Past Semesters
Spring 2015
Move your mousepointer on the title of a talk to see an abstract (if available). The schedule is also kept up to date in a google calendar, which you can find below.
January 15  Michael Wemyss (Edinburgh)  Aspects of the Homological MMP I will outline the main ideas of arXiv:1411.7189, which uses noncommutative deformations and universal properties to jump between minimal models in the MMP in a satisfyingly algorithmic fashion. As part of this, a flop is constructed not by changing GIT, but instead by changing the algebra keeping GIT fixed, and flops are detected by whether certain contraction algebras are finite dimensional. Carrying this extra information allows us to continue to flop, and thus continue the MMP, without having to calculate everything at each stage. Proving things in this canonical categorical manner allows us then to say things about GIT. In fact the HomMMP computes the full wall and chamber structure, and also gives a method for determining which walls produce flops and which do not. If there is time, I will explain that it also can be used to prove that flop functors braid in dimension three, however the combinatorics are not the expected one, and higher length braid relations naturally appear.  
February 5  Mario García Fernández (ICMAT)  Stability data, irregular connections and tropical curvesI will give an overview of recent joint work with S. Filippini and J. Stoppa, in which we construct isomonodromic families of irregular meromorphic connections on P1, with generalized monodromy in the automorphisms of a class of infinitedimensional Poisson algebras. Our main results concern the limits of the families as we vary a scaling parameter R. In the R → 0 “conformal limit” we recover a semiclassical version of the connections introduced by Bridgeland and Toledano Laredo (and so the Joyce holomorphic generating functions for DT invariants). In the R → ∞ “large complex structure limit” the families relate to tropical curves in the plane and tropical/GW invariants. The connections we construct are a rough but rigorous approximation to the (mostly conjectural) fourdimensional tt*connections introduced by Gaiotto–Moore–Neitzke.  
February 12  Alice Rizzardo (Edinburgh)  An example of a nonFourierMukai functor between derived categories of coherent sheaves  
February 26  Sergey Arkhipov (Aarhus)  Quasicoherent Hecke categories and affine braid group actions We propose a geometric setting leading to categorical braid group actions. First we consider the quasicoherent Hecke category QCHecke(G,B) for a reductive group G with a Borel subgroup B. We show that a monoidal action of QCHecke(G,B) on a triangulated category gives rise to a categorification of degenerate Hecke algebra representation known as Demazure Descent Data. Next we replace the group G by the derived group scheme LG of topological loops with values in G and consider QCHecke(LG,LB). A monoidal action of the category QCHecke(LG,LB) gives rise to a categorical action of the affine Braid group.
 
March 5  No EDGE seminar  (GLEN in Glasgow)  
March 12  Michael Groechenig (Imperial)  Infinitedimensional vector bundles and reciprocity  
March 19  No seminar  
March 26 (two talks!)  Joseph Karmazyn (Edinburgh)  Moduli, McKay, and Minimal Models Moduli spaces are often used to realise derived equivalences in algebraic geometry. I will recall the examples of the derived equivalence of 3fold flops in the minimal model program and the derived SL2 McKay correspondence. These derived equivalences can be translated to noncommutative algebra where they have been extended to include more general settings. I will discuss how a moduli interpretation can be extended to include these derived equivalences with noncommutative algebras.  
Rebecca Tramel (Edinburgh)  Bridgeland stability on surfaces with curves of negative selfintersection I consider X a smooth projective complex surface containing a curve C whose selfintersection is negative. In 2002, Bridgeland defined a notion of stability for the objects in Db(X), which generalized the notion of slope stability for vector bundles on curves. The space of such stability conditions is a complex manifold, Stab(X). If we fix a numerical class, then we can decompose Stab(X) into open chambers where the moduli space of stable objects of this class remains constant, and codimension one walls where this moduli space may change.
 
April 23  Tyler Kelly (Cambridge)  Equivalences of (Stacky) CalabiYaus in Toric VarietiesGiven CalabiYau complete intersections in a fixed toric variety, there are possibly various constructions to compute its mirror. Sometimes these mirrors are isomorphic but sometimes not. Mirror symmetry predicts a relationship amongst these socalled double mirrors. In this talk, we will show that the stacky versions of these varieties are derived equivalent. In the proving of this theorem, we get some applications which involve polarisations of K3 surfaces, special degenerate families of CY hypersurfaces in toric varieties, and a generalization of the BHK mirror constructions to families.  
