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Past Seminars:
- Vladimir Dokchitser
Elliptic curves: parity phenomena
Tuesday 15th July 2025 - Radu Toma
Automorphic forms in cryptography
Wednesday 11th June 2025 - Jessica Alessandri
Integral solutions of a Fermat's near miss
Wednesday 28th May 2025 - Soumya Sankar
Local-global principles for generalized Fermat equations via stacks
Wednesday 21st May 2025 - Marta Pieropan
m-full zeroes of diagonal forms
Wednesday 14th May 2025 - Martin Azon
Effective Darmon's program for the generalised Fermat equation
Wednesday 7th May 2025 - Diego Izquierdo
Transfer principles for Galois cohomology and Serre's conjecture II
Wednesday 2nd April 2025 - Jef Laga
Vanishing criteria for Ceresa cycles
Wednesday 26th March 2025 - Martin Orr
Height bounds for very unlikely intersections in abelian varieties using G-functions
Wednesday 19th March 2025 - Thibaut Misme
Towards an automatized 2-descent on Jacobians of general curves.
Wednesday 12th March 2025 - Andrea Dotto
Gelfand--Kirillov dimension and mod p cohomology for quaternion algebras.
Wednesday 5th March 2025 - Sacha Mangerel
Analogues of the binary Goldbach problem for the Liouville function
Wednesday 26th February 2025 - Richard Griffon
A parallelogram inequality for abelian varieties over function fields.
Wednesday 19th February 2025 - Glenn Stevens
Modular Symbols with Values in Beilinson-Kato Distributions
Wednesday 12th February 2025 - Alec Shute
Local solubility of generalised Fermat equations
Wednesday 5th February 2025 - Lassina Dembele
Parametrising abelian surfaces with RM by Z[√2] using Richelot isogenies
Wednesday 29th January 2025 - Andrew Pearce-Crump
Number Theory versus Random Matrix Theory: the joint moments story
Wednesday 15th January 2025 - Kevin Kwan
Poisson and Reciprocity
Wednesday 4th December 2024 - Margherita Pagano
The wild Brauer-Manin obstruction.
Wednesday 27th November 2024 - Luis Garcia
The elliptic gamma function and Stark units
Wednesday 20th November 2024 - Sam Streeter
Semi-integral points on toric varieties
Wednesday 13th November 2024 - Jori Merikoski
Twisted correlations of the divisor function via discrete averages of SL(2,R) Poincaré series
Wednesday 6th November 2024 - Harry Spencer
Wild conductor exponents of curves
Wednesday 30th October 2024 - Maxim Gerspach
The third moment of the logarithm of the Riemann zeta function
Wednesday 23rd October 2024 - Eugenia Rosu
A higher degree Weierstrass function
Wednesday 16th October 2024 - John Cremona
On the equivalence of binary forms over a field
Wednesday 9th October 2024 - Raymond van Bommel
17T7 as a Galois group over Q through Hilbert modular forms
Wednesday 2nd October 2024 - Zeev Rudnick
Zeros of modular forms
Wednesday 4th September 2024 - Simon Rydin Myerson
Forms with real coefficients and differing degrees
Wednesday 12th June 2024 - Peter Koymans
Averages of class numbers
Wednesday 5th June 2024 - Matteo Bordignon
Weyl sums with multiplicative coefficients and joint equidistribution
Wednesday 22nd May 2024 - Jean-Louis Colliot-Thélène
On the arithmetic of intersections of two quadrics
Wednesday 8th May 2024 - Aleksander Horawa
The equivariant BSD conjecture via p-adic L-functions
Wednesday 1st May 2024 - Samir Siksek
Galois groups of low degree points on curves
Wednesday 24th April 2024 - Vivian Kuperberg
Consecutive sums of two squares in arithmetic progressions
Wednesday 17th April 2024 - Beth Romano
Generalizing the LLL algorithm
Wednesday 13th March 2024 - Mike Daas
A p-adic analogue of a formula by Gross and Zagier
Wednesday 6th March 2024 - Christian Wuthrich
The Mordell-Weil group as a Galois module
Wednesday 28th February 2024 - Damaris Schindler
Density of rational points near manifolds
Wednesday 21st February 2024 - Elisa Lorenzo-Garcia
On the conductor of Ciani plane quartics
Wednesday 14th February 2024 - Tim Browning
Sums of three cubes over a function field
Wednesday 7th February 2024 - Sam Frengley
Congruences and the geometry of Humbert surfaces
Wednesday 31st January 2024 - Oleksiy Klurman
Partition regularity of Pythagorean pairs
Wednesday 13th December 2023 - Jacques Benatar
Polynomials with multiplicative coefficients, and related questions.
