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 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.  
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).  
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  

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.  
Giulia Gugiatti ggugiatt at ed.ac.uk  
My research is in algebraic geometry. In particular, my work focuses on mirror symmetry for Fano varieties, in both its Hodgetheoretic and homological formulations.  
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.  
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.  
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.  
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.  
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.  
Hannah Dell H.Dell at sms.ed.ac.uk  
I am a PhD student working with Arend Bayer. I am interested in algebraic geometry, in particular derived categories.  
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.  
Patrick Kinnear P.Kinnear at ed.ac.uk  
I am a PhD student working with David Jordan. I am interested in algebra.  
Vivek Mistry  
I am a PhD student of Ben Davison in Edinburgh since 2018. I'm interested in algebraic geometry.  
Luke Naylor  
I am a PhD student working with Antony Maciocia.  
Dora Puljic  
I am a PhD student working with Agata Smoktunowicz.  
William Reynolds  
I began as a PhD student at Edinburgh in September 2018, and my advisor is Milena Hering.  
Emily Roff  
I'm a PhD student working with Tom Leinster.  
Arman Sarikyan  
I am a PhD student working with Ivan Cheltsov.  
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. 