations and their connection to the study of complex (Riemann) surfaces. His discovery of the role of non-Euclidean geometry in the theory of Riemann surfaces led to a competition with the German mathematician Felix Klein, and to the conjecture of the uniformisation theorem, which was to resist proof for a further 25 years. + 14.05-15.00 Jeremy Gray (Open) "Poincaré and the creation of the theory of 3-manifolds" In the opening years of the 20th century Poincaré was led to create a theory of three-dimensional manifolds, and to try to impose some order on a new subject in mathematics. How can three-dimensional manifolds be defined, and how can they be classified? Poincaré’s attempts to answer these questions led him to deepen the tools of algebraic topology and to pose – but, famously, not to answer – what became known as the Poincaré conjecture.{MOUSEOVER} * [http://puremaths.open.ac.uk/People/june.barrow-green|June Barrow-Green (Open)] +15.30-16.30 June Barrow-Green (Open) "GD Birkhoff and the development of dynamical systems theory" In October 1912, the young American mathematician GD Birkhoff 'astonished the mathematical world' by providing a proof of Poincaré's last geometric theorem. The theorem, which was connected to Poincaré's longstanding interest in the periodic solutions of the three-body problem, had been proposed by Poincaré only months before he died. Birkhoff continued to work on aspects of dynamical systems throughout his career, his aim being to create a general theory. Many of his ideas are contained in his book Dynamical Systems (1927), the first book to develop the qualitative theory of systems defined by differential equations and where he effectively 'created a new branch of mathematics separate from its roots in celestial mechanics and making broad use of topology. +16.40-17.40 Julia Collins (Edinburgh) A Knot's Tale: the story of Peter Guthrie Tait")}Peter Guthrie Tait (1831 - 1901) was significantly less famous than his friends Maxwell and Kelvin, but unfairly so because he was an important and prolific mathematical physicist. He was Professor of Natural Philosophy at the University of Edinburgh from 1859, narrowly beating Maxwell to the post, and worked on a variety of topics including thermodynamics and the kinetic theory of gases. In a fantastic experiment involving smoke rings, Tait and Kelvin came up with a new atomic theory based around the idea of knots and links. This took on a mathematical life on its own, with Tait becoming one of the world's first topologists and inventing conjectures which remained unproven for over a hundred years.
• TOPOLOGY SEMINAR (A.Reid, Texas)
  28th November 2013, 4:10pm to 5:10pm Alan Reid (U. Texas, Austin) 4.10PM, Room 4312, JCMB -- Show/hide abstract
  Abstract: Recognizing Surface groups and Kleinian groups by their finite quotients
• SCOTTISH TOPOLOGY SEMINAR IN ABERDEEN
  31st March 2023, 8:46am to 8:46am ABERDEEN
• TOPOLOGY SEMINAR (Diarmuid Crowley, MPIM, Bonn)
  18th November 2013, 4:10pm to 5:10pm Room 6301, JCMB -- Show/hide abstract
  Abstract: Diarmuid Crowley (MPIM, Bonn) 4.10PM, Room 6301, JCMB "Free involutions on Kervaire manifolds" The Kervaire manifold M_K is a certain closed simply-connected piecewise linear manifold of dimension 4k+2 with the same homology as the product of a pair of (2k+1)-spheres. Here are two questions about the Kervaire manifold: Q1. When the does M_K admit a smooth structure? Q2. When does M_K admit a free orientation preserving involution? In dimensions greater than 14, Q1 is a formulation of the Kervaire invariant problem and is now solved in all dimensions except 126. In this talk, I will report on joint research with Ian Hambleton on Q2 and its relationship with Q1. For example, if Q1 has a positive answer then so does Q2. One of our main results is that Q2 has a positive answer in dimension 126. Our work is based on deep theorems of Brumfiel, Madsen and Milgram from the 70s and is shaped by the recent breakthrough of Hill, Hopkins and Ravenel concerning Q1. http://front.math.ucdavis.edu/1305.6546
• TOPOLOGY SEMINAR (Margaret Beck, Heriot-Watt)
  14th November 2013, 4:00pm to 5:00pm Room 4312, JCMB -- Show/hide abstract
  Abstract: Title: Using the Maslov Index as a stability index for PDEs Abstract: One important aspect of understanding the behavior of solutions to PDEs is determining if a given stationary (time-independent) state is stable. The reason is that, as time evolves, often solutions will be attracted to the stable stationary states and, therefore, knowing which ones are stable enables one to qualitatively predict the large-time behavior of the system. Although there are many approaches to studying stability, many of them begin by investigating the spectrum of the linear operator one obtains by linearizing the PDE about a particular stationary solution. One technique for analyzing this spectrum involves using the Maslov Index as a tool for computing the Morse Index (the number of eigenvalues of a linear operator that have positive real part). Although the connection between the Maslov and Morse indices is not new, it is only recently that certain parts of the PDE community have become interested in the Maslov index as a practical tool in this regard. In this talk, I will outline the connection between stability, the Maslov index, and the Morse index. In addition, I will discuss some recent results and mention open problems that could potentially benefit from collaboration between the topology and PDE communities.
• TOPOLOGY SEMINAR (Maxime Bourrigan, Paris)
  1st November 2013, 4:00pm to 5:00pm ROOM 6206,JCMB
• SCOTTISH TOPOLOGY SEMINAR (in GLASGOW)
  20th September 2013, 12:15pm to 5:10pm 515 Mathematics Building, Glasgow -- Show/hide abstract
  Abstract: 12:15-1PM Lunch in Maths Common Room* 1-1:50 Liam Watson (Glasgow) Khovanov homology and the symmetry group of a knot 2-2:50 Stefan Friedl (Regensburg) Splittings of knot groups 2:50-3:20PM Tea break 3:20-3:50 Patrick Orson (Edinburgh) Doubly slice knots and algebraic L-theory 4-4:30 Pouya Adrom (Glasgow) Modelling homotopy types by internal categories 4:40-5:10 Sophie Raynor (Aberdeen) Towards a topological model of the brain
• TOPOLOGY SEMINAR (BROWDER)
  9th September 2013, 10:00am to 11:00am Room 5327, JCMB -- Show/hide abstract
  Abstract: 'How big a finite group can act freely on a product of spheres?'
• BRITISH TOPOLOGY MEETING, ABERDEEN
  31st March 2023, 8:46am to 8:46am
• TOPOLOGY SEMINAR (FRIEDL)
  31st July 2013, 4:00pm to 5:00pm Room 5327, JCMB -- Show/hide abstract
  Abstract: HNN-splittings of knot groups
• TOPOLOGY SEMINAR (Frank Quinn)
  9th May 2013, 4:15pm to 5:15pm Room 6206, JCMB -- Show/hide abstract
