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

Sir Michael Atiyah  
Sir Michael passed away on the 11th of January 2019 aged 89. He had been honorary professor at the University of Edinburgh since 1997. He was a great mathematician whose work will continue to influence scientists, far in to the future. To us in Edinburgh he was a tremendous colleague, to the community of mathematicians and physicists he was an inspiration, and to people all across the world he was a wonderful friend. The Atiyah 80+ website has a wealth of material about Sir Michael, including an 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 arithmetic 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.  
Francesca Carocci  
My research interests are deformation theory, moduli problems and enumerative invariants arising from them. In particular I am interested in GromovWitten and DonaldsonThomas type invariants and relations among them.  
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.  
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.  
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.  
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.  
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Graduate Students  

Matt Booth  
I'm a PhD student of Jon Pridham, interested in algebraic geometry, algebraic topology and homological algebra.  
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.  
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.  
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  
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.  
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  
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Ruth Reynolds  
I am a PhD student working with Sue Sierra.  
William Reynolds  
I began as a PhD student at Edinburgh in September 2018, and my advisor is Milena Hering.  
Fatemeh Rezaee  
I'm a PhD student working with Arend Bayer.  
Emily Roff  
I'm a PhD student working with Tom Leinster.  
Sebastian Schlegel Mejia  
I am a PhD student of Ben Davison since September 2019.  
Nivedita Viswanathan  
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