May 28, JCMB 6206  Daniel HalpernLeistner (Columbia)  Equivariant Hodge theoryRecent results have revealed a mysterious foundational phenomenon: some quotient stacks for algebraic groups G acting on nonproper schemes X still behave as if they are proper schemes. I will report on one instance of this yoga: one can consider the noncommutative HodgetodeRham sequence, from Hochschild homology to periodic cyclic homology, for the derived category of coherent sheaves. This spectral sequence degenerates on the first page for smooth and proper schemes, and it turns out that this degeneration also occurs for many "cohomologically proper" quotient stacks. With a little work, this leads to a canonical weight 0 Hodge structure on the AtiyahSegal equivariant Ktheory of the complex analytification of X. The associated graded of the Hodge filtration is the space of functions on the "derived loop space" of the stack. 
Autumn 2014
September 18  No Seminar  
September 25  Ivan Cheltsov (Edinburgh)  What are the worst singular points of plane curves of given degree?  
October 2  Martin Kalck (Edinburgh)  Relative singularity categories(Relative) singularity categories are triangulated categories associated with (noncommutative resolutions of) singular varieties. I will explain these notions and their mutual relations focusing on the simplest examples  the singularities of type A_1, e.g. k[x/x^2. For these examples, everything can be understood in a rather elementary way. In particular, familiarity with triangulated categories will NOT be necessary to follow the talk. In the end, I will mention what we know for ADEsingularities in general. This is based on joint work with Dong Yang.  
October 9  Brent Pym (Oxford)  Quantum deformations of projective threespaceIn noncommutative projective geometry, quantum versions of projective space are often described in terms of their homogeneous coordinate rings, which are noncommutative analogues of polynomial rings. The algebras corresponding to quantum projective planes were classified in geometric terms by Artin, Tate and Van den Bergh in a celebrated 1990 paper. The related problem for projective threespace has received considerable attention, but the full classification remains elusive. I will describe some recent progress on this problem, in which deformation quantization is combined with Cerveau and Lins Neto's classification of foliations on projective space to give a classification of the flat deformations of the polynomial ring in four variables as a graded CalabiYau algebra.  
October 16  Balazs Szendroi (Oxford)  Motivic DonaldsonThomas series of deformed CalabiYau geometriesMotivic DT theory gives a refined count of objects in 3CY categories, for example sheaves on CalabiYau threefolds. At least in the local quiver setting, it is easy to ask about motivic counts of objects in categories defined by deformed CalabiYau spaces, such as quantum threespace or the affine cone over the Jordan plane. We compute the answer in some cases, and conjecture it in some others, based on an intriguing and sofar not always precise formula involving the motivic count of simple objects only. (Joint work with Andrew Morrison and Brent Pym)  
October 23  Evgeny Smirnov (HSE Moscow)  Spherical double flag varieties Classical Schubert calculus deals with orbits of a Borel subgroup in GL(V) acting on a Grassmann variety Gr(k,V) of kplanes in a finitedimensional vector space V. These orbits (Schubert cells) and their closures (Schubert varieties) are very well studied both from the combinatorial and the geometric points of view. One can go one step farther, considering the direct product of two Grassmannians Gr(k,V)x Gr(l,V) and the Borel subgroup in GL(V) acting diagonally on this variety. In this case, the number of orbits still remains finite, but their combinatorics and geometry of their closures become much more involved. However, something still can be said about them. I will explain how to index the closures of a Borel subgroup in Gr(k,V)xGr(l,V) combinatorially and construct their desingularizations, which are similar to BottSamelson desingularizations for ordinary Schubert varieties. I will also mention the analogues of these results for direct products of partial flag varieties for reductive groups of type different from A_n.  
October 30  Chunyi Li (Edinburgh)  Topics on the Hilbert scheme of points on projective planeThe Hilbert scheme of n points in P2 parameterizes all 0dimensional subschemes on P2 with length n. It is a smooth version of nth symmetric product of P2. I will introduce some of its 'neighborhoods' in the area of birational geometry and deformation theory.  
