An EPSRC Doctoral Training Centre in Geometry and Number Theory


London School of Geometry & Number Theory


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.

Student first-year projects

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

Student Publications, newest first

Bernasconi, Fabio, Non-normal purely log terminal centres in characteristic p ≥ 3,

Morgan Brown, Enrica Mazzon, The Essential Skeleton of a product of degenerations,

Yang Li, Local Nahm transform and singularity formation of ASD connections,

Alex Kite, Discriminants and Quasi-symmetry,

Sam Porritt, A note on exponential-Möbius sums over Fq[t],

Jakub Witaszek, On the canonical bundle formula for fibrations of relative dimension one in positive characteristic,

Sam Porritt, Irreducible polynomials over a finite field with restricted coefficients,

Nicholas Lindsay, Dmitri Panov, S1-invariant symplectic hypersurfaces in dimension 6 and the Fano condition,

Luca Battistella, Navid Nabijou, A Lefschetz-type Theorem for Quasimap Invariants via Relative Quasimaps,

Yin Li, Koszul duality via suspending Lefschetz fibrations,

Fabio Bernasconi, Kawamata-Viehweg vanishing fails for log del Pezzo surfaces in char. 3,

Ardavan, Afshar, Sam Porritt, The function field Sathé-Selberg formula in arithmetic progressions and `short intervals',

Piotr Achinger, Jakub Witaszek, Maciej Zdanowicz, Liftability of the Frobenius morphism and images of toric varieties,

Andrea Dotto, The inertial Jacquet-Langlands correspondence,

Yang Li, On collapsing Calabi-Yau fibrations,

Pierrick Bousseau, Tropical refined curve counting from higher genera and lambda classes,

Stephanie Chan, Rational Right Triangles of a Given Area,

Christopher Hacon, Jakub Witaszek,On the rationality of Kawamata log terminal singularities in positive characteristic,

Yang Li, A new complete Calabi-Yau metric on C3,

Momchil Konstantinov, Higher rank local systems in Lagrangian Floer theory,

Otto Overkamp, Finite descent obstruction and non-abelian reciprocity,

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,

Paolo Cascini, Hiromu Tanaka, Jakub Witaszek, On log del Pezzo surfaces in large characteristic, To appear in Compositio Mathematica

Paolo Cascini, Hiromu Tanaka, Jakub Witaszek, Klt del Pezzo surfaces which are not globally F-split,

Francesca Carocci and Zak Turcinovic, Homological projective duality for linear systems with base locus,

Jakub Witaszek, Effective bounds on singular surfaces in positive characteristic,

Elana Kalashnikov, with Alessandro Chiodo and Davide Cesare Veniani, Semi-Calabi-Yau varieties and mirror pairs,

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,