Wednesday 6th December 2023 - Matthew Bisatt
Adventures in L-functions
Wednesday 29th November 2023 - Vladimir Dokchitser
Decomposing L-functions of curves
Wednesday 22nd November 2023 - Nicolas Billerey
On Darmon's program for the generalised Fermat equation of signature (r,r,p)
Wednesday 15th November 2023 - Stephanie Chan
Integral points in families of elliptic curves
Wednesday 8th November 2023 - Aled Walker
Correlations of multiplicative functions along Beatty sequences
Wednesday 1st November 2023 - Anna Medvedovsky
Counting congruences between modular forms in Atkin-Lehner eigenspaces
Wednesday 25th October 2023 - Efthymios Sofos
100% Hasse principle for Châtelet surfaces
Wednesday 18th October 2023 - Julian Demeio
Hilbert Property for Hilbert modular surfaces
Wednesday 11th October 2023 - Catherine Hsu
Explicit non-Gorenstein R=T via rank bounds
Wednesday 4th October 2023 - Mathilde Gerbelli Gauthier
Fourier Interpolation and the Weil Representation
Wednesday 27th September 2023 - Kevin Kwan
Some Aspects of Moments
Wednesday 14th June 2023 - Seoyoung Kim
Various results related to a conjecture of Nagao
Wednesday 31st May 2023 - Alex Torzewski
Lawrence-Venkatesh bounds for curves in families
Wednesday 17th May 2023 - Youngmin Lee
Newman's conjecture for the partition functions modulo composite numbers
Wednesday 3rd May 2023 - Julian Lyczak
Paucity of rational points on fibrations with multiple fibres
Wednesday 26th April 2023 - Vaidehee Thatte
Understanding the Defect via Ramification Theory
Wednesday 19th April 2023 - Tim Santens
Rational points of bounded height on toric stacks
Wednesday 22nd March 2023 - Adam Morgan
Hasse principle for Kummer varieties in the case of generic 2-torsion
Wednesday 15th March 2023 - Jonathan Bober
Integrals of Z-functions
Wednesday 8th March 2023 - Kyle Pratt
Half-isolated zeros and zero-density estimates
Wednesday 1st March 2023 - Jack Buttcane
The (Archimedean) Langlands spectral expansion and Kuznetsov formulas for GL(3)
Wednesday 22nd February 2023 - Rosa Winter
Weak weak approximation for del Pezzo surfaces of degree 2
Wednesday 15th February 2023 - Fredrik Strömberg
A reduction algorithm for Hilbert modular groups
Wednesday 8th February 2023 - Steve Lester
Spacing statistics for lattice points on circles
Wednesday 1st February 2023 - Abhishek Saha
Mass equidistribution for Siegel cusp forms of degree 2
Wednesday 14th December 2022 - Daniel Loughran
Rational points on diagonal conics
Wednesday 7th December 2022 - Tal Horesh
p-adic directions of primitive vectors
Wednesday 30th November 2022 - Alexander Smith
Simple abelian varieties over finite fields with extreme point counts
Wednesday 16th November 2022 - Valentijn Karemaker
The Gauss problem for central leaves
Wednesday 9th November 2022 - Lucile Devin
Extending the unconditional support in an Iwaniec--Luo--Sarnak family
Wednesday 2nd November 2022 - Fabio Ferri
On reduction steps for Leopoldt's conjecture
Wednesday 26th October 2022 - Ofir Gorodetsky
Smooth numbers and polynomials, and the Dickman function
Wednesday 19th October 2022 - Nikolaos Diamantis
Values of L-series associated with weakly holomorphic forms and of their derivatives
Wednesday 12th October 2022 - Rachel Newton
Distribution of genus numbers of abelian number fields
Wednesday 5th October 2022 - Joshua Drewitt
Applications of real-analytic modular forms
Wednesday 28th September 2022 - Tom Oliver
Murmurations of elliptic curves
Wednesday 15th June 2022 - Yukako Kezuka
Arithmetic of elliptic curves at the small primes
Wednesday 8th June 2022 - Vasudevan Srinivas