  Abstract: THE TRIANGULATION OF TOPOLOGICAL MANIFOLDS Visit supported by the Edinburgh Mathematical Society
• TOPOLOGY SEMINAR (ROUKEMA)
  3rd May 2013, 3:00pm to 4:00pm Room 6206, JCMB -- Show/hide abstract
  Abstract: Dehn surgery on hyperbolic knots Fionntan Roukema, Marseilles Abstract: A knot in the 3-sphere whose complement admits a hyperbolic structure is called a hyperbolic knot. The process of gluing a solid torus to the boundary component of the exterior of a knot is called Dehn surgery. A well known result, due to Thurston, states that a surgery on a hyperbolic knot that produces a non-hyperbolic 3-manifold is, in some sense, exceptional. In this talk we will describe a classification of the exceptional surgeries on the minimally twisted 5-chain link. We will then use this classification to describe hyperbolic knots with exceptional surgeries at ``maximal" distance.
• TOPOLOGY SEMINAR (STOLTZFUS) Double Knot Concordance
  5th April 2013, 4:00pm to 5:00pm ROOM 4312, JCMB
• TOPOLOGY SEMINAR (KURLIN) Topological data analysis
  2nd April 2013, 3:00pm to 4:00pm Room 4.31/4.33 INFORMATICS FORUM
• SCOTTISH TOPOLOGY SEMINAR
  21st March 2013, 2:00pm to 5:30pm Newhaven Room, ICMS, 15 South College Street -- Show/hide abstract
  Abstract: 2.00-3.00PM "Geometry in the 21st Century" Sir Michael Atiyah (SMSTC lecture) 3.10-4.10PM "Polynomial upper bounds on Reidemeister moves" Marc Lackenby (Oxford) 4.10-4.40PM Tea break 4.40-5.40PM "50 years of index theory" Sir Michael Atiyah Please email a.ranicki@ed.ac.uk before March 14 to register attendance. The Scottish Topology Seminar is generously supported by the Glasgow Mathematical Journal Trust
• POPULAR TOPOLOGY LECTURE (HORNIG)
  8th March 2013, 4:00pm to 5:00pm Room 5215, JCMB -- Show/hide abstract
  Abstract: Knots, links and braids in magnetic fields Gunnar Horning, Dundee The relation between knot theory and magnetic fields can be traced back to Gauss' linking integral, which is used to calculate the linking number between two closed curves (knots). The linking integral can be generalised to measure the average linking number of pairs of field lines in a magnetic field (V.I. Arnold 1974). This integral, called magnetic helicity, plays an important role in technical and astrophysical plasmas. We will explain the properties of magnetic helicity and give an overview of the attempts to generalise further notions of knot theory to magnetic fields. In particular we will present integrals for higher order linking numbers in three and four dimensions and discuss their relevance for magnetic fields in plasmas.
• TRANSVERSALITY IN ALGEBRA AND TOPOLOGY III. (ANDREW RANICKI)
  20th February 2013, 5:00pm to 6:00pm Lecture Room A, JCMB
• TRANSVERSALITY IN ALGEBRA AND TOPOLOGY II. (ANDREW RANICKI)
  13th February 2013, 5:00pm to 6:00pm Lecture Room A, JCMB -- Show/hide abstract
  Abstract: Video http://www.dailymotion.com/video/xxccoh_a-ranicki-transversality-in-algebra-and-topology-i_tech#.UROHzKUzySo
• TRANSVERSALITY IN ALGEBRA AND TOPOLOGY I. (ANDREW RANICKI)
  6th February 2013, 5:00pm to 6:00pm Lecture Room A, JCMB -- Show/hide abstract
  Abstract: Video http://www.dailymotion.com/video/xxccoh_a-ranicki-transversality-in-algebra-and-topology-i_tech#.UROHzKUzySo
• TOPOLOGY SEMINAR (FOURMAN)
  1st February 2013, 4:00pm to 5:00pm ROOM 6301, JCMB (NOTE ROOM CHANGE) -- Show/hide abstract
  Abstract: Random points on spheres ------------------------------------- I will use geometric arguments, in the style of Archimedes, to derive recurrences for the volume of an n-dimensional ball and the 'area' of its surface, the (n-1)-sphere. The constructions used provide a simple process that produces random points on the n-sphere. We also derive the distribution of the distance between two points drawn independently at random from the n-sphere, which has applications in statistics.
• TOPOLOGY : KIRBY COURSE
  30th November 2012, 5:00pm to 6:00pm Lecture Room A, JCMB -- Show/hide abstract
  Abstract: A 12 lecture course on "Topological manifolds and their triangulations"
• TOPOLOGY : KIRBY COURSE
  28th November 2012, 5:00pm to 6:00pm Lecture Room A, JCMB -- Show/hide abstract
  Abstract: A 12 lecture course on "Topological manifolds and their triangulations"
• TOPOLOGY SEMINAR (KIRBY)
  27th November 2012, 5:30pm to 6:30pm Lecture Room A, JCMB -- Show/hide abstract
  Abstract: "Morse 2-functions and trisections of 4-manifolds" Abstract: In joint work with David Gay, we show existence and uniqueness of Morse 2-functions (also known as broken Lefschetz fibrations), and then existence and uniqueness (up to stabilization) of trisections of 4-manifolds (analogous to Heegaard splittings of 3-manifolds).
• TOPOLOGY : KIRBY COURSE
  26th November 2012, 5:00pm to 6:00pm Lecture Room A, JCMB -- Show/hide abstract
  Abstract: A 12 lecture course on "Topological manifolds and their triangulations"
• TOPOLOGY : KIRBY COURSE
  23rd November 2012, 5:00pm to 6:00pm Lecture Room A, JCMB -- Show/hide abstract
  Abstract: A 12 lecture course on "Topological manifolds and their triangulations"
• TOPOLOGY : KIRBY COURSE
  21st November 2012, 5:00pm to 6:00pm Lecture Room A, JCMB -- Show/hide abstract
  Abstract: A 12 lecture course on "Topological manifolds and their triangulations"
• TOPOLOGY : KIRBY COURSE
  19th November 2012, 5:00pm to 6:00pm Lecture Room A, JCMB -- Show/hide abstract
  Abstract: A 12 lecture course on "Topological manifolds and their triangulations"
• TOPOLOGY : KIRBY COURSE
  16th November 2012, 5:00pm to 6:00pm Lecture Room A, JCMB -- Show/hide abstract
  Abstract: A 12 lecture course on "Topological manifolds and their triangulations"
• TOPOLOGY : KIRBY COURSE
  14th November 2012, 5:00pm to 6:00pm Lecture Room A, JCMB -- Show/hide abstract
  Abstract: A 12 lecture course on "Topological manifolds and their triangulations"
• TOPOLOGY : KIRBY COURSE
  12th November 2012, 5:00pm to 6:00pm Lecture Room A, JCMB -- Show/hide abstract
  Abstract: A 12 lecture course on "Topological manifolds and their triangulations"
• TOPOLOGY : KIRBY COURSE
  9th November 2012, 5:15pm to 6:15pm Lecture Room A, JCMB -- Show/hide abstract
  Abstract: A 12 lecture course on "Topological manifolds and their triangulations" Website http://www.maths.ed.ac.uk/~aar/kirby.htm
• ROCHLIN INVARIANT TALKS (ATIYAH+KIRBY)
  7th November 2012, 3:30pm to 6:00pm Lecture Room C, JCMB
• TOPOLOGY : KIRBY COURSE (RM 5325)
  5th November 2012, 5:00pm to 6:00pm Room 5325, JCMB -- Show/hide abstract
  Abstract: A 12 lecture course on "Topological manifolds and their triangulations"
• Rokhlin Invariant Talks: (Room 6310)
  2nd November 2012, 11:00am to 1:00pm 6310 JCMB, King's Buildings
• EMPG/TOPOLOGY SEMINAR (L.Kauffman, UIC)
  31st October 2012, 4:00pm to 5:00pm David Hume Tower 7.01 -- Show/hide abstract
