Information about potential PhD advisors in the Hodge Institute for the upcoming PhD admissions (the deadline is 31st January 2022, but we also encourage applications before the deadline for possible early offers; candidates whose undergraduate degree is from a Scottish university are encouraged to apply by 10th January, and then when available to apply for the Carnegie scholarship by its deadline of 24th January). For information on the application process, see this link.

Available Supervisors | |
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Clark Barwick | |

Currently, my focus in on a project that lies at the intersection of homotopy theory, arithmetic, and quantum field theory. The website for this is here. At MIT, I had three Ph.D students at MIT. I currently have three. I will happily have more! | |

Arend Bayer | |

Recently I have mostly worked on applications of derived categories/stability conditions/wall-crossing to fundamental questions in algebraic geometry: taking abstract categorical machinery and extract concrete geometric results. Currently, Tza-Yung (just started), Hannah (2nd year) and Augustinas (3rd 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 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 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 algebra, combinatorics of planar partitions. I currently have four PhD students, and so I am unlikely to take more for the moment. | |

Tudor 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 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 Head of School in Edinburgh, so I'd only be interested in co-supervising PhD students with members of the group! | |

Milena Hering | |

I work on algebraic geometry, especially with connections to combinatorics and commutative algebra. I am particularly interested to further 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; see also my website. I have one student at the moment and I would be happy to take more students. | |

David 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 one second-year student, and am open to taking 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 old webpage. | |

Tom Leinster | |

I work in category theory and its applications. I have many interests and would be happy to take on another student. | |

Antony 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 Calabi-Yau spaces and projective 3-space. Currently I supervise Husniyah Azubaidi and Luke Naylor. I might be interested in a new student but I am unlikely to be able to offer funding. If you have a scholarship already then I would be looking for a good background in homological algebra and algebraic geometry. | |

Johan 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 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 currently involved in the supervision of two students, Jon Eugster and Harry Gindi. I am open to taking on a student in 2022. | |

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). I currently have two PhD students and might take on another student in 2022. | |

Alexander 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 am looking to take on two PhD students in 2022. | |

Nick 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 student, and am looking to take on one more in 2022. | |

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. Much of my research is motivated by the programme to classify connected graded domains of GK-dimension 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. I probably will not take another student in 2022. | |

Agata 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.