On finite presentation for the tame fundamental group
Wednesday 8th June 2022 - Richard Griffon
Isogenies of elliptic curves over function fields
Wednesday 1st June 2022 - Lola Thompson
Summing mu(n): an even faster elementary algorithm
Wednesday 25th May 2022 - Vandita Patel
Values of the Ramanujan tau-function
Wednesday 18th May 2022 - Kevin Hughes
Square function estimates for planar curves over local fields
Wednesday 11th May 2022 - Bartosz Naskręcki
Higher moments of elliptic curves
Wednesday 4th May 2022 - Henri Johnston
Computation of lattice isomorphisms and the integral matrix similarity problem
Wednesday 27th April 2022 - Cecília Salgado
Large Mordell-Weil rank jumps and the Hilbert Property
Wednesday 30th March 2022 - Jens Funke
Theta series and (singular) theta lifts
Wednesday 23rd March 2022 - Vlad Mitankin
Semi-integral points and quadrics
Wednesday 16th March 2022 - Ross Paterson
Average Ranks of Elliptic Curves After p-Extension
Wednesday 9th March 2022 - Dan Fretwell
Definite orthogonal modular forms: Computations, Excursions and Discoveries
Wednesday 2nd March 2022 - Gene Kopp
Wannabe modularity, the Shintani-Faddeev cocycle, and Stark units
Wednesday 23rd February 2022 - Daniel Fiorilli
Omega results for cubic field counts via the Katz-Sarnak philosophy
Wednesday 16th February 2022 - Masahiro Nakahara
Uniform potential density for rational points on algebraic groups and elliptic K3 surfaces
Wednesday 2nd February 2022 - Junxian Li
Hardy-Littlewood problems with almost primes
Wednesday 26th January 2022 - Alina Ostafe
Multiplicative and additive relations for values of rational functions and points on elliptic curves
Wednesday 8th December 2021 - Jolanta Marzec
Some evidence towards Resnikoff-Saldana conjecture
Wednesday 1st December 2021 - Alexandre de Faveri
Simple zeros of GL(2) L-functions
Wednesday 24th November 2021 - Gonzalo Tornaria
Quinary forms and paramodular forms
Wednesday 17th November 2021 - Assif Zaman
An approximate form of Artin's holomorphy conjecture and nonvanishing of Artin L-functions
Wednesday 10th November 2021 - Luis Garcia
Eisenstein cocycles and values of L-functions
Wednesday 3rd November 2021 - Samantha Fairchild
Analogs of the primitive Gauss circle problem
Wednesday 27th October 2021 - Youness Lamzouri
Zeros of linear combinations of L-functions near the critical line
Wednesday 20th October 2021 - Andrei Yafaev
Lower bounds for Galois orbits of special points and the Andre-Oort conjecture
Wednesday 13th October 2021 - Harry Smit
Characterizing number fields using L-series
Wednesday 6th October 2021 - Sam Streeter
Weak approximation for del Pezzo surfaces of low degree
Wednesday 29th September 2021 - Brad Rodgers
The distribution of random polynomials with multiplicative coefficients
Wednesday 2nd June 2021 - David Zywina
Modular curves and Serre's open image theorem
Wednesday 26th May 2021 - Naser Sardari
Higher Fourier interpolation on the plane
Wednesday 19th May 2021 - Seonhee Lim
Effective Hausdorff dimension of Bad sets
Wednesday 12th May 2021 - Claire Burrin
A sparse equidistribution problem for expanding horocycles on the modular surface
Wednesday 5th May 2021 - Fang-Ting Tu
A Whipple Formula Revisited
Wednesday 28th April 2021 - Laura Capuano
GCD results for certain divisibility sequences of polynomials and a conjecture of Silverman
Wednesday 21st April 2021 - Maki Nakasuji
Schur multiple zeta functions and their properties
Wednesday 24th March 2021 - John Voight
Counting elliptic curves with torsion, and a probabilistic local-global principle
Wednesday 17th March 2021 - YoungJu Choie
