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.  
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  
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. I currently help to direct 4 PhD students, all working on different projects, not necessarily very closely related to my own research. 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  
Although retired, I am continuing with research in Commutative Algebra. You can find my papers on the arXiv, on google scholar (ignoring the obvious nonmathematical ones) and on MathSciNet. Only very recent papers and preprints are on the arXiv, and only papers up to 2010 are on the departmental webpage.  
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 JCMB 5609, Tel. +44 131 650 5073 a.ranicki at ed.ac.uk  
Being the only topologist in the School, I am on the endangered species list. I work in the applications of algebra to the topology of manifolds in dimensions high and low, using the Algebraic Surgery of which I am Professor. I am currently particularly interested in applying algebraic surgery to topological quantum field theories. I currently have one graduate student, Juliet Cooke. Last year I had 4 students submit their theses with me: Supreedee Dangskul, Patrick Orson, Chris Palmer and Carmen Rovi, working on different aspects of manifolds.  
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.  
Michael Wemyss  
I am motivated mainly by problems in algebraic geometry and its interactions with noncommutative algebra, in particular resolutions of singularities and the minimal model program. As part of this, my research encompasses many of the related commutative and homological algebra structures and their representation theory, especially CohenMacaulay modules, triangulated and derived categories, clustertilting and higher AR theory.  
Julia Collins  
I was formerly a researcher in the field of Knot Theory (topology); specifically, looking at slice knots and the structure of the knot concordance group. Occasionally I still publish papers, but my main job is to do outreach and teaching in the School of Mathematics. 
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 Physcis group. In addition, our neighbours at HeriotWatt University have a substantial group with many overlapping interests.
PostDocs  

Adrien Brochier  
I'm mostly interested in KZ equations, Drinfeld associators and related topics like quantum groups, knot theory, Cherednik algebras and operads.  
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.  
Martin Kalck  
I am interested in homological structures arising in representation theory, singularity theory and geometry.  
Dimitra Kosta  
My research originally lay in the area of birational geometry, yet recently I have also been interested in applications and the interplay between algebraic geometry and statistics.  
Chunyi Li  
My research interested lies in algebraic geometry and noncommutative algebra. Specifically, I am interested in dervied category, stability condition, quiver representation and birational geometry. I am currently working on the derived category of coherent sheaves on commutative/noncommutative smooth Fano surfaces.  
Alice Rizzardo  
I work in Algebraic Geometry, and specifically on derived categories of coherent sheaves on a projective variety. In particular, I have been studying functors between derived categories of coherent sheaves and how they can be expressed in a geometric way. In general, I am interested in investigating the behavior of the derived category of a scheme using techniques ranging from homological algebra to representation theory. 
Graduate Students  

Wafa Alagal  
I am a PhD student working with Antony Maciocia.  
Jenny August  
I am a PhD student working with Michael Wemyss.  
Tom Avery  
I am PhD student working with Tom Leinster. I'm interested in category theory, and at the moment I'm working on Isbell duality.  
Sjoerd Beentjes  
I am a PhD student of Arend Bayer, studying algebraic geometry and derived categories.  
Matt Booth  
I'm a PhD student of Jon Pridham, interested in algebraic geometry, algebraic topology, homological algebra and category theory.  
Chris Campbell  
I am PhD student under Iain Gordon and Sue Sierra. I am interested in noncommutative algebraic geometry, specifically using geometric ideas to study noncommutative rings.  
Juliet Cooke j.cooke848 at gmail.com  
I am a PhD student of Andrew Ranicki, interested in the topology of manifolds.  
Simon Crawford  
I am a PhD student of Sue Sierra, interested in noncommutative algebraic geometry.  
Supreedee Dangskul  
I am a PhD student working with Andrew Ranicki.  
Barry Devlin  
I am PhD student under Tom Leinster, studying category theory.  
Salvatore Dolce  
I am PhD student under Johan Martens, studying representation theory and algebraic geometry.  
Soheyla Feyzbakhsh  
I am a PhD student working with Arend Bayer.  
Igor Krylov  
I am PhD student of Ivan Cheltsov. My interests are: birational geometry and theory of singularities. I am currently working on birational geometry of del Pezzo fibration of degree one and existence of good models.  
Przemyslaw Pobrotyn  
I am a PhD student of Prof. Agata Smotkunowicz interested in noncommutative ring theory.  
Bach Tran  
I am a PhD student working with Dr. Milena Hering and Dr. Antony Maciocia.  
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.  
Noah White  
I started my PhD studies in Edinburgh, in September 2012. My supervisors are Michael Wemyss and Iain Gordon. I am primarily interested in representation theory with a Lie theoretic flavour. My current research involves quantum groups and crystals which I am studying using the combinatorics and geometry they produce. 