  Abstract: The Jones Polynomial, the Potts Model and Khovanov Homology Abstract: The Jones polynomial invariant in knot theory and the Potts model in statistical mechanics are closely related through the bracket state sum model -- a partition function defined on knot diagrams that specializes to the Jones polynomial and can, by different specialization, represent the dichromatic and Tutte polynomials for plane graphs. Via this connection, one can use knot and link diagrams to represent the partition function for the Potts model. The loops in the bracket expansion then correspond to boundaries of regions of constant spin in the Potts model. These states (loop collections) in the bracket model are elevated to a category whose homology is Khovanov homology, an invariant more powerful than the Jones polynomial. From the point of view of the physics of the Potts model it is natural to ask for a physical interpretation of this homology theory based on states delineating regions of constant spin. We will raise these questions and discuss how Khovanov homology and its graded Euler characteristic look from the point of view of the Potts model. We will also point out how this way of thinking leads to a quantum-information theoretic reformulation of Khovanov homology and the Jones polynomial.
• TOPOLOGY SEMINAR, Julia Collins "A knot's tale"
  26th October 2012, 4:10pm to 5:10pm Lecture Room A, JCMB -- Show/hide abstract
  Abstract: A knot's tale - The story of P.G.Tait
• Rokhlin Invariant Talks: Chris Palmer (Room 6310)
  19th October 2012, 11:00am to 1:00pm 6310 JCMB, King's Buildings
• Rokhlin Invariant Talks: Patrick Orson (Room 4311)
  17th October 2012, 3:00pm to 5:00pm 4311 JCMB, King's Buildings
• TOPOLOGY SEMINAR (VEJDEMO-JOHANSSON) The topology of US politics
  15th October 2012, 4:10pm to 5:10pm Room 6206, JCMB -- Show/hide abstract
  Abstract: We analyze the US political climate using topological data analysis techniques on publicly available datasets on representative voting behavior and on donor cash flows. The talk will not assume a topological background beyond the notion of a simplicial complex.
• Rokhlin Invariant Talks: Patrick Orson (Room 6310)
  12th October 2012, 11:00am to 1:00pm 6310 JCMB, King's Buildings
• Rokhlin Invariant Talks: Carmen Rovi (Room 5325)
  8th October 2012, 3:30pm to 5:30pm 5325 JCMB, King's Buildings
• TOPOLOGY SEMINAR, Mathias Kreck (Bonn), "Invertible topological quantum field theories"
  1st October 2012, 3:00pm to 4:00pm Room 4312, JCMB -- Show/hide abstract
  Abstract: Visit supported by GMJ Abstract: I will explain the rather delicate definition of d-dimensional topological quantum field theories for manifolds with additional structures on the stable normal bundle (B-manifolds). The isomorphism classes form a monoid under tensor products and so it is natural to determine the units, the invertible field theories.This is the main aim of the talk. The answer is in terms of an exact sequence involving the SKK-groups which were studied about 40 years ago and $B$-bordism groups. A fundamental invariant of a field theory is the partition function, which is a diffeomorphism invariant of closed d-manifolds. As an application we determine all diffeomorphism invariants of B-manifolds which are partition functions of invertible field theories and discuss the problem how to construct a corresponding field theory and in how many ways this can be done.
• GEOMETRY/TOPOLOGY SEMINAR (M.Hering, A.Bayer)
  20th September 2012, 4:00pm to 6:00pm Room 4312, JCMB -- Show/hide abstract
  Abstract: Milena Hering (Edinburgh) "Cox rings of toric bundles" Abstract: Section rings of arbitrary line bundles on toric varieties are polytopal semigroup rings and thus always finitely generated. A related question is whether the section ring of the Serre line bundle on the projectivization of a toric vector bundle is always finitely generated. It turns out that this is not the case. We show this by finding toric vector bundles whose Cox ring is isomorphic to the Cox ring of the blow up of points in projective space. The latter is well known not to be finitely generated in general. This is joint work with José González, Sam Payne and Hendrik Süss. Arend Bayer (Edinburgh) "Wall-crossing and birational geometry".
• ICMS Meeting on cubical complexes
  31st March 2023, 8:46am to 8:46am ICMS, 15 South College Street -- Show/hide abstract
  Abstract: http://icms.org.uk/workshop.php?id=206
• TOPOLOGY SEMINAR (NORA SEELIGER)
  24th May 2012, 2:00pm to 3:00pm ROOM 4312, JCMB -- Show/hide abstract
  Abstract: String Topology of simply connected four manifolds
• POINCARE AND THE EARLY HISTORY OF 3-MANIFOLDS (STILLWELL)
  23rd May 2012, 4:00pm to 5:00pm Lecture Room A, JCMB
• Whittaker Colloquium
  22nd May 2012, 4:00pm to 5:00pm TBC -- Show/hide abstract
  Abstract: Speaker: Professor John Stillwell.
• TOPOLOGY SEMINAR (ELIZABETH GASPARIM, CAMPINAS)
  17th May 2012, 4:00pm to 5:00pm Room 4312, JCMB -- Show/hide abstract
  Abstract: Lefschetz fibrations on adjoint orbits
• SURGERY GROUP: Surgery Exact Sequence - Andrew Ranicki
  17th May 2012, 2:00pm to 3:00pm 4312 JCMB
• TOPOLOGY SEMINAR (MARK POWELL (BLOOMINGTON))
  15th May 2012, 2:00pm to 3:00pm Room 4312, JCMB -- Show/hide abstract
  Abstract: Homology cobordism and the orbit category
• SURGERY GROUP: Classifying Exotic Spheres - Patrick Orson
  11th May 2012, 10:00am to 12:00pm 4312 JCMB
• SURGERY GROUP: Constructing Exotic Spheres - Andrew Ranicki
  4th May 2012, 12:00pm to 2:00pm 4312 JCMB
• QUANTUM seminar
  29th March 2012, 10:00am to 11:30am JCMB 4312, Edinburgh -- Show/hide abstract
  Abstract: This talk will be mostly about Chern-Simons theory and the relation of gauge-theoretic TQFT to knot invariants.
• Carmen
  21st March 2012, 10:00am to 12:00pm Room 6206 JCMB, King's Buildings, Edinburgh
• SINGULARITIES, KNOTS AND SURGERY
  16th March 2012, 2:00pm to 5:30pm Room 4312, JCMB -- Show/hide abstract
  Abstract: 2.00-3.00 Maciej Borodzik (Warsaw) "Topological aspects of semicontinuity of spectra of singular points" 3.00-4.00 Andras Nemethi (Budapest) "Milnor fibers for non-isolated singularities" 4.00-4.30 Tea in Common Room 4.30-5.30 Andrew Ranicki (Edinburgh) "Algebraic surgery in codimensions 1 and 2" The visiting speakers are supported by the Research Fund of the Edinburgh Mathematical Society.
• Surgery Group
  16th March 2012, 10:00am to 12:00pm Room 4312 JCMB, King's Buildings, Edinburgh
• Surgery Group: Andrew Ranicki: The Poincare Duality Theorem and Its Converse II.
  14th March 2012, 10:00am to 12:00pm Room 6206 JCMB, King's Buildings, Edinburgh
• Surgery Group: Andrew Ranicki - The Poincare duality theorem and its converse I
