The London research grouping in geometry and number theory covers around 40 academics (faculty) and, at the time of writing (September 2015) two student cohorts, with approximately 15 in each cohort. There are also many other research students working in these areas in London.

Our research covers very large areas of modern geometry and number theory. In geometry, we cover the spectrum from algebraic geometry, complex geometry, symplectic geometry, through to differential and riemannian geometry, geometric analysis, including techniques from nonlinear elliptic and parabolic partial differential equations. Subjects such as geometric group theory, knot theory, discrete systems and inverse problems are also represented.

Number theory is similarly broad, with researchers in both analytic and algebraic number theory, with specialists in (p-adic) Galois representations, modular and automorphic forms, arithmetic geometry, arithmetic aspects of spectral theory, multiplicative functions and additive combinatorics.

Topics at the interface include the Langlands Programme, Arithmetic Geometry, Mirror symmetry, and Moduli spaces.

Please browse to our academic staff pages for more detailed information.

The following gives an idea of the project work that our 2014 cohort of students undertook in their first year.

Student | Projects |
---|---|

Robin Bartlett | p-adic Hodge theory Adic Spaces |

Luca Battistella | Moduli spaces of stable maps Construction of the virtual fundamental class |

James Cann | Modular curves as moduli spaces Dirichlet's divisor problem |

Francesca Carocci | (with Zak Turcinovic) Homological Projective Duality and Blow-up Virtual fundamental class and Gromov-Witten theory |

Antonio Cauchi | Hida families of modular ordinary modular forms |

Celso Dos Santos Viana | Lagrangian mean curvature flow and the Whitney sphere Isoperimetric surfaces in 3-manifolds with positive Ricci curvature |

Elana Kalashnikov | Mirror symmetry for toric varieties Four dimensional Fano representation quotients in Grassmannians |

Alexandre Kite | Transitions galore Family Floer Theory and Mirror Symmetry |

Momchil Konstantinov | Negatively stabilised contact manifolds are not symplectically fillable Floer Theory with local coefficients in the presence of Maslov 2-discs and an application to the Chiang Lagrangian |

Nick Lindsay | Localisation of circle actions JSJ decompositions of groups |

Otto Overkamp | p-adic Galois representations Finite descent obstruction and non-abelian reciprocity The moduli space of hyperelliptic curves and its compactification |

Kwok-Wing Tsoi | CM-forms and non-commutative Iwasawa theory Kolyvagin systems and their applications |

Zak Tukinovic | (with Francesca Carocci) Homological Projective Duality and Blow-up Mirror candidates for toric complete intersections |

Jakub Witaszek | Different viewpoints on multiplier ideal sheaves and singularities of theta divisors Effective bounds in positive characteristic and other applications of Frobenius techniques |

Mirko Mauri, Enrica Mazzon, Matthew Stevenson, *Essential skeletons of pairs and the geometric P=W conjecture*, https://arxiv.org/abs/1810.11837

Yang Li, *A gluing construction of collapsing Calabi-Yau metrics on K3 fibred 3-folds*, https://arxiv.org/abs/1809.08120

Andrea Dotto, *Breuil-Mézard conjectures for central division algebras*, https://arxiv.org/abs/1808.06851

Lucas das Dores, Mirko Mauri, *G-birational superrigidity of del Pezzo surfaces of degree 2 and 3*, https://arxiv.org/abs/1808.05023

Mirko Mauri, *The dual complex of log Calabi-Yau pairs on Mori fibre spaces*, https://arxiv.org/abs/1808.03706

Yang Li, *Dirichlet problem for maximal graphs of higher codimension*, https://arxiv.org/abs/1807.11795

Sam Porritt, *Residue races of the number of prime divisors function*. https://arxiv.org/abs/1806.01585

Clifford Blakestad, Damián Gvirtz, Ben Heuer, Daria Shchedrina, Koji Shimizu, Peter Wear, Zijian Yao, *Perfectoid covers of abelian varieties*, https://arxiv.org/abs/1804.04455

Andrea Dotto, *Canonical β-extensions*, https://arxiv.org/abs/1802.06909

Gvirtz, Damian, *The dual complex of log Calabi-Yau pairs on Mori fibre spaces*, https://arxiv.org/abs/1808.03706

