The London research grouping in geometry and number theory covers around 60 academics (faculty) and 30 postdocs. At the time of writing (October 2023) the LSGNT has four current 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, arithmetic statistics and additive combinatorics.
Topics at the interface include the Langlands programme, arithmetic geometry, mirror symmetry, motives 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 |
Christopher G Evans, Ben Lambert, Albert Wood, Lagrangian mean curvature flow with boundary, https://arxiv.org/abs/1911.04977
Gregorio Baldi, Giada Grossi, Finite descent obstruction for Hilbert modular varieties, https://arxiv.org/abs/1910.12303
Albert Wood, Singularities of Equivariant Lagrangian Mean Curvature Flow, https://arxiv.org/abs/1910.06122
Gregorio Baldi, Some remarks on motivical and derived invariants, https://arxiv.org/abs/1910.04733
Mladenov, Boris, Degeneration of spectral sequences and complex Lagrangian submanifolds, https://arxiv.org/abs/1907.04742
Pol van Hoften, A geometric Jacquet-Langlands correspondence for paramodular Siegel threefolds, https://arxiv.org/abs/1906.04008
Vladimir Dokchitser, Robert Evans, Hanneke Wiersema, On a BSD-type formula for L-values of Artin twists of elliptic curves, https://arxiv.org/abs/1905.04282
Ashwin Iyengar, Deformation theory of the trivial mod p Galois representation for GLn, https://arxiv.org/abs/1904.05996
Tibor Backhausz, Change of coefficients in the p≠ℓ local Langlands correspondence for GLn, https://arxiv.org/abs/1812.04208v1
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
Giulia Gugiatti, Alessio Corti, Hyperelliptic Integrals and Mirrors of the Johnson-Kollár del Pezzo Surfaces, https://arxiv.org/abs/1901.09026
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
Mirko Mauri, The dual complex of log Calabi-Yau pairs on Mori fibre spaces, https://arxiv.org/abs/1808.03706
Gregorio Baldi, On a conjecture of Buium and Poonen, https://arxiv.org/abs/1803.04946
Fabio Bernasconi, Non-normal purely log terminal centres in characteristic p ≥ 3, https://arxiv.org/abs/1802.04896
Gregorio Baldi, On the geometric Mumford-Tate conjecture for subvarieties of Shimura varieties, https://arxiv.org/abs/1802.04682
Gregorio Baldi, Local to global principle for the moduli space of K3 surfaces, https://arxiv.org/abs/1802.02042
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