November 6, JCMB 5215  Gavin Brown (Loughborough)  Elliptic Gorenstein projection following Coughlan The archetype elliptic Gorenstein singularity on a 3fold
 
November 13  Susan J. Sierra (Edinburgh)  Moduli of point representations, the enveloping algebra of the Virasoro algebra, and noetherianityI will explain the geometric methods underlying my 2013 proof (with Walton) that the universal enveloping algebra of the Virasoro algebra is not noetherian. This was a problem that had been open for more than 20 years and had resisted many attempts at an algebraic proof.  
November 20  Georg Oberdieck (Zurich)  Curve counting in K3 x P1 and the Hilbert scheme of points of a K3 surfaceLet S be a K3 surface. Recent results suggest a correspondence between the GromovWitten and DonaldsonThomas theory of S x P1 and the genus 0 GW theory of the Hilbert scheme of points of S. I will explain these results and how they lead to precise conjectures about the correspondence. As an application, I will discuss a conjecture for the full GW theory of the Calabi Yau threefold S x E, where E is an elliptic curve. This is joint work with R. Pandharipande.  
November 27  No seminar  
December 11, 3pm, JCMB 6206  Cristina Manolache (Imperial)  Mirror symmetry without localizationMirror Symmetry predicts a surprising relationship between the number of curves in a target space X and certain hypergeometric functions. Existing proofs rely on complicated localisation computations. I will describe a new, more conceptual proof. 
Spring 2014
January 16, JCMB 4312  Francesco Sala (HeriotWatt)  Framed sheaves on root stacks and gauge theory on ALE spacesThis talk is about a new approach to the study of supersymmetric gauge theories on ALE spaces of type $A_{k1}$, for $k\geq 2$, by using the theory of framed sheaves on 2dimensional root toric stacks. In particular, I will describe a ``stacky compactification" of a minimal resolution $X_k$ of the $A_{k1}$ toric singularity $\mathbb{C}^2/\mathbb{Z}_{k}$ and moduli spaces of framed sheaves on it. These moduli spaces provide a new setting for the study of gauge theories on ALE spaces and can be used to define new geometric realizations of representations of affine/vertex algebras. In the last part of the talk I will focus on the case of rank one framed sheaves: in that case I will describe a geometric construction of a highest weight representation of $\widehat{\mathfrak{sl}}(k)$ at level one and will characterize some CarlssonOkounkov type vertex operators on $\widehat{\mathfrak{sl}}(k)$ that have a gaugetheoretic meaning.  
January 23, 4 pm, JCMB 5326  Diane Maclagan (Warwick)  Tropical schemes, tropical cycles, and valuated matroidsThe tropicalization of a subvariety of a torus records the cycle of its compactification in an ambient toric variety. In a recent preprint Jeff and Noah Giansiracusa introduced a notion of scheme structure for tropical varieties, and showed that the tropical variety as a set is determined by this tropical scheme structure. I will introduce these notions, and outline how to also recover the tropical cycle from this information. The lurking combinatorics is that of valuated matroids. This is joint work with Felipe Rincon  
January 30  Alastair King (Bath)  Grassmannian cluster categories and dimers on a disc  
February 6  Pierre Schapira (Paris VI)  Microlocal Euler classes and Hochschild homology This is a joint work with Masaki Kashiwara.
 
February 13  Adam Boocher  Closures of a linear spaceLet L be an affine linear space. Once we fix coordinates, it makes sense to discuss the closure of L inside a product of projective lines. In this talk I'll present joint work with Federico Ardila concerning the defining ideal of the closure. It turns out that the combinatorics of this ideal are completely determined by a matroid associated to L and we are able to explicitly compute its degree, universal Groebner basis, Betti numbers, and initial ideals. I'll include several examples along the way and discuss how this closure operation comes up naturally when one searches for ideals with "nice" behavior upon degeneration.  
March 6  Tara Holm (Cornell)  The topology of toric origami manifoldsA folded symplectic form on a manifold is a closed 2form with the mildest possible degeneracy along a hypersurface. A special class of folded symplectic manifolds are the origami manifolds. In the classical case, toric symplectic manifolds can classified by their moment polytope, and their topology (equivariant cohomology) can be read directly from the polytope. In this talk we examine the toric origami case: we will describe how toric origami manifolds can also be classified by their combinatorial moment data, and present some theorems, almosttheorems, and conjectures about the topology of toric origami manifolds.  