  9th March 2012, 10:00am to 12:00pm Room 4312 JCMB, King's Buildings, Edinburgh
• Quantum Seminar - Mumford Conjecture
  8th March 2012, 10:00am to 11:30am JCMB 4312, Edinburgh -- Show/hide abstract
  Abstract: Carmen Rovi will give an introduction to the Mumford Conjecture about the cohomology of the mapping class group (proved by Madsen and Weiss). This is closely related to the homotopy type fo the 2-dimensional cobordism category.
• Surgery Group
  2nd March 2012, 10:00am to 12:00pm Room 4312 JCMB, King's Buildings, Edinburgh
• QUANTUM SEMINAR - Intro to C*-algebras
  1st March 2012, 10:00am to 11:30am JCMB 4312, Edinburgh -- Show/hide abstract
  Abstract: I'll introduce C*-algebras, including the Gelfand-Naimark-Segal construction.
• Surgery Group
  29th February 2012, 10:00am to 12:00pm Room 6206 JCMB, King's Buildings, Edinburgh
• QUANTUM SEMINAR - Cobordism hypothesis
  23rd February 2012, 10:00am to 11:30am JCMB 4312, Edinburgh -- Show/hide abstract
  Abstract: I'll explain what I can about the Cobordism Hypothesis proved in Lurie's "On the classification of Topological Field Theories". This is basically a big generalisation of the result about 2-dimensional TQFTs being Frobenius algebras. It's also closely related to the Galatius-Tillman-Madsen-Weiss theorem, which some of you know.
• TOPOLOGY SEMINAR (Friedl)
  10th February 2012, 4:10pm to 5:10pm Room 4312, JCMB -- Show/hide abstract
  Abstract: "The algebraic unknotting number of a knot" Abstract: The algebraic unknotting number of a knot K in S3 is defined to be the minimal number of crossing changes needed to turn K into a knot with trivial Alexander polynomial.We will talk about various results (new and old) which make it possible in many cases to determine the algebraic unknotting number for a given knot K. This is joint work with Maciej Borodzik.
• QUANTUM SEMINAR - Low-dimensional QFTs and finite gauge theory
  2nd February 2012, 10:00am to 11:30am JCMB 4312, Edinburgh -- Show/hide abstract
  Abstract: Teru Thomas will describe some examples of low-dimensional topological quantum field theories. He will sketch the classification of 2+1-dimensional theories in terms of Frobenius algebras, and, in particular, how the representation theory of finite groups pops out of gauge theory (following Freed).
• QUANTUM SEMINAR - Introduction to TQFT
  26th January 2012, 10:00am to 11:30am JCMB 4312, Edinburgh -- Show/hide abstract
  Abstract: Will Donovan will introduce the idea of a topological quantum field theory and explain the classification of low-dimensional TQFTs.
• TOPOLOGY/EMPG SEMINAR (Blohmann)
  25th November 2011, 3:00pm to 4:00pm Room 6311 -- Show/hide abstract
  Abstract: Christopher Blohmann (MPIM, Bonn) Singular symplectic manifolds
• TOPOLOGY SEMINAR (Mikael Vejdemo Johansson, St.Andrews)
  22nd November 2011, 3:00pm to 4:00pm Room 4312, JCMB -- Show/hide abstract
  Abstract: Topological data analysis
• QUANTUM SEMINAR - QFT as particle physics
  3rd November 2011, 2:00pm to 3:30pm Edinburgh, JCMB 6309 -- Show/hide abstract
  Abstract: This week I will talk about the quantization of particle physics and how this fits into the alternative view that QFT is a quantized theory of fields. Mathematically, the main ingredient is the representation theory of the Poincar\'e group. I will sketch Wigner's famous classification of the irreducible representations and its relation to geometric quantization. (T Thomas)
• Surgery Group - L11: Dimension 2 Surgery - Carmen Rovi
  3rd November 2011, 11:00am to 12:00pm JCMB 4312, King's Buildings
• SMSTC/M.Sc. Geometry-Topology Lecture (Baker III)
  27th October 2011, 1:00pm to 3:00pm JCMB Room 5323 (videoconference)
• Surgery Group - L10: Normal Invariants (ii) - Fillip Levikov
  27th October 2011, 11:00am to 12:00pm 4312 JCMB, King's Buildings
• TOPOLOGY SEMINAR: O. Randal-Williams (Copenhagen)
  26th October 2011, 4:00pm to 5:00pm Room 4312, JCMB -- Show/hide abstract
  Abstract: Stable moduli spaces of high-dimensional manifolds -------------------------------------------------------------------------- Madsen and Weiss' theorem---identifying the stable homology of moduli spaces of Riemann surfaces---and the theorem of Barratt--Priddy, Quillen, and Segal---identifying the stable homology of classifying spaces of symmetric groups---fit into a natural hierarchy of statements concerning the homology of moduli spaces of (n-1)-connected 2n-manifolds. I will discuss recent joint work with Soren Galatius which as a special case proves these statements for all n = 3, 4, ...
• Surgery Group - L10: Normal Invariants (i), Filipp Levikov
  26th October 2011, 10:00am to 11:00am JCMB 4312, King's Buildings
• TOPOLOGY SEMINAR (BORODZIK)
  21st October 2011, 3:00pm to 4:00pm Room 2.12 Appleton Tower -- Show/hide abstract
  Abstract: Speaker: M.Borodzik (Warsaw) Title: Unknotting number and classical invariants. Abstract. For a given knot K we define n(K) as the size of smallest matrix over Z[t,t^{-1}] which represents the Blanchfield pairing. We show that n(K)<=u(K). Moreover, n(K) is, up to now, gives best possible bound that can be achieved using Seifert matrices, for example n(K)>=|sigma(K)|/2. During the talk I will give a precise definition of n(K), explain, why does it bound the unknotting number and show some applications. This is joint work with Stefan Friedl (Cologne)
• QUANTUM SEMINAR - Axiomatic Approaches to QFT
  20th October 2011, 2:00pm to 3:30pm Edinburgh, JCMB 6309 -- Show/hide abstract
  Abstract: I will describe some attempts to articulate axiomatically what quantum field theory is about. I will focus on what might be called "analytic-algebraic" approaches (Wightman axioms, correlation functions, cosheaves of algebras) - the hope is to have a few talks about topological QFT in the second semester. (Teru Thomas)
• SURGERY GROUP Problem session
  12th October 2011, 10:00am to 12:00pm JCMB 4312
• SURGERY GROUP L9, The Spivak Normal Fibration - Patrick Orson
  7th October 2011, 11:00am to 12:30pm Room 4312, James Clerk Maxwell Building, University of Edinburgh -- Show/hide abstract
  Abstract: Twice weekly talk for the Surgery Theory study group. http://www.maths.ed.ac.uk/~pho/surgerygroup/
• QUANTUM SEMINAR - Will Donovan
  6th October 2011, 2:00pm to 3:30pm Edinburgh, JCMB 6309 -- Show/hide abstract
  Abstract: Quantization of Elementary Dynamical Systems Will will explain how representations of Lie groups can be constructed through the quantization of coadjoint orbits.
• SURGERY GROUP L8, Whitehead Torsion and the s-cobordism Theorem - Spiros Adams-Florou
  3rd October 2011, 11:00am to 12:30pm Room 4312, James Clerk Maxwell Building, University of Edinburgh -- Show/hide abstract
  Abstract: Twice weekly talk for the Surgery Theory study group. http://www.maths.ed.ac.uk/~pho/surgerygroup/