A generating functions of periods of modular forms
Wednesday 10th March 2021 - Mahesh Kakde
Brumer-Stark units
Wednesday 3rd March 2021 - Andrew Obus
Fun with Mac Lane valuations
Wednesday 24th February 2021 - Adam Morgan
4-ranks of class groups of biquadratic fields
Wednesday 17th February 2021 - Christina Roehrig
Siegel theta series for indefinite quadratic forms
Wednesday 10th February 2021 - Par Kurlberg
Distribution of lattice points on hyperbolic circles
Wednesday 3rd February 2021 - Daniel Gulotta
Vanishing theorems for Shimura varieties at unipotent level and Galois representations
Wednesday 27th January 2021 - Ayla Gafni
Asymptotics of Restricted Partition Functions - FRIDAY
Friday 22nd January 2021 - Chantal David
Moments and non-vanishing of cubic Dirichlet L-functions at s =1/2
Wednesday 16th December 2020 - Arul Shankar
The number of D_4-extensions of Q
Wednesday 9th December 2020 - Amanda Folsom
Eisenstein series, cotangent-zeta sums, knots, and quantum modular forms
Wednesday 2nd December 2020 - Ghaith Hiary
An Omega-result for S(t)
Wednesday 25th November 2020 - Heekyoung Hahn
Poles of triple tensor product L-fuctions involving monomial representations
Wednesday 18th November 2020 - Pedro Lemos
Residual Galois representations of elliptic curves with image in the normaliser of a non-split Cartan
Wednesday 11th November 2020 - Misha Rudnev
On convexity and sumsets
Wednesday 4th November 2020 - Matthew Young
The Weyl bound for Dirichlet L-functions
Wednesday 28th October 2020 - Sug Woo Shin
On GSpin(2n)-valued automorphic Galois representations
Wednesday 21st October 2020 - Lior Bary-Soroker
Random Polynomials, Probabilistic Galois Theory, and Finite Field Arithmetic
Wednesday 14th October 2020 - Gabriele Nebe
Automorphisms of extremal modular lattices
Wednesday 7th October 2020 - Vesselin Dimitrov
No shadowing bounds on Galois orbits in the complex plane
Wednesday 30th September 2020 - Danylo Radchenko
Fourier interpolation from zeros of the Riemann zeta function
Wednesday 23rd September 2020 - Dzmitry Badziahin
Diophantine approximation on the Veronese curve
Wednesday 16th September 2020 - Jennifer Balakrishnan
Quadratic Chabauty over number fields
Wednesday 17th June 2020 - Dmitrii Zhelezov
Logarithmic coordinate complexity and the few products-many sums phenomenon
Tuesday 16th June 2020 - Dave Platt
Numerical verification of the Riemann Hypothesis to 3•10^{12}
Wednesday 3rd June 2020 - Elisa Lorenzo García
Primes of bad reduction for genus 3 CM curves and their exponents on the discriminant (joint work with S. Ionica, P. Kilicer, K. Lauter, A. Manzateanu and C. Vincent)
Wednesday 27th May 2020 - Chan-Ho Kim
On the quantitative variation of congruence ideals of modular forms
Wednesday 20th May 2020 - Peter Humphries
Small Scale Equidistribution of Lattice Points on the Sphere
Wednesday 29th April 2020 - Brendan Murphy
Approximate subgroups in soluble linear groups over finite fields
Wednesday 22nd April 2020 - Netan Dogra
Higher heights and rational points on curves
Wednesday 4th March 2020 - Rosa Winter
Density of rational points on a family of del Pezzo surfaces of degree 1
Wednesday 26th February 2020 - Daniel Loughran
Probabilistic Arithmetic Geometry
Wednesday 19th February 2020 - Oleksiy Klurman
Small discrepancy sequences over Fq[x]
Wednesday 12th February 2020 - Steven Charlton
An explicit quadruple ratio
Wednesday 5th February 2020 - Diego Izquierdo
Homogeneous spaces, algebraic K-theory and cohomological dimension of fields
Wednesday 29th January 2020 - Nuno Freitas
A multi-Frey approach to the Darmon program for Fermat-type equations