March 13  Paolo Stellari (Milano)  FourierMukai functors: derived vs dg categoriesFourierMukai functors play a distinct role in algebraic geometry. Nevertheless a basic question is still open: are all exact functors between the bounded derived categories of smooth projective varieties of FourierMukai type? We discuss the recent advances in the subject and study the same question in the context of dg categories where the problem has been settled by B. Toen. In this talk we propose a simpler approach not based on the notion of model category. This is a joint work with A. Canonaco.  
March 20, 4pm, JCMB 4312  Vladimir Baranovsky (UC Irvine)  Deformation quantization of smooth Lagrangian subvarietyWe consider a smooth algebraic variety X with an algebraic symplectic form and a deformation O_h (with a formal parameter h) of the structure sheaf compatible with this form. For a smooth Lagrangian subvariety Y in X and a line bundle L on Y, we describe when L also admits a deformation to a module over O_h. Joint work with V. Ginzburg, D. Kaledin and J. Pecharich.  
March 21 3 pm, Faculty Room North, David Hume Tower, George Square Hodge Seminar  Etienne Ghys (Lyon)  Some remarks on singularities of real analytic curves in the planeThe topological nature of singularities of planar complex analytic curves has been understood for many years. Indeed, NewtonPuiseux series allow a complete understanding of the link of the singularity. Amazingly, the analogous question in the real domain leads to interesting combinatorial developments. I will start my discussion with a clever remark of M. Kontsevich.  
March 27, 4 pm, JCMB 5325  Nicolò Sibilla  Ribbon graphs, skeleta and homological mirror symmetryIn this talk I will review recent work of mine, partially in collaboration with H. Ruddat, D. Treumann and E. Zaslow, which centers on various aspects of Kontsevich's Homological Mirror Symmetry in the large complex limit. The onedimensional case will be emphasized, as a convenient testing ground for more general constructions.  
April 3, JCMB 5325, 3pm5pm  Klaus Altmann  Update on deformations of toric varieties We give a summary about methods and known results in the deformation theory of affine toric varieties. The convex geometric counterpart of this is the decomposition of polyhedra into Minkowski summands.
 
Wednesday, May 21, 11.3012.30, JCMB 5205  Sam Payne (Yale)  Nonarchimedean methods for multiplication maps Multiplication maps on linear series are among the most basic structures in algebraic geometry, encoding, for instance, the product structure on the homogeneous coordinate ring of a projective variety. I will discuss joint work with Dave Jensen, developing tropical and nonarchimedean analytic methods for studying multiplication maps of linear series on algebraic curves in terms of piecewise linear functions on graphs, with a view toward applications in classical complex algebraic geometry. This work is parallel in many ways to the limit linear series of Eisenbud and Harris. One key difference is that we focus on degenerations in which the special fiber is not of compact type. In this context, the tropical RiemannRoch theory of Baker and Norine and Baker’s specialization lemma are starting points for sometimes intricate calculations in component groups of Neron models and on skeletons of Berkovich curves.  
Tuesday, May 27, 2pm3pm, JCMB 5215  Jason Lo (MPI Bonn)  FourierMukai transforms on elliptic fibrationsIn their 2002 JAG paper, BridgelandMaciocia laid out a few ideas for computing FourierMukai transforms for sheaves on elliptic threefolds, which allowed them to construct an isomorphism between two moduli spaces of stable sheaves. I will explain how their ideas can be developed into a toolchest for computing FourierMukai transforms on elliptic fibrations. On elliptic fibrations of any dimension, this toolchest can be used to construct an open immersion from a moduli of polynomial stable complexes to a moduli of stable sheaves, as well as a 11 correspondence between line bundles and spectral sheaves.  
Tuesday, May 27, 3pm4pm, JCMB 5215  Ziyu Zhang (Bath)  Birational geometry of singular moduli spaces of O'Grady typeWe consider 10 dimensional singular moduli spaces of semistable objects on a projective K3 surface with respect to generic Bridgeland stability conditions. We will show that they admit symplectic resolutions, which are all deformation equivalent to the exceptional 10 dimensional holomorphic symplectic manifold constructed by O'Grady. Moreover, many properties of smooth holomorphic symplectic manifolds still hold for these singular moduli spaces. By generalizing work of Bayer and Macri, we can relate wall crossing on the stability manifold of the K3 surface to birational transformations of these singular moduli spaces. This is a joint work with C.Meachan.  
