Information about potential PhD advisors in the Hodge Institute for the upcoming PhD admissions (the deadline is 31st January 2020, 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 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 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 much more to work to do in that direction, and I am looking to take on more students in 2020. Two of my students who worked on such questions finished last year - Sjoerd and Soheyla. Currently, Fatemeh, now in her last year, and Augustinas, who just started, are also working on problems in that general 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 two PhD students in Edinburgh (Vivek Mistry and Sebastian Schlegel-Mejia) and co-supervise one in Glasgow (Okke van Garderen) but I would be happy to take more. | |

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 student finishing this year, two having just graduated. So I am happy to take more students. | |

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 2020. 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. Some of my work was on degenerate symplectic structures called origami manifolds, and more recently I have been working on symplectic embedding problems. I may be open to taking on a student in 2020. | |

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, who have just started. My last student, Matt Booth, recently completed his thesis on a derived non-commutative deformation problem in algebraic geometry. I am unlikely to take on a student in 2020. | |

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 looking to take on another in 2020. | |

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. My current student Ruth Reynolds is graduating this year, and I would like to take another student in 2020. I have projects available relating to the classification of noncommutative projective surfaces (graded domains of cubic growth) and on enveloping algebras of infinite-dimensional Lie algebras. | |

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.