• TOPOLOGY SEMINAR (C.Roitzheim, Glasgow)
  30th September 2011, 4:10pm to 5:10pm Room 4312, JCMB -- Show/hide abstract
  Abstract: Derived A-infinity algebras In the 1960s, A-infinity algebras were introduced to study the cohomology of topological spaces with products and are now known to arise widely in various areas of mathematics. Roughly speaking, A-infinity algebras are generalisations of associative algebras. We are going to explain how to extend the definition of Hochschild cohomology from associative algebras to A-infinity algebras and how this will help solving realizability problems in topology and present some new results concerning derived A-infinity algebras. This talk will be very basic and will require no preliminaries about A-infinity algebras or Hochschild cohomology at all.
• QUANTUM SEMINAR - Will Donovan
  29th September 2011, 2:00pm to 3:30pm Edinburgh, JCMB 6309 -- Show/hide abstract
  Abstract: Quantization for elementary dynamical systems
• SURGERY GROUP L7, The h-cobordism Theorem - Chris Palmer
  29th September 2011, 11:00am to 12:30pm Room 4312, James Clerk Maxwell Building, University of Edinburgh -- Show/hide abstract
  Abstract: Twice weekly talk for the Surgery Theory study group. http://www.maths.ed.ac.uk/~pho/surgerygroup/
• SURGERY GROUP L6, Algebraic/Geometric intersections and the Whitney trick - Filipp Levikov
  26th September 2011, 11:00am to 12:30pm Room 4312, James Clerk Maxwell Building, University of Edinburgh -- Show/hide abstract
  Abstract: Twice weekly talk for the Surgery Theory study group. http://www.maths.ed.ac.uk/~pho/surgerygroup/
• SURGERY GROUP L5, Cobordism Theory (ii) - Carmen Rovi
  22nd September 2011, 11:00am to 12:30pm Room 4312, James Clerk Maxwell Building, University of Edinburgh -- Show/hide abstract
  Abstract: Twice weekly talk for the Surgery Theory study group. http://www.maths.ed.ac.uk/~pho/surgerygroup/
• SURGERY GROUP L4, Cobordism theory (i) - Carmen Rovi
  19th September 2011, 11:00am to 12:30pm Room 4312, James Clerk Maxwell Building, University of Edinburgh -- Show/hide abstract
  Abstract: Twice weekly talk for the Surgery Theory study group. http://www.maths.ed.ac.uk/~pho/surgerygroup/
• SURGERY GROUP L3, Vector Bundles and Surgery - Patrick Orson
  15th September 2011, 11:00am to 12:30pm Room 4312, James Clerk Maxwell Building, University of Edinburgh -- Show/hide abstract
  Abstract: Twice weekly talk for the Surgery Theory study group. http://www.maths.ed.ac.uk/~pho/surgerygroup/
• SURGERY GROUP L2, Poincare Duality and the Effects on Surgery - Spiros Adams-Florou
  12th September 2011, 11:00am to 12:30pm Room 4312, James Clerk Maxwell Building, University of Edinburgh -- Show/hide abstract
  Abstract: Twice weekly talk for the Surgery Theory study group. http://www.maths.ed.ac.uk/~pho/surgerygroup/
• SURGERY GROUP L1, Surgery, Handles and Morse Theory - Spiros Adams-Florou
  8th September 2011, 11:00am to 12:30pm Room 4312, James Clerk Maxwell Building, University of Edinburgh -- Show/hide abstract
  Abstract: Twice weekly talk for the Surgery Theory study group. http://www.maths.ed.ac.uk/~pho/surgerygroup/
• SURGERY GROUP L0, Introduction to Surgery Theory - Andrew Ranicki
  5th September 2011, 11:00am to 12:30pm Room 4312, James Clerk Maxwell Building, University of Edinburgh -- Show/hide abstract
  Abstract: Twice weekly talk for the Surgery Theory study group. http://www.maths.ed.ac.uk/~pho/surgerygroup/
• British Topology Meeting in Edinburgh
  31st March 2023, 8:46am to 8:46am ICMS, 15 SOUTH COLLEGE STREET -- Show/hide abstract
  Abstract: http://www.icms.org.uk/workshops/btm
• SPECULATIONS ON THE RIEMANN HYPOTHESIS (C.DENINGER, MUENSTER)
  22nd August 2011, 4:00pm to 5:00pm Room 6301, JCMB
• TOPOLOGY SEMINAR (PIERRE ALBIN)
  10th May 2011, 4:10pm to 5:10pm Room 4312, JCMB -- Show/hide abstract
  Abstract: "The signature operator on stratified pseudomanifolds" Pierre Albin, Paris Abstract: The signature operator of a Riemannian metric is an important tool for studying topological questions with analytic machinery. Though well-understood for smooth metrics on compact manifolds, there are many open questions when the metric is allowed to have singularities. I will report on joint work with Eric Leichtnam, Rafe Mazzeo, and Paolo Piazza on the signature operator on stratified pseudomanifolds and some of its topological applications.
• ICMS workshop "The Kervaire invariant and stable homotopy theory"
  31st March 2023, 8:46am to 8:46am -- Show/hide abstract
  Abstract: Organized by John Greenlees, Andrew Ranicki and Neil Strickland
• SCIENCE FESTIVAL LECTURE (GHRIST)
  12th April 2011, 7:00pm to 8:00pm ICMS, 15 SOuth College Street -- Show/hide abstract
  Abstract: The Mathematics of Holes (Robert Ghrist) http://www.sciencefestival.co.uk/whats-on/categories/talk/the-mathematics-of-holes
• Robert Ghrist "Euler calculus for data"
  12th April 2011, 2:00pm to 3:00pm Room 4.31/4.33 Informatics Forum, Crichton Street -- Show/hide abstract
  Abstract: This talk explains an ingenious integral calculus based on Euler characteristic, stemming from work on sheaves due to MacPherson and Kashiwara in the 1970s, and connecting back further to classical integral geometry. I will emphasize its novel utility in data management, particularly in aggregation of redundant data and inverse problems over sensor networks. Applications to target counting, localization, and shape detection will be discussed. Issues of numerical analysis & integral transforms in Euler calculus are particularly interesting open problems. Joint with Informatics
• TOPOLOGY SEMINAR (LUPTON)
  29th March 2011, 4:10pm to 5:10pm Room 4312, JCMB -- Show/hide abstract
  Abstract: The Toral Rank Conjecture." Greg Lupton (Cleveland State University, Cleveland, Ohio) A brief review of rational homotopy methods, followed by a survey of results known about or related to this conjecture.
• Whittaker Colloquium (Carlsson)
  14th March 2011, 4:10pm to 5:10pm Lecture Room C, JCMB -- Show/hide abstract
  Abstract: Topology and Data
• TOPOLOGY SEMINAR (JOINT WITH GEOMETRY) PANTEV
  24th February 2011, 4:10pm to 5:10pm Room 4312, JCMB -- Show/hide abstract
  Abstract: Mirror symmetry for del Pezzo surfaces Tony Pantev (Penn) I will discuss the general mirror symmetry question for del Pezzo surfaces in a setup that goes beyond the Hori-Vafa ansatz. I will describe the mirror map explicitly and will describe non-trivial consequences of homological mirror symmetry that can be proven directly. This is a joint work with Auroux, Katzarkov and Orlov.
• TOPOLOGY SEMINAR (JOINT WITH GEOMETRY) BEN-BASSAT
  17th February 2011, 4:10pm to 5:10pm Room 4312, JCMB -- Show/hide abstract