Thursday, June 12, 2pm, JCMB 6311  Nathan Ilten (Berkeley)  Vanishing of Higher Cotangent Cohomology and Applications  
Monday, June 16, 3pm, JCMB 6206  Dave Anderson (IMPA)  Schubert calculus and the Satake correspondenceRecent work of Laksov, Thorup, Gatto, and Santiago has given a perspective in which Schubert calculus on Grassmannians can be realized via certain operators on exterior algebras. This point of view also applies to equivariant and quantum versions of Schubert calculus. In this mostly expository talk, I will explain how their work fits into a more general framework via the geometric Satake correspondence.  
Wednesday, June 18, 3pm, JCMB 5215  Pablo Solis (Berkeley)  Degenerations of the Moduli space of G bundles on a curveThis talk is about three things: infinite dimensional Lie groups, representation theory and moduli problems. The group in question is called the loop group; it is the space of maps from a circle into a topological group. The loop group has a class of representations positive energy representations that generalize the highest weight representations of semisimple groups over the complex numbers. These representations allow one to construct an infinite dimensional space that one can relate to the finite dimensional moduli problem of parametrizing G bundles on a compact Riemann surface. I'll explain this setup and show how it can be used to compactify this moduli space of G bundles when the Riemann surface is allowed to develop singularities. Over the last 30 years other compactifications have been presented by Caparoso, Gieseker, Pandharipande, Seshadri and Nagaraj but this is the first construction that provides a compactification not just for vector bundles but for principal G bundles for an arbitrary simple group over the complex numbers.  
Tuesday, July 29, 2pm  Emanuele Macri (Ohio State)  Stability conditions on abelian threefolds I will present a new proof of a result by Maciocia and Piyaratne on the existence of Bridgeland stability conditions on abelian threefolds.

Autumn 2013
September 9 (Monday!), 4pm  Hendrik Süß (Edinburgh)  Equivariant vector bundles on TVarietiesBy Klyachko's work there is an equivalence of categories between equivariant vector bundles on toric varieties and families of vector space filtrations. In this talk I will discuss an generalization of this equivalence to bundles on varieties with smaller torus actions. Now, vector space filtrations are replaced by filtrations of vector bundles on some quotient space. This description comes with a nice splitting criterion and allows to prove that vector bundles of low rank on projective space, which are equivariant with respect to special subtori of the maximal acting torus must split. Notes  
September 9 (Monday!), 5pm  Francois Petit (Edinburgh)  FourierMukai transform in the quantized settingAfter reviewing some elements of the theory of Deformation Quantization modules (DQmodules), I will show that a coherent DQkernel induces an equivalence between the derived categories of coherent DQmodules if and only if the graded commutative kernel associated to it induces an equivalence between the derived categories of coherent Omodules.Notes  
September 19, 3pm JCMB 5215  Evgeny Shinder (Edinburgh)  Exceptional collections on fake projective planesFake projective planes are surfaces of general type with the same rational cohomology as a projective plane CP^2. These surfaces appear as quotients of a complex 2ball by an arithmetic subgroup of PU(2,1) and are completely classified into finitely many isomorphism classes. We study the derived category of coherent sheaves on fake projective planes. For fake projective planes with an automorphism group of order 21 we show that O, O(1), O(2) form an exceptional collection in the derived category. The orthogonal complement to this collection provides an example of a quasiphantom (a category with vanishing Hochschild homology).Notes  
September 19, 4pm JCMB 5215  Ciaran Meachan (Edinburgh)  Derived autoequivalences of hyperkähler varietiesP functors are a natural generalisation of Huybrechts and Thomas' P objects and as such, they determine autoequivalences of the codomain category. We will report on the latest developments in this direction when the codomain category is the derived category of coherent sheaves on a hyperkähler variety. Notes  
September 26, JCMB 5326  Costya Shramov (Steklov)  Finite groups of birational automorphismsGiven a variety X over some field K, one may wonder what are the restrictions on finite groups that act on X by birational automorphisms. In a joint work with Yu. Prokhorov we have recently showed (modulo some standard conjectures of birational geometry) that for a given X such groups are always bounded if K is finitely generated over Q. I will speak about this result and relevant results over algebraically closed fields.  
