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.
|Robin Bartlett||p-adic Hodge theory
|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 Turkinovic) 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
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