  Abstract: Meromorphic Line Bundles and Holomorphic Gerbes Oren Ben-Bassat (Haifa) This talk will be about the sheaf of non-zero meromorphic functions on a complex manifold from the point of view of cohomology. More specifically, we relate the first Betti number of divisors to meromorphic line bundles and higher Betti numbers to cohomology of the sheaf of non-zero meromorphic functions as well as cohomology of the sheaf of nowhere zero holomorphic functions. We will also compare non-zero rational functions to non-zero meromorphic functions from the perspective of cohomology in the classical topology on a smooth projective variety over the complex numbers. This is joint work with E. Ballico which can be found at http://arxiv.org/abs/1101.2216.
• SPITALFIELDS DAY (Atiyah, Hirzebruch, Ranicki)
  31st March 2023, 8:46am to 8:46am Royal Society of Edinburgh, 22 George Street, Edinburgh -- Show/hide abstract
  Abstract: Please register at http://www.icms.org.uk/workshops/hirzebruch if you wish to attend! 11.00 Sir Michael Atiyah "The Hodge signature theorem past, present and future" 15.00 Friedrich Hirzebruch "125 years of the Schubert calculus" 16.00 Tea and coffee 16.30 Andrew Ranicki "Aspects of quadratic forms in the work of Hirzebruch and Atiyah"
• BRITISH TOPOLOGY MEETING, OXFORD
  31st March 2023, 8:46am to 8:46am
• ICMS SYMPLECTIC GEOMETRY MEETING
  31st March 2023, 8:46am to 8:46am
• 4 talks on Knot theory (Kim, Collins, Owens, Powell)
  1st July 2010, 2:00pm to 6:00pm Room 5327, JCMB -- Show/hide abstract
  Abstract: 2.00-3.00 Taehee Kim (Konkuk) "The cobordism group of homology cylinders and torsions". 3.15-3.45 Julia Collins (Edinburgh) "Concordance orders of knots" 4.15-5.15 Brendan Owens (Glasgow) "Is this anything?" Abstract: In 1967, Hosokawa described an equivalence relation on links in S3 whose equivalence classes form a group L containing the knot concordance group C as a subgroup, and in fact proved that L is a direct sum of C and the integers. I will describe a different link concordance group (or two) containing C as a subgroup. It is hoped that the audience will help to answer the question in the title. 5.30-6.00 Mark Powell (Edinburgh) "A second order algebraic knot concordance group"
• Topology seminar
  30th June 2010, 4:00pm to 5:00pm Room 4312, JCMB -- Show/hide abstract
  Abstract: Speaker: Lino S. Grama (University of Campinas) Title: Ricci Flow on Homogeneous Spaces Abstract: In this talk we discuss some properties of the Ricci flow of left invariant metrics on generalized flag manifolds.
• 2 talks at ICMS meeting "ICMS Hodge theoretic reflections on the string landscape"
  14th June 2010, 10:00am to 12:00pm 14 India Street (Old home of ICMS) -- Show/hide abstract
  Abstract: 10.00-11.00 Michael Atiyah (University of Edinburgh) Models of matter? 11.00-12.00 John Jones (University of Warwick) The Kervaire invariant
• ICMS Hodge theoretic reflections on the string landscape
  31st March 2023, 8:46am to 8:46am 14 india Street (the old ICMS location) -- Show/hide abstract
  Abstract: http://www.icms.org.uk/workshop.php?id=115
• Topology seminars (Hepworth, Borodzik)
  28th May 2010, 3:10pm to 5:40pm Room 6311, JCMB -- Show/hide abstract
  Abstract: 3.10-4.10 Hepworth: Groups, discs and cacti Abstract: http://www.maths.ed.ac.uk/~aar/topology/hepworth.pdf 4.30-5.30 Borodzik: Abelian rho-invariant of iterated torus knots and its applications to deformations of singularities of complex plane curves.
• Topology seminar (J.Davis) Are almost flat manifolds boundaries?
  20th May 2010, 4:00pm to 5:00pm Room 6311, JCMB -- Show/hide abstract
  Abstract: Jim Davis (Bloomington and Bonn)
• ASTRONOMY, STATISTICS AND GEOMETRY (Forgan,Heavens, Kitching)
  14th May 2010, 3:00pm to 4:30pm Lecture Room C, JCMB -- Show/hide abstract
  Abstract: 3.00 D.Forgan "Using Monte Carlo Realisation Techniques to Model SETI" 3.30 A.Heavens "Hunting for Inflation" 4.00 T.Kitching "The transformation of gravitational lensing: illuminating dark matter and dark energy" 4.30 -- Tea + discussion in 3rd floor snack bar
• Topology Seminar (Carbery)
  7th May 2010, 4:30pm to 5:30pm Room 4312, JCMB -- Show/hide abstract
  Abstract: The Borsuk--Ulam theorem -- a simple proof.
• Topology seminar: Laurent Bartholdi (Goettingen)
  26th March 2010, 3:00pm to 4:00pm Room 4312, JCMB -- Show/hide abstract
  Abstract: SELF-SIMILARITY FOR LIE ALGEBRAS I will give the general definition of a self-similar Lie algebras: an algebra that contains "infinitesimal", tightly bound copies of itself, and show that important examples of Lie algebras fall into that class, in particular constructions by Petrogradsky, Shestakov and Zelmanov. In analogy with Burnside's problem, one is interested to understand infinite-dimensional algebraic algebra (every element generates a finite-dimensional subalgebra), and in particular nil algebras (every element raised to some power becomes 0). I will show that important such examples of algebra arise within self-similar Lie algebras, and will give sufficient conditions for a self-similar Lie algebra to be nil. I will also relate these self-similar Lie algebras to self-similar groups such as examples by Grigorchuk and Gupta-Sidki, and will also show their connection to Caranti's classification of algebras of maximal class.
• EGA Seminar: Alexey Bondal (Aberdeen)
  17th March 2010, 4:45pm to 5:45pm JCMB 4312 -- Show/hide abstract
  Abstract: Grand unification theories and geometry of homogeneous spaces
• EGA Seminar: Alex Quintero Velez (Glasgow)
  17th March 2010, 3:15pm to 4:15pm JCMB 4312 -- Show/hide abstract
  Abstract: A-infinity structures associated with brane tilings and D-brane categories
• EGA Seminar: Richard Szabo (Heriot-Watt)
  17th March 2010, 2:00pm to 3:00pm JCMB 4312 -- Show/hide abstract
  Abstract: Instantons and Crystal Melting
• Topology Seminar: David Mond (Warwick)
  12th March 2010, 5:00pm to 6:00pm JCMB 4312 -- Show/hide abstract
  Abstract: Linear free divisors and Frobenius structures
• Topology Seminar: Alessandro Valentino (Goettingen)
  26th February 2010, 4:00pm to 5:00pm Room 4312, JCMB -- Show/hide abstract
  Abstract: T-duality and differential K-theory
• Topology Seminar: Jarek Kedra (Aberdeen)
  19th February 2010, 3:00pm to 4:00pm Room 7.01 David Hume Tower -- Show/hide abstract
  Abstract: Title: Characteristic classes in symplectic topology. Abstract: I will define certain characteristic classes of symplectic fibrations and calculate some of them.
• Topology Seminar: Iain Aitchison (Melbourne)
  8th February 2010, 4:00pm to 5:00pm JCMB 4312 -- Show/hide abstract
  Abstract: Explicit moduli for closed genus 2 surfaces
• GEOMETRY SEMINAR (THOMAS)
  14th January 2010, 4:00pm to 5:00pm