Wednesday 22nd January 2020 - Céline Maistret
Arithmetic invariants and parity of ranks of abelian surfaces
Wednesday 18th December 2019 - Chloe Martindale
Non-interactive post quantum key exchange from isogeny graphs of elliptic curves
Wednesday 11th December 2019 - Alice Pozzi
The values of the Dedekind-Rademacher cocycle at RM multiplication points
Wednesday 11th December 2019 - Morten Risager
Arithmetic statistics of modular symbols
Wednesday 4th December 2019 - Joe Gunther
Slicing the stars: counting algebraic numbers
Wednesday 27th November 2019 - Valentina Di Proietto
A non-abelian algebraic criterion for good reduction of curves
Wednesday 20th November 2019 - Philippe Michel
Algebraic Twists of automorphic forms
Wednesday 13th November 2019 - Jaclyn Lang
The Hodge and Tate Conjectures for self-products of K3 surfaces with non-symplectic group actions
Wednesday 30th October 2019 - André Macedo
Explicit methods for the Hasse norm principle and applications
Wednesday 23rd October 2019 - Joni Teräväinen
Chowla's conjecture at almost all scales
Wednesday 16th October 2019 - Ellen Eischen
p-adic L-functions, with a view toward unitary groups
Wednesday 9th October 2019 - Haluk Şengün
A K-theoretic Selberg trace formula
Wednesday 2nd October 2019 - Sander Zwegers
Theta Series for Indefinite Quadratic Forms
Wednesday 12th June 2019 - Katherine Stange
An illustration in number theory: abelian sandpiles and Schmidt arrangements
Wednesday 5th June 2019 - Lejla Smajlovic
Spectral construction of non-holomorphic Eisenstein-type series, their Kronecker limit formula and applications
Wednesday 29th May 2019 - Junehyuk Jung
On the sparsity of positive-definite automorphic forms
Wednesday 22nd May 2019 - Tobias Berger
Paramodularity of abelian surfaces
Wednesday 15th May 2019 - Farrell Brumley
Concentration properties of theta lifts
Wednesday 1st May 2019 - Adam Harper
High moments of random multiplicative functions
Wednesday 3rd April 2019 - Jessica Fintzen
Representations of p-adic groups
Wednesday 27th March 2019 - Damaris Schindler
On prime values of binary quadratic forms with a thin variable
Wednesday 20th March 2019 - Jim Wright
Hensel's classical lemma – a variant
Wednesday 13th March 2019 - Holly Krieger
Uniform Manin-Mumford in genus 2
Wednesday 6th March 2019 - Roger Heath-Brown
Counting Rational Points on Conics
Wednesday 27th February 2019 - Jan Vonk
Singular moduli for real quadratic fields
Wednesday 20th February 2019 - Beth Romano
Arithmetic statistics via graded Lie algebras
Wednesday 13th February 2019 - Nicole Looper
Dynamical uniform boundedness and the abc-conjecture
Wednesday 6th February 2019 - Árpád Tóth
Modular cocycles and linking numbers
Wednesday 30th January 2019 - Zeev Rudnick
On Cilleruelo's conjecture for the least common multiple of polynomial sequences
Wednesday 23rd January 2019 - Paul Beirne
Knots, the colored Jones polynomial and stability
Wednesday 16th January 2019 - Carl Wang-Erickson
The rank of Mazur's Eisenstein ideal
Wednesday 12th December 2018 - Marc Masdeu
p-adic analytic constructions of algebraic points
Wednesday 5th December 2018 - Sarah Peluse
Bounds for sets lacking x, x+y, x+y^2
Wednesday 28th November 2018 - Andreas Strömbergsson
Rogers' mean value formula: some applications and extensions
Wednesday 21st November 2018 - Kathrin Maurischat
Phantom holomorphic projection
Wednesday 14th November 2018 - Winston Heap
Upper bounds for moments of the Riemann zeta function
Wednesday 7th November 2018 - Nils-Peter Skoruppa
The Macdonald identities and Jacobi forms of lattice index
