You can find former members of the Hodge Institute on our Alumni page.
Faculty  

Sir Michael Atiyah  
Sir Michael Atiyah has been honorary professor at the University of Edinburgh since 1997. In 2008/09, he delivered the Edinburgh Lectures on Geometry, Analysis and Physics. The Atiyah 80+ website has a wealth of material about Sir Michael, including the recent interview.  
Clark Barwick  
I am interested in the connections between homotopy theory and arithmetic. In the past this meant thinking about algebraic Ktheory. These days, I'm more interested in étale homotopy types and related invariants.  
Arend Bayer JCMB 5616, arend.bayer at ed.ac.uk  
I have been working on questions in algebraic geometry motivated by string theory and mirror symmetry; for a while that meant GromovWitten theory, in the last few years mostly derived categories and stability conditions. Recently that has led me to very classical questions in algebraic geometry, via wallcrossing and birational geometry of moduli spaces. Google scholar ArXiv 

Ivan Cheltsov  
I am interested in birational geometry and its connections with algebra, geometry and topology. My interests include classification of singular del Pezzo surfaces, nonrationality of singular Fano threefolds, finite subgroups in Cremona groups, automorphisms of affine cones over del Pezzo surfaces, birational transformations of threefold fibred in del Pezzo surfaces, alphainvariants of log Fano varieties, quotient singularities, topology of singular del Pezzo surfaces and Fano threefolds. I currently supervise 1 PhD student, Igor Krylov, who is working on del Pezzo fibrations. You can find all my papers here. My PhD adviser and my exPhD students can be found here  
Ben Davison JCMB 5310, ben.davison at ed.ac.uk  
I work on applications of refined and categorified DonaldsonThomas theory. This includes work in cluster algebras, quantum groups, nonabelian Hodge theory and enumerative geometry of 3CalabiYau varieties and noncommutative varieties.  
Iain Grant Gordon (Head of School) JCMB 5321, Tel. +44 131 650 5062  
I am interested in Lie theoretic representation theory and its connections with combinatorics, geometry and noncommutative things. You can find my papers on the arXiv, Google Scholar, MathSciNet, or my homepage. Not everything is on the arXiv.  
Milena Hering  
I am working on algebraic geometry, commutative algebra, and combinatorics. My interests include positivity properties of line bundles and syzygies, toric varieties, and tropical varieties. Google scholar ArXiv 

David Jordan  
I study various algebraic systems which lie between representation theory and physics. More precisely, my research falls roughly into three distinct areas: firstly, I study tensor categories in their various flavors (fusion, braided, symmetric, stable oo…)  their classification, and their representation theory. Secondly, I study the interplay between noncommutative algebra and algebraic geometry. Finally, I study quantization problems involving quantum groups, quantum orbit spaces, and their geometry. You can find my papers on the ArXiv.  
Tom Leinster  
Most of what I do is about category theory and its many applications, including some nonstandard ones such as geometric measure and aspects of both analysis and theoretical ecology. They are loosely unified by the themes of size and measurement. I am one of the hosts of the nCategory Café, a research blog where I have written about many of my interests. My papers, talks and blog entries can all be found through my home page.  
Tom Lenagan  
I am interested in noncommutative algebra, in particular in growth of algebras and quantum algebras. I'm also interested in totally nonnegative matrices. Click on my name to reach my webpage where publications are listed.  
Antony Maciocia  
My primary interests are in moduli spaces of objects in the derived category of sheaves on low dimensional algebraic varieties, especially CalabiYau varieties and more especially abelian and K3 surfaces. I am also interested in triangulated categories and hyperkahler geometry more generally. I am especially fond of the FourierMukai transform as a means to understand the detailed structure of varieties and their moduli spaces of sheaves. See arxiv for a list of papers.  
Johan Martens  
I study algebrogeometric and symplectic structures of various moduli spaces, mostly with links to physics (gauge theory, conformal field theory, integrable systems).  
Liam O'Carroll  
Liam passed away on the 25th of October 2017 aged 72. He was a wonderful colleague, a great mentor to many of us in the Hodge Institute, and an excellent mathematician. You can find details of his papers on google scholar and on MathSciNet.  
Ana Rita Pires apires at ed.ac.uk  
I work in symplectic geometry, in particular using hamiltonian actions and moment maps. My work on degenerate symplectic structures — origami manifolds and bsymplectic or logsymplectic manifolds — led me to connections with toric topology, contact geometry, and Poisson geometry. More recently I have become interested in quantitative symplectic geometry by woking on symplectic embedding problems. ArXiv 