Friday, 9th October Paul Kirk (Bloomington/MPIM Bonn) Studying knots in 3-manifolds via spaces of SU(2) representations of their fundamental group 4.10PM, Room 6311, JCMB

Abstract: The most powerful invariant of a 3 manifold (such as the complement of a knotted circle in the 3-sphere) is its fundamental group. One approach to probing this group is to study the spaces of homomorphisms from the fundamental group into a Lie group such as SU(2). The topological properties of these representation spaces reflect geometric properties of the 3-manifold. I will illustrate, mostly via examples, what some of these representation spaces look like, and discuss some approaches to extract invariants of 3 manifolds and knots by studying the properties of their representation spaces.

Spring/Summer 2015

Wednesday, 18th February Michelle Bucher-Karlsson (Geneva) Characteristic numbers and volumes of hyperbolic representations 4PM, Room 4325B, JCMB

Thursday, 19 March Scottish Topology Seminar at ICMS. Speakers: Saul Schleimer (Warwick), Maciej Borodzik (Warsaw), J. Rasmussen (Cambridge).

Thursday, 9th April George Szpiro (New York/Jerusalem) Math for the Masses: The Truth, the Whole Truth, Nothing but the Truth 4PM, Room 6206 (tbc), JCMB. Abstract: In this seminar I will discuss the difficulties a journalist faces who writes about mathematics for the general reader. Mathematics is a very technical subject and, unlike other sciences, like physics, medicine or biology, cannot be easily explained to non-specialists. Nevertheless, the writer must try to communicate at least an idea of what our subject is about, strictly avoiding to ‘dumb down,’ and all the while trying to keep the reader interested.

Thursday, 14 May Scottish Topology Seminar at ICMS. Hydrodynamics and Topology: Meeting in honour of Keith Moffatt's 80th birthday 2-6PM at ICMS, 15 South College Street.

2.55-3.45 Etienne Ghys (ENS-Lyon) Is helicity a topological invariant?

3.45-4.15 Tea

4.15-5.05 Michael Proctor (DAMTP, Cambridge) Mean-field Electrodynamics in the nonlinear regime?Keith Moffatt has made seminal contributions to the theory of mean-field electrodynamics - the theory of magnetic field generation on scales large compared to those of the velocity fields that drive the dynamo. But there is another kind of dynamo, usually called a small-scale dynamo, which has magnetic field and velocity scales that are comparable. It is thus possible to have a state of essentially homogeneous MHD turbulence where the small scale magnetic field is dynamically active. What does it then mean to look for large scale magnetic instabilities? In this case the induction and momentum equations are on an equal footing, and the linear perturbation problem has to involve both the equations. The question then arises: can a coherent mean-field theory be constructed for the analysis of such long-wavelength modes? For relatively simple states the answer is in the affirmative, producing extended mean field equations with new coupling terms, providing a unification of the AKA instability of Frisch and the usual mean-field electrodynamics. However the validity of the ansatz seems to depend on properties of the basic state, and I will try to show by means of simple examples how things can go wrong. At present the question of whether the new mean field system is useful is open, pending more detailed numerical investigation.

