Information about potential PhD advisors in the Hodge Institute for the upcoming PhD admissions (deadline December 2017).

Available Supervisors | |
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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 information from it. There is more to work to do in that direction, and I'd be happy to take on another student in 2018. I currently have three students working in this general direction: Sjoerd and Soheyla, who will both finish this year, and Fatemeh, who has just started her 2nd year. | |

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. | |

Iain Grant Gordon | |

Noah White is a PhD student working with me at the moment, on questions around the symmetric group combinatorics, Calogero-Moser spaces and the KZ equations. You can find out more 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, and am not planning to take more in 2018. I am happy to be a second supervisor, however. | |

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. Currently I supervise Graham Manuell who is looking at schemes without points and Trang Nguyen who is working on stability and Fourier-Mukai transforms. | |

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. | |

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 third year and working on a derived noncommutative deformation problem in algebraic geometry. I am open to taking on students in the coming year. | |

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 two students, and am not planning 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 have also several faculty in neighbouring fields with strong interest in algebra and geometry. For full PhD information for the Mathematical Physics group, see here. This group includes José Figueroa-O'Farrill, and:

Mathematical Physicists. | |
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Harry Braden | |

Integrable systems are those that can be solved exactly and they appear in significant physical and mathematical settings. Their modern study involves many branches of mathematics, particularly algebra, geometry and algebraic geometry with computational aspects of these also important. Examples of such systems range from classical mechanics to (quantum) field theory and indeed supersymmetric gauge theories relate both of these. I am happy to supervise a suitably well-qualified student on any of the above aspects depending on their interests. | |

James Lucietti | |

I work on general relativity and gravitational aspects of string theory and holography. I have a particular interest in higher-dimensional black hole solutions in these contexts. I currently have one student and I am open to taking on another next year. | |

Joan Simon | |

I work on holography. I currently supervise one student, and do not plan to take on another in the coming year. |