Jon Pridham  
I work on applications of abstract homotopy theory to algebraic geometry. My research has two main strands: derived algebraic geometry, and homotopy theory of algebraic varieties (including numbertheoretical and motivic aspects). You can find my papers on the arXiv or my homepage.  
Andrew Ranicki  
Andrew passed away on the 20th of February 2018 aged 69. He had an extraordinary appreciation of people and was a remarkable colleague. To find out more, please go to http://www.maths.ed.ac.uk/~v1ranick/.  
Nick Sheridan  
I work on homological mirror symmetry and symplectic topology. My papers are available on my webpage.  
Sue Sierra  
I am a noncommutative ring theorist, specialising in interactions between ring theory and algebraic geometry, particularly the use of geometric techniques to solve problems in algebra. I am particularly interested in birationally commutative algebras (graded algebras that embed in a skew polynomial extension over a commutative ring) and in graded domains of low GKdimension. Much of my research is motivated by the attempt to classify connected graded domains of GKdimension 3. I am also interested in moduli problems for graded rings and in algebraic geometry, and recently I have begun to work on problems coming from Lie theory. My papers are available on my webpage.  
Agata Smoktunowicz  
I am interested in noncommutative algebra. You can see my publications on MathSciNet.  
Chris Smyth  
I am a number theorist. 
We have also several faculty in neighbouring fields with strong interest in geometry, including Harry Braden, José FigueroaO'Farrill, James Lucietti and Joan Simon in the Edinburgh Mathematical Physics group. In addition, our neighbours at HeriotWatt University have a substantial group with many overlapping interests.
PostDocs  

Andrea Appel  
My research is in representation theory, with a special focus on the interplay between algebra, geometry and combinatorics in quantum groups. I am interested in infinitedimensional Lie algebras, quantum groups and braid groups, quantization and deformation theory, integrable systems, and categorification.  
Sjoerd Beentjes JCMB 5401, sjoerd.beentjes at ed.ac.uk  
My research is in algebraic geometry, in particular applications of the theory of stability conditions and derived categories to the enumerative geometry of curves on CalabiYau threefolds, such as DonaldsonThomas, PandharipandeThomas, and BPS invariants. At the moment, I am interested in their underlying motivic and categorical refinements.  
Francesca Carocci  
.  
Sam Gunningham  
My research is centered around Geometric Representation Theory. I study things like Dmodules on reductive groups and associated moduli spaces using tools from topological field theory and derived algebraic geometry.  
Natalia Iyudu  
I am interested in noncommutative algebra and its interplay with (noncommutative) geometry, representation theory, operads, homological algebra, Ktheory. The structures originated in physics, topology, geometry, such as CalabiYau algebras, Novikov algebras, operads of CFT, etc. are of particular interest. My papers are available at ArXiv.  
Travis Mandel  
My research focuses on algebrogeometric and tropical aspects of mirror symmetry and enumerative geometry, with a particular focus on cluster varieties. I am especially interested in how canonical bases of regular functions on one cluster variety are related to counts of algebraic curves (log GromovWitten invariants) in the mirror cluster variety. I am also interested in quantum and motivic refinements of this correspondence.  
Diletta Martinelli  
My research interests are in algebraic geometry and in particular in higher dimensional birational geometry. My work aims to study effectivity questions on algebraic varieties related to their underlying topology as complex manifolds. I am also interested in positive characteristic methods, moduli spaces and CalabiYau manifolds.  
Brent Pym  
I work at the interface between differential, algebraic and noncommutative geometry. I am particularly interested in topics that have close ties with physics, including: the structure and classification of algebraic Poisson varieties; deformation quantization and noncommutative projective geometry; the Stokes phenomenon and resurgence; moduli spaces of bundles and connections; and links with derived symplectic and Poisson geometry.  
Alexander Shapiro  
. 
Graduate Students  

Jenny August  
I am a PhD student working with Michael Wemyss.  
Matt Booth  
I'm a PhD student of Jon Pridham, interested in algebraic geometry, algebraic topology and homological algebra.  
Ben Brown Bayes Centre 5.33, B.Brown at ed.ac.uk  
I am a PhD student of Johan Martens as of September 2018. My research interests are in the interactions between algebraic, complex and symplectic geometry, with an occasional foray into mathematical physics.  
Juliet Cooke j.cooke848 at gmail.com  
I am a PhD student of Andrew Ranicki, interested in the topology of manifolds.  
Graham Manuell  
I am a PhD student working with Antony Maciocia.  
Vivek Mistry  
I am a PhD student of Ben Davison in Edinburgh since 2018. I'm interested in algebraic geometry.  
Anna Mkrtchyan  
I am a PhD student working with David Jordan.  
Trang Nguyen  
.  
Ruth Reynolds  
I am a PhD student working with Sue Sierra.  
William Reynolds  
.  
Fatemeh Rezaee  
I'm a PhD student working with Arend Bayer.  
Emily Roff  
I'm a PhD student working with Tom Leinster.  
Nivedita Viswanathan  
.  
Tim Weelinck  
I'm a PhD student working with David Jordan. I'm interested in representation theory and geometry, and areas where the two collide e.g. quantum groups at roots of unity. 