Available Supervisors

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Information about potential PhD advisors in the Hodge Institute for the upcoming PhD admissions (the deadline for funding is 22nd January 2024, but we also encourage applications before the deadline for possible early offers. For information on the application process, see this link.

                     Available Supervisors
Clark Barwick
My research relates homotopy theory, category theory, and arithmetic. These days, I’m particularly interested in chromatic homotopy theory. I am open to taking new students, but my availability is starting to become limited.
Arend BayerArend Bayer
I have been working the abstract machinery of derived categories/stability conditions/wall-crossing and how it relates to concrete geometric questions in algebraic geometry. Currently, Tza-Yung (3rd year) and Hannah (4th year) are working on such questions. This year, I would only be looking to take on a new student in case there is a very good fit. If in doubt, don’t hesitate to drop me an email!
Ivan CheltsovIvan Cheltsov
I work on geometry of mildly singular Fano varieties. This includes rationality type questions, equivariant birational geometry, existence of extremal metrics, and classification in low dimensions.
Ben DavisonBen Davison
I work on mathematics inspired by the enumerative geometry of 3-Calabi-Yau varieties. This takes many forms – quantum groups, geometric representation theory, motivic invariants, cluster algebras, nonabelian Hodge theory, combinatorics of planar partitions, and more. I currently have two PhD students, and will be looking to take on more in 2024.
Tudor DimofteTudor Dimofte
My current work centers around the algebraic and geometric structure of operators in quantum field theories — in particular, supersymmetric gauge theories and their topological twists. This tends to involve modern methods in derived algebraic and symplectic geometry. One current goal is to develop a 3d analogue of homological mirror symmetry. I am happy to discuss this and related work. However, I am already supervising several Ph.D. students at various stages, and am unfortunately unable to take on any new students this year.
Iain GordonIain Grant Gordon
You can find out about topics I work on, basically Representation Theory and its connections to Lie theory, algebraic combinatorics, algebraic geometry and noncommutative algebra, by going to my webpage and following the links to publications (for some survey articles) or to PhD students (for some talks, plus theses of all my graduated students). I’m currently the Head of the College of Science and Engineering in Edinburgh, so I’m not able to supervise PhD students right now.
Milena HeringMilena Hering
I work on algebraic geometry, especially with connections to combinatorics and commutative algebra. Much of my research is motivated by deepening the understanding of the dictionary between geometric properties of projective toric varieties, combinatorial properties of the corresponding lattice polytopes, and algebraic properties of the corresponding toric ideals; I am currently particularly interested in stability of toric vector bundles; see also my website. My student Will Reynolds is finishing this year and I would be happy to take more students.
David JordanDavid Jordan
The problems that interest me the most concern the interactions between low dimensional topology (braid groups, mapping class groups, topological field theories), non-commutative algebra (quantization, symplectic structures, derived algebraic geometry), and representation theory (quantum groups, algebraic groups, tensor categories), especially as these interactions arise in mathematical physics and gauge theory. I currently have two fourth year students and three first-year students so I am unfortunately unlikely to be able to take any more students.
Minhyong Kim
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 webpage.
Dimitra KostaDimitra Kosta
My current research lies in combinatorial and applied algebraic geometry and commutative algebra. My research interests include studying generating sets of toric ideals (i.e. Markov and Graver bases), algebraic geometry for singular learning theory and algebraic varieties arising from phylogenetics. I would be happy to supervise a student.
Tom LeinsterTom Leinster
I work in category theory and its applications. I have many interests and would be happy to take on another student.
Antony MaciociaAntony Maciocia
My interests lie in Algebraic Geometry and particularly in understanding moduli of holomorphic sheaves. Current work has focused on applications of Bridgeland stability to various classical and non-classical questions about varieties and especially Abelian varieties and projective 3-space. Currently I supervise Husniyah Alzubaidi and Luke Naylor. I would be interested in a new student. I would be looking for a solid background in homological algebra and algebraic geometry.
Johan MartensJohan Martens
My research mainly involves the study of various moduli spaces in symplectic and algebraic geometry. Most of these have links to physics and representation theory, and involve some sort of symmetry. I am open to take on another student.
Ana Rita PiresAna Rita Pires
I work on symplectic geometry, mostly the kind that uses hamiltonian group actions (in particular toric actions) and moment maps. Lately I have been working in quantitative symplectic geometry, in particular symplectic embedding problems. I am open to taking on a new student this year.
Jon Pridham
My research is concerned with the interactions between abstract homotopy theory and algebraic geometry. I am open to taking on a student in 2024 if a suitable project can be found.
Pavel SafronovPavel 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). I currently have three PhD students (one graduating this year), so will be looking for another student in 2024.
Alexander ShapiroAlexander Shapiro
My work centres around representation theory, Poisson geometry, and cluster algebra. Problems that I am most interested in concern quantum groups, integrable systems, low-dimensional topology, higher Teichmuller theory, and are motivated by questions in mathematical physics. I currently have three PhD students, and am unlikely to take any more this year unless there is an exceptionally good fit.
Nick SheridanNick Sheridan
I work on mirror symmetry, which is a relationship between symplectic and algebraic geometry. My papers are available on my webpage. I currently supervise two students, and am looking to take on one more in 2024.
Sue SierraSue Sierra
I am a noncommutative ring theorist. I work on interactions between ring theory and algebraic geometry, particularly the use of geometric techniques to solve problems in algebra. I also study enveloping algebras of infinite-dimensional Lie algebras, which are some of the most mysterious objects in ring theory. I have successfully applied geometric techniques to these algebras, but many interesting open questions remain. My papers are available on my webpage. I have two Ph.D. students currently (one finishing this year), and am open to taking another student in 2024.
Agata SmoktunowiczAgata Smoktunowicz
I work on noncommutative ring theory. I do not plan to take another student in the coming year.

We also have a lot of common interests with colleagues in neighbouring fields, in particular the Mathematical Physics group has a similar webpage listing potential advisors.