Friday, 15 May School Colloquium by Etienne Ghys

Monday, 18 May Triangulation Conjecture, Ciprian Manolescu (UCLA), Lecture Room 6206, JCMB, 4.00-5.00PM. Visit supported by LMS Scheme 2. This is one of the three talks in the "Structure and Symmetry Symposium". The other two are
13:30-14:30 Arkady Vaintrob (Oregon, visiting Edinburgh) Non-commutative spaces, singularities and mirror symmetry
14:30-15:30 Ivan Smith (Cambridge) Symplectic Khovanov cohomology

Monday, 20 July — Friday, 24 July "Topological methods in Singularity Theory" ICMS Conference

Autumn 2014

Monday, 22nd September "Riemann and topology in Goettingen", Paddy Patterson (Goettingen), Lecture Room 6206, JCMB, 4.10-5.10PM VIDEO

Spring/Summer 2014

There was a special double topology seminar on Monday, 4th August, 15.00-17.00, in Lecture Room C, James Clerk Maxwell Building, featuring two speakers who are topologists actively involved both in the theory and practice of the artistic representations of spaces. The talks were introduced by Michael Atiyah. The poster was made by Julia Collins TopologyArtPoster.pdf The videos were made by Carmen Rovi.

VIDEO
http://www.segerman.org/
https://www.math.okstate.edu/~segerman/#art_exhibitions
https://www.shapeways.com/shops/henryseg
https://www.youtube.com/user/henryseg
http://www.thingiverse.com/henryseg/designs

VIDEO

Monday, 9th June Carl McTague (Johns Hopkins), Room 6301, JCMB, 4.15-5.15PM New applications of differential geometry to big dataEuler calculus is an emerging method for extracting information from high-dimensional discrete data. The idea is to integrate data using the Euler characteristic as measure. Baryshnikov & Ghrist pioneered this method and explored ways to extend it to continuous data. I will extend the method to continuous data in a new way which, unlike previous methods, is additive and satisfies a Fubini theorem. More than this, I will use geometry to extend the theory to a functor. Functoriality enables tomographic-type information extraction from projections.

Tuesday, 27th May (M.Boileau, T.Riley, A.Stipsicz) 1.15-5.00PM Scottish Topology Seminar Glasgow

Tuesday, 29th April Wolfgang Lueck (HIM, Bonn) Room 6301, JCMB. 2.30-3.30PM Introduction to L2-invariantsWe give an introduction to L2-invariant such as the L2-Betti numbers and the L2-torsion which are the L2-analogues of the classical Betti numbers and Reidemeister torsion. Originally these were defined for Riemannian manifolds but they can be extended to more general spaces. This leads to surprising applications to problems in geometry, topology, group theory and K-theory. Video
4.10-5.10PM On the possible values of L2-invariantsWe discuss questions due to Atiyah and Lehmer asking what the possible values of L2-invariants are. In general there are only a few constraints for the L2-Betti numbers, but if the group under consideration is torsionfree, no example of an L2-Betti number is known which is not an integer. Finally we discuss an extension of Lehmer's problem about the Mahler measure of polynomials to arbitrary groups. Video

Thursday, 20th March A chaotic afternoon at ICMS Scottish Topology Seminar with Etienne Ghys

Tuesday, 18th February Three informal talks on knot theory. 2.00-5.00PM Cramond Room, ICMS, 15 South College Street
Gunnar Hornig (Dundee), 2.00-2.45PM, On the problem of third order invariants for magnetic fieldsWe explore the reasons why the programme, first envisaged by V.I. Arnold, to generalise link invariants from knot-theory to integral invariants of magnetic fields, has so far not led to any practically useable invariant beyond the magnetic helicity. We do this by first looking into the properties of magnetic helicity (a second order integral invariant) and its relation to the Gauss' linking number, before analysing what prevents us from generalising the third order Massey linking number to a corresponding integral for magnetic fields.
Brendan Owens (Glasgow), 3.00-3.45PM, Searching for slice disksA knot in the three-sphere is slice if it bounds a smoothly embedded disk in the four-dimensional ball. It is alternating if it admits an alternating projection. Mysteriously, many geometric properties can be immediately determined from an alternating diagram. Is it possible to quickly tell from an alternating diagram if a knot is slice or not? In joint work with Frank Swenton we have implemented an algorithm which has found slice disks for approximately 29,000 alternating knots. I will describe this algorithm and also some examples which the algorithm just misses.
Andrew Ranicki (Edinburgh), 4.15-5.00PM, Surgery theory and braidsBraids are well-known representations of knots. n-strand braids are classified by the automorphisms of the n-punctured 2-disk which are the identity on the outside boundary circle and a permutation of the n inside boundary circles. Concatenation of braids corresponds to the composition of the automorphisms. In my talk I shall describe an algebraic surgery version of such automorphisms, which can be used to recover the Ghys-Gambaudo-Bourrigan signature invariants of braids.

Friday, 24th January

Friday, 17th January
Michael Atiyah (Edinburgh) 3.00-4.00PM, Room 6206, JCMB Discrete groups, von Neumann algebras and L^2 Betti numbersNearly 40 years ago I wrote a about index theory on the universal covering Y of a compact manifold X. Assuming the fundamental group is infinite, Y is non-compact and one wants L2 solutions of the differential equations. Using the dimension theory introduced by von Neumann (where dimensions are real numbers) one can define the L2 index on Y and prove that it is the same as the index on X. This is useful, and of course the L2 index is then an integer. But the individual dimensions are in principle just real numbers. A case of special interest occurs in the Hodge theory of harmonic forms, which gives the Betti numbers. I raised the question of whether there were manifolds Y for which the L2 Betti numbers were not integral or even rational. Over the past 40 years much work has been done on this problem and the lecture by Lukasz Grabowski which follows will bring the story up to date. (1976 paper)

Autumn 2013

Thursday, 19th December
Scottish Topology Seminar, ICMS, Edinburgh,
Jeremy Gray (Open), June Barrow-Green (Open), Julia Collins (Edinburgh) 1.00PM--5.30PM.

Thursday, 28th November
Alan Reid (U. Texas, Austin) 4.10PM, Room 4312, JCMB Recognizing Surface groups and Kleinian groups by their finite
quotientsThis talk will discuss recent work on distinguishing certain classes of finitely presented groups by their finite quotients. If time permits this will include a surprising application of the work of Agol and Wise.

Wednesday, 20th November
Scottish Topology Seminar, Aberdeen.
D.Crowley (MPIM Bonn), B.Hanke (Augsburg), A.Thomas (Glasgow).

Monday, 18th November

Thursday, 14th November

Friday, 1st November

Friday, 20th September
Scottish Topology Seminar, Glasgow.

Monday, 9th September
How big a finite group can act freely on a product of spheres?'
William Browder (Princeton and Arhus) 10.00AM, Room 5327, JCMB

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