Information about potential PhD advisors in the Hodge Institute for the upcoming PhD admissions (the deadline is 31st January 2019, but we also encourage applications before the deadline for possible early offers). For information on the application process, see this link.

Available Supervisors | |
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Clark Barwick | |

Currently, my main interests currently have to do with the connections between homotopy theory and arithmetic. I have had three Ph.D students at MIT, and I currently have two. I will happily have more. | |

Arend Bayer | |

Recently I have mostly worked on applications of derived categories/stability conditions/wall-crossing to basic questions in algebraic geometry - in other words, taking abstract categorical machinery (some of it invented in order to make precise sense of more fuzzy concepts in string theory) and extract concrete geometric results from it. There is more to work to do in that direction, and I am looking to take on more students in 2019. Two of my students who worked on such questions have just finished - Sjoerd and Soheyla, while Fatemeh, now in her 3rd year, is also working on problems in that direction. | |

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 one PhD student in Edinburgh (Vivek Mistry) and co-supervise one in Glasgow (Okke van Garderen) and am looking to take on two more in 2019. | |

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. My current student, Bach Tran is finishing this year, and I would be happy to take another student next year. | |

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 three students; two will graduate this year, so I am open to taking more students. | |

Tom Leinster | |

I work in category theory and its applications. I have many interests; here's a list of potential PhD topics. I'd 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 Graham Manuell who is looking at schemes without points via quantales. I am very happy to take new student starting in 2019. It 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 sympletic geometry, mostly the kind that uses hamiltonian group actions and moment maps. I am currently on maternity leave and will probably not take a student this year. | |

Jon Pridham | |

My research is concerned with the interactions between abstract homotopy theory and algebraic geometry. I currently have one student, Matt Booth, who is now in his fourth year and working on a derived noncommutative deformation problem in algebraic geometry. I would like to take on a student in 2019. | |

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 one student, and am open to taking another. | |

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 attempt 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 currently supervise one student, and would like to take another next year. | |

Agata Smoktunowicz | |

I work on noncommutative ring theory. I currently supervise one student, and do not plan to take another 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.