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

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 

Sjoerd Beentjes sjoerd.beentjes at ed.ac.uk  
I am interested in algebraic geometry, in particular the enumerative geometry of CalabiYau threefolds, such as (noncommutative) DonaldsonThomas theory. In recent years, I have become interested in applications of pure mathematics and mathematical statistics to causal questions in population biomedicine and public health policy.  
Ivan Cheltsov  
I am birational geometer interested in Kstability and rationality of Fano varieties, subgroups of Cremona groups, polarized cylinders in rational varieties, and relevant classification type problems. I currently supervise 1 PhD student, Niveditha Viswanathan. You can find my papers here and pictures of my bike 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.  
Tudor Dimofte  
My research lies at the interface of theoretical physics and pure mathematics, inspired by the dual questions: What algebraic and geometric structures govern the behavior of elementary quantum particles and fields? Conversely, how can physics intuition be used to derive new predictions and results in algebra, geometry, and other branches of mathematics?  
Iain Grant Gordon (Head of College)  
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.  
Minhyong Kim (Director of ICMS)  
My research is mostly in arithmetic geometry, the study of structures that have a combination of arithmetic and geometric natures, Recently, I’ve been mostly interested in the interface between arithmetic geometry and quantum field theory. You can see some of my papers listed on this old webpage.  
Dimitra Kosta  
My research originally lay in the area of birational geometry, yet since then I have been interested in the interplay between algebra, geometry and statistics. My research interests have expanded to include algebraic statistics, phylogenetic algebraic geometry, computational commutative algebra and applied algebraic geometry.  
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).  
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 arithmetic and motivic aspects). You can find my papers on the arXiv or my homepage.  
Pavel Safronov  
I am interested in problems lying at the intersection of representation theory (of quantum groups), algebraic geometry (in particular, derived algebraic and derived symplectic geometry) and mathematical physics (supersymmetric field theories, topological field theories, deformation quantization).  
Alexander Shapiro  
I am interested in representation theory and Poisson geometry. My work concerns quantum groups, cluster algebra, character varieties, and integrable systems.  
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 programme 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, particularly chain conditions in enveloping algebras of infinitedimensional Lie algebras. 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 Tim Adamo, 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  

Léa Bittmann JCMB 5422, lea.bittmann at ed.ac.uk  
My area of research is representation theory. I am particularly interested in representations of quantum groups, quantum affine algebras, and Hecke algebras. I am also intestrested in their relations with (quantum) cluster algebras.  
Dougal Davis  
My research is in algebraic geometry and representation theory. I am particularly interested in moduli of principal bundles on elliptic curves, and their relations to objects of classical algebraic geometry, such as del Pezzo surfaces and certain resolutions of singularities, and to more algebraic gadgets like elliptic quantum groups.  
Lucien Hennecart  
My research revolves around Hall algebras, from their earliest version as convolution algebras on constructible functions on points on some moduli spaces (of quivers, of coherent sheaves on a curve) to more modern avatars involving cohomology, and the relations between them.  
Jeff Hicks jeff.hicks at ed.ac.uk  
I work in symplectic geometry and homological mirror symmetry. My research studies the relation between tropical geometry and symplectic geometry, and Lagrangian cobordisms.  
Qingyuan Jiang JCMB 5601, Qingyuan.Jiang at ed.ac.uk  
My research area is algebraic geometry, especially on derived category of coherent sheaves on algebraic varieties. More concretely, I work on homological projective duality (HPD), CalabiYau and hyperkahler categories, and the relations between derived categories and birational geometry.  
Naoki Koseki JCMB 5419, nkoseki at ed.ac.uk  
My research area is algebraic geometry, especially Bridgeland stability, moduli spaces, (dcritical) birational geometry, and DonaldsonThomas invariants.  
Cheuk Yu Mak cheukyu.mak at ed.ac.uk  
My research area is symplectic topology. More specifically, I study Fukaya category, homological mirror symmetry, symplectic Khovanov homology and rational/ruled symplectic 4manifolds.  
Alexandre Minets JCMB 5420, alexandre.minets at ed.ac.uk  
My research area is geometric representation theory. More specifically, I focus on the study of moduli spaces associated to quivers and varieties of low dimension, their combinatorial structure, and representationtheoretic interpretation of their invariants. Keywords: quiver varieties, stable sheaves, KLR, CoHAs, Higgs bundles.  
Tomasz Przeździecki  
I work in representation theory. I am particularly interested in categorification, Hecke and KLR algebras and their generalizations, rational Cherednik algebras, modern incarnations of SchurWeyl duality as well as cohomological Hall algebras.  
Jan Pulmann JCMB 4622, jan.pulmann at ed.ac.uk  
I am interested in various mathematical aspects of the ChernSimons theory: moduli spaces of flat connections, their quantizations, quantum groups.  
Fatemeh Rezaee  
I am interested in Bridgeland wallcrossing, Hilbert schemes, derived algebraic geometry, geometric analysis.  
Emily Roff  
My research has to do with numerical and homological invariants of metric spaces that derive from an interpretation of a metric space as a type of enriched category. More generally, I am interested in enriched category theory and its applications within and beyond pure mathematics.  
Kostya Tolmachov k.tolmachov at ed.ac.uk  
I am interested in various topics in geometric representation theory and its applications (in particular, to knot homology theories).  
Brian R. Williams brian.williams at ed.ac.uk  
My research revolves around mathematical structures related to quantum field theory. I am particularly interested in studying algebraic and geometric structures present in higher dimensional generalizations of conformal field theory using tools in homological algebra, derived geometry, and geometric analysis.  
Fei Xie fei.xie at ed.ac.uk  
My research area is algebraic geometry. I am interested in derived categories of coherent sheaves on algebraic varieties and their relations to moduli spaces and rationality.  
Shizhuo Zhang JCMB 5419  
My research area is algebraic geometry, in particular, I work on derived category of coherent sheaves on surfaces, moduli space of quiver representations, moduli space of sheaves on rational surfaces. Recently I am interested in Bridgeland stability conditions on rational surfaces and its wall crossing behavior.  
Filip Živanović f.zivanovic at ed.ac.uk  
I am a postdoc with Nick Sheridan since Fall 2020. I am interested in Symplectic Topology, Geometric Representation Theory, Knot Invariants, and the interplay between these. 
Graduate Students  