Wednesday 31st October 2018 - Lola Thompson
Bounded gaps between primes and the length spectra of arithmetic hyperbolic 3-orbifolds
Wednesday 24th October 2018 - Kim Klinger-Logan
The Riemann Hypothesis, unbounded operators and a tie to physics
Wednesday 17th October 2018 - David Lowry-Duda
Half-integral weight modular forms are special too
Wednesday 10th October 2018 - Alexander Gamburd
Arithmetic and Dynamics on Markoff-Hurwitz Varieties
Monday 18th June 2018 - Piper Harron
Equidistribution of Shapes of Number Fields of degree 3, 4, and 5
Wednesday 13th June 2018 - Jeffrey Lagarias
Number Theory Problems Related to Toric Integer Orbits
Tuesday 12th June 2018 - Sean Prendiville
Partition regularity and non-linear Diophantine equations
Wednesday 30th May 2018 - Gergely Harcos
The prime geodesic theorem in square mean
Wednesday 23rd May 2018 - Laura Capuano
Unlikely intersections in families of abelian varieties
Wednesday 16th May 2018 - Cameron Franc
Bounded primes for hypergeometric series
Wednesday 9th May 2018 - Masha Vlasenko
Gamma functions, monodromy and Apéry constants
Wednesday 2nd May 2018 - Jack Thorne
Arithmetic statistics for odd genus 2 curves
Wednesday 25th April 2018 - Min Lee
Twist-minimal trace formulas and applications
Wednesday 18th April 2018 - Péter Pal Pach
On some Applications of Graph Theory to Number Theoretic Problems
Wednesday 21st March 2018 - Olivia Beckwith
Class numbers of imaginary quadratic fields
Wednesday 14th March 2018 - Ayla Gafni
Extremal primes of non-CM elliptic curves
Wednesday 7th March 2018 - Wojciech Gajda
Geometric families of Galois representations
Wednesday 7th March 2018 - Catherine Hsu
Higher Eisenstein Congruences
Wednesday 28th February 2018 - Lassina Dembele
Abelian varieties with everywhere good reduction over certain real quadratic fields
Wednesday 21st February 2018 - Haluk Sengun
Arithmetic Manifolds, Hecke operators and Diophantine Equations
Wednesday 14th February 2018 - Bartosz Naskrecki
Hypergeometric motives of low degrees
Wednesday 7th February 2018 - Fredrik Stromberg
Maass forms and spectral theory for noncongruence subgroups
Wednesday 31st January 2018 - James Maynard
Kloosterman sums and Siegel zeros
Wednesday 24th January 2018 - Titus Hilberdink
Matrices with multiplicative entries
Wednesday 17th January 2018 - Chloe Martindale
Isogeny graphs of abelian varieties and applications to the discrete logarithm problem
Wednesday 13th December 2017 - John Cremona
Elliptic Curves of prime power conductor over imaginary quadratic fields with class number one.
Wednesday 6th December 2017 - Valentin Blomer
Wednesday 29th November 2017 - Lejla Smajlovic
Modular Dedekind symbols associated to Fuchsian groups and higher-order Eisenstein series
Wednesday 22nd November 2017 - Tom Oliver
Cancellation of zeros between L-functions
Wednesday 15th November 2017 - Kevin Destagnol
The Manin-Peyre conjectures for an infinite family of projective hypersurfaces in higher dimension.
Wednesday 8th November 2017 - Oliver Roche-Newton
On the size of the set AA+A over the reals
Wednesday 1st November 2017 - Chris Skinner
Some recent results on the arithmetic of elliptic curves and modular forms.
Wednesday 25th October 2017 - Jeff Hoffstein
Digital signatures based on quadratic forms over the ring R=(Z/qZ)[x]/(x^N -1).
Wednesday 18th October 2017 - Andreea Mocanu
Eisenstein Series for Jacobi Forms of Lattice Index
Wednesday 11th October 2017 - Martin Bright
Failure of strong approximation on an affine cone
Wednesday 4th October 2017 - Julie Desjardins
Density of rational points on elliptic surfaces
Wednesday 26th April 2017