Fabio Bernasconi, *Non-normal purely log terminal centres in characteristic p ≥ 3*, https://arxiv.org/abs/1802.04896

Morgan Brown, Enrica Mazzon, *The Essential Skeleton of a product of degenerations*, https://arxiv.org/abs/1712.07235

Yang Li, *Local Nahm transform and singularity formation of ASD connections*, https://arxiv.org/abs/1712.00765

Alex Kite, *Discriminants and Quasi-symmetry*, https://arxiv.org/abs/1711.08940

Sam Porritt, *A note on exponential-Möbius sums over Fq[t]*, https://arxiv.org/abs/1711.08729

Jakub Witaszek, *On the canonical bundle formula for fibrations of relative dimension one in positive characteristic*, https://arxiv.org/abs/1711.04380

Sam Porritt, *Irreducible polynomials over a finite field with restricted coefficients*, https://arxiv.org/abs/1711.06243

Nicholas Lindsay, Dmitri Panov, *S1-invariant symplectic hypersurfaces in dimension 6 and the Fano condition*, https://arxiv.org/abs/1711.03126

Luca Battistella, Navid Nabijou, *A Lefschetz-type Theorem for Quasimap Invariants via Relative Quasimaps*, https://arxiv.org/abs/1710.11158

Yin Li, *Koszul duality via suspending Lefschetz fibrations*, https://arxiv.org/abs/1710.09186

Fabio Bernasconi, *Kawamata-Viehweg vanishing fails for log del Pezzo surfaces in char. 3*, https://arxiv.org/abs/1709.09238

Ardavan Afshar, Sam Porritt, *The function field Sathé-Selberg formula in arithmetic progressions and `short intervals'*, https://arxiv.org/abs/1709.01963

Piotr Achinger, Jakub Witaszek, Maciej Zdanowicz, *Liftability of the Frobenius morphism and images of toric varieties*, https://arxiv.org/abs/1708.03777

Andrea Dotto, *The inertial Jacquet-Langlands correspondence*, https://arxiv.org/abs/1707.00635

Yang Li, *On collapsing Calabi-Yau fibrations*, https://arxiv.org/abs/1706.10250

Pierrick Bousseau, *Tropical refined curve counting from higher genera and lambda classes*, https://arxiv.org/abs/1706.07762

Stephanie Chan, *Rational Right Triangles of a Given Area*, https://arxiv.org/abs/1706.05919

Christopher Hacon, Jakub Witaszek,*On the rationality of Kawamata log terminal singularities in positive characteristic*, https://arxiv.org/abs/1706.03204

Yang Li, *A new complete Calabi-Yau metric on C3*, https://arxiv.org/abs/1705.07026

Andrea Tirelli, *Symplectic resolutions for Higgs moduli spaces*, https://arxiv.org/abs/1701.07468

Momchil Konstantinov, *Higher rank local systems in Lagrangian Floer theory*, https://arxiv.org/abs/1701.03624

Otto Overkamp, *Finite descent obstruction and non-abelian reciprocity*, https://arxiv.org/abs/1611.05341

Yusuke Nakamura, Jakub Witaszek, *On base point free theorem and Mori dream spaces for log canonical threefolds over the algebraic closure of a finite field*, http://arxiv.org/abs/arXiv:1603.06197

Paolo Cascini, Hiromu Tanaka, Jakub Witaszek, *On log del Pezzo surfaces in large characteristic*, To appear in Compositio Mathematica http://arxiv.org/abs/arXiv:1601.03583

Paolo Cascini, Hiromu Tanaka, Jakub Witaszek, *Klt del Pezzo surfaces which are not globally F-split*, http://arxiv.org/abs/1601.03578

Francesca Carocci and Zak Turcinovic, *Homological projective duality for linear systems with base locus*, http://arxiv.org/abs/1511.09398

Jakub Witaszek, *Effective bounds on singular surfaces in positive characteristic*, http://arxiv.org/abs/1510.08885

Elana Kalashnikov, with Alessandro Chiodo and Davide Cesare Veniani, *Semi-Calabi-Yau varieties and mirror pairs*, http://arxiv.org/abs/1509.06685

Jakub Witaszek, with Diletta Martinelli and Yusuke Nakamura, *On base point free theorem for log canonical threefolds over the algebraic closure of a finite field*, http://arxiv.org/abs/1407.5146