Husniyah Alzubaidi  
I am a PhD student working with Antony Maciocia.  
William Bevington  
I am a PhD student working with Clark Barwick.  
Ben Brown JCMB 5622, B.Brown at ed.ac.uk  
I am a PhD student of Johan Martens as of September 2018, and my research is (currently) on hypertoric varieties and geometric quantisation. I am on the right in the photograph.  
Lucas Buzaglo  
I am a PhD student working with Sue Sierra. I am interested in noncommutative ring theory.  
Yan Yau Cheng  
I am a PhD student working with Minhyong Kim since September 2022. My interests are in Algebraic Number Theory and Arithmetic Geometry.  
TzuYang Chou  
I am a PhD student working with Arend Bayer.  
Hannah Dell  
I am a PhD student working with Arend Bayer. I am interested in algebraic geometry, in particular derived categories of coherent sheaves and Bridgeland stability conditions on them.  
Elena Denisova  
I am a PhD student working with Vanya Cheltsov and Milena Hering.  
Adrián Doña Mateo  
I am PhD student working with Tom Leinster since September 2022. I am interested in Category Theory and its applications.  
Jon Eugster j.eugster at sms.ed.ac.uk  
As of September 2019 I am a PhD student supervised by Jon Pridham and Clark Barwick. I am interested in arithmetic geometry, algebraic geometry, and homotopy theory. At the moment I am working on topics around étale topoi and reconstruction of schemes.  
Harry Gindi  
As of September 2019 I am a PhD student supervised by Clark Barwick and Jon Pridham. My mathematical interests are homotopy theory, algebraic geometry, Ktheory, higher category theory, and motives.  
Kai Hugtenburg  
I am a PhD student supervised by Nick Sheridan. I am working on symplectic topology.  
Augustinas Jacovskis a.jacovskis at sms.ed.ac.uk  
I'm a PhD student of Arend Bayer at Edinburgh since 2019. I'm interested in algebraic geometry, in particular derived categories and Bridgeland stability conditions.  
Shivang Jindal  
I am a PhD student working with Ben Davison.  
Sarunas Kaubrys  
I am a PhD student working with Pavel Safronov and Ben Davison since 2021.  
Patrick Kinnear  
I am a PhD student working with David Jordan and Pavel Safronov. I am interested in algebra and topology.  
Theodoros Lagiotis T.Lagiotis at sms.ed.ac.uk  
I am a PhD student working with Pavel Safronov since 2021. My current focus is on topological field theories.  
Vivek Mistry  
I am a PhD student of Ben Davison in Edinburgh since 2018. I'm interested in algebraic geometry.  
Alvaro Muniz Brea  
I am a PhD student working with Nick Sheridan.  
Luke Naylor  
I am a PhD student working with Antony Maciocia.  
Antoine Pinardin  
I am a PhD student working with Vanya Cheltsov.  
Dora Puljic  
I am a PhD student working with Agata Smoktunowicz since 2020. I am working on brace theory.  
Karim Rega  
I am a PhD student working with Johan Martens.  
William Reynolds  
I began as a PhD student at Edinburgh in September 2018, and my advisor is Milena Hering.  
Arman Sarikyan  
I am a PhD student working with Ivan Cheltsov. My main area of research is algebraic geometry, in particular Fano varieties, rationality problems, equivariant geometry, arithmetic geometry.  
Sebastian Schlegel Mejia  
I am a PhD student of Ben Davison since September 2019.  
Alisa Sheinkman  
I am a PhD student working with David Jordan.  
Ruben van Belle  
I am a PhD student working with Tom Leinster.  
Nivedita Viswanathan  
I am a PhD student working with Ivan Cheltsov. 