October 1, 3pm, joint with MAXIMALS  David Andrew Jordan (Edinburgh)  Quantum differential operators and the torus \( T^2 \)  
October 1, 4pm, joint with MAXIMALS  Natlia Iyudu (Edinburgh)  A proof of the Kontsevich conjecture on noncommutative birational transformations  
October 3  GLEN in Liverpool  
October 4, 9:30 am  6:00 pm  Maxwell colloquium on Combinatorial Algebraic Geometry  
October 10  Burt Totaro (Cambridge/UCLA)  The integral Hodge conjecture for 3folds Hodge originally conjectured that every Hodge class
 
October 17  Yuri Fedorov (UPC Barcelona)  Prym varieties in integrable systems: their algebraic description and separation of variablesThe most powerful method of explicit solving algebraic completely integrable systems is their Lax representation. The complex invariant tori of the systems are known to be Jacobian varieties of the corresponding spectral curves or, in most cases, Abelian subvarieties of the Jacobians, called Prym varieties. Then, if one wants to make a separation of variables for the system, it is nesesary to relate the Prym variety with an algebraic curve. I will show how to do this this in several cases by using the results of D. Mumford, A. Dalaljan, V. Enolski, P. van Moerbeke, A. Levin, and F. Koetter.  
October 24  Jihun Park (Pohang)  Fano threefold hypersurfacesIn 1979 Reid discovered the 95 families of K3 surfaces in three dimensional weighted projective spaces. After this, Fletcher, who was a Ph.D. student of Ried, discovered the 95 families of weighted Fano threefold hypersurfaces in his Ph.D. dissertation in 1988. These are quasismooth hypersurfaces of degrees d with only terminal singularities in weighted projective spaces P(1,a1,a2,a3,a4), where d =a1+a2+a3+a4. The 95 families are determined by the quadruples of nondecreasing positive integers (a1, a2, a3, a4). All Reid’s 95 families of K3 surfaces arises as anticanonical divisors in Fletcher’s 95 families of Fano threefolds.  
October 31  Vasily Golyshev (IITP Moscow)  \(\Gamma\) class and \(\Gamma\) conjectures for Fano varietiesWe state Gamma conjectures I and II, explain why these may be viewed as a quantum refinement of RiemannRochHirzebruch, and prove Gamma I for a particular Fano threefold, V_12, by relating it to the equation Apery had used back in 1979 in his proof of irrationality of zeta(3) (joint work with Don Zagier).  
November 7  Gregory Sankaran (Bath)  Stable homology of toroidal compactificationsI will describe work still in progress with J. Giansiracusa (Swansea) in which we aim to show that the homology of the matroidal partial compactification of the moduli space of abelian gfolds stabilises in small degree. Similar but not identical results have recently been obtained, independently and by entirely different methods, by Grushevsky, Hulek and Tommasi.  
November 14  Johan Martens  Conformal Blocks and Kummer SurfacesOriginating in statistical mechanics, bundles of conformal blocks have in the last few decades increasingly been found to be useful objects by geometers and topologists. I will sketch a brief overview of some such developments, all of which are concerned with large level asymptotics. I will then try to convince the audience that also sporadic lowlevel behaviour is interesting, by focusing on (WZW) conformal blocks for SU(2) at level 4, in particular on genus 2 curves. This is ongoing joint work with T. Baier and M. Bolognesi.  
November 21, 3.10pm  Will Donovan  The PfaffianGrassmannian correspondence, via LandauGinzburg BmodelsIf two CalabiYau threefolds are birationally equivalent, then there is an induced FourierMukai equivalence of their derived categories by a theorem of Bridgeland. The converse is not true however, as there exist pairs of CalabiYau threefolds which can be proved not to be birational, but are nevertheless derived equivalent. Intriguing examples were produced by Borisov and Caldararu in 2006. We give a new proof of the associated PfaffianGrassmannian equivalences, using the technology of LandauGinzburg Bmodels. Our proof uses ideas from a physical construction of HoriTong. It shows that even though these equivalences relate nonbirational varieties, they are a consequence of relations between certain LandauGinzburg models which are birational. This is joint work with Nicolas Addington and Ed Segal.  
November 21, 4.10pm  Jonathan Pridham  Tannaka duality for dg categories and motivesTannaka duality originally looked at reconstructing compact Lie groups or linear algebraic groups from their categories of representations, and characterised such categories. Joyal and Street generalised this to recover a coalgebra from its finitedimensional comodules. I will explain how to extend this to dg coalgebras and dg categories, via derived Morita theory. This has consequences for associating homotopy groups to cohomology theories, and in particular for motives of algebraic varieties.  
December 16, 3pm, JCMB 4312  Miles Reid  Resolution of threefold singularities and quiver representations 
Spring 2013
June 05, 2013  Alastair Craw  Geometric Reids recipe for dimer modles.  mp4  
April 04, 2013  Michael Thaddeus  A tale of two compactifications.  mp4  
March 15, 2013  Daniel Greb  Compact moduli spaces for slope semistable sheaves.  mp4  
March 14, 2013  Ugo Bruzzo  Noether lefschetz theory for hypersurfaces in toric 3 folds.  mp4  
March 12, 2013  Emma Praviato  The cavalcade of poncelet s theorem.  mp4  
March 07, 2013  John Ottem  Ample subschemes and partially ample line bundles  
February 28, 2013  Tom Bridgeland  Cluster varieties and stability conditions.  mp4  
February 07, 2013  Victor Lozovanu  An extension of kodaira vanishing in arbitrary codimension  mp4 
Autumn 2012
November 29, 2012  Timothy Logvinenko  Spherical dgfunctors  mp4  D 
November 27, 2012  Yuji Odaka  Towards algebrogeometric understanding of kstability of fano varieties  mp4  D 
November 08, 2012  Dave Anderson  Pfaffian formulas for symplectic degeneracy loci  
November 01, 2012  Alastair Craw  Mori dream spaces as fine moduli of quiver representations  mp4  D 
October 25, 2012  Charles Vial  Noncommutative resolutions and grothendieck groups  mp4  D 
October 18, 2012  Andrei Trepalin  Rationality of quotients of projective plane over nonclosed fields  
October 11, 2012  Jonathan Pridham  Semiregularity and reduced obstruction theories  
October 04, 2012  Jason Lotay  Uniqueness of lagrangian selfexpanders  
September 21, 2012  Arend Bayer  Wall crossings and birational geometry  D  
September 20, 2012  Milena Hering  Cox rings of toric bundles  D 
Spring 2012
May 31, 2012  Hugues Auvray  Uniqueness and obstructions to existence of constant scalar curvature kahler metrics: the quasiprojective case  
May 25, 2012  Julius Ross  Local moment maps associated to okounkov bodies  
March 29, 2012  Michael Singer  Partial bergman kernels and toric kstability  
March 08, 2012  Kuzma Khrabrov  Graded rings and qfano threefolds with exotic weil class group  
March 01, 2012  Jose Miguel FigueroaO'Farrill  Why we like homogeneous manifolds  
February 16, 2012  Jesus Martinez Garcia  Degenerations of del pezzo surfaces after hacking and prokhorov  
February 09, 2012  Antony Maciocia  Computing the walls for bridgeland stability  
February 02, 2012  Damiano Testa  The surface of cuboids and siegel modular threefolds  mp4  D 
January 26, 2012  Sergey Grigorian  Deformations of g2structures with torsion  mp4  D 
January 19, 2012  Rafael Torres  Constructions of generalized complex structures in dimension four  mp4  D 
Autumn 2011
December 08, 2011  Alexander Kasprzyk  Small polygons and toric codes  
December 01, 2011  Joan Simon  Topology from cosmology  mp4  D 
November 24, 2011  Dmitrijs Sakovics  Weaklyexceptional quotient singularities  mp4  D 
November 17, 2011  Will Donovan  Derived autoequivalences of hyperkahler manifolds from heisenberg categorification  
November 10, 2011  Andriy Haydys  Higher dimensional gauge theory and fueter maps  mp4  D 
November 03, 2011  Ed Segal  Windowshifts and grassmannian twists  mp4  D 
October 27, 2011  Costya Shramov  Rationality of quotients by pgroups  mp4  D 
October 20, 2011  Sue Sierra  Moduli spaces in graded ring theory  mp4  D 
October 13, 2011  Victor Przyjalkowski  Laurent polynomials in mirror symmetry  mp4  D 
October 06, 2011  Michael Wemyss  Noncommutative minimal models and applications to geometry  mp4  D 
September 29, 2011  Sergey Galkin  More symmetries of k3  mp4  D 