2018-19
Unless otherwise specified, the seminars are held on Mondays at 15:00 in Room B3.03 – Mathematics Institute
2018-19 Term 2
Organiser: Martin Orr
7 January | No seminar |
14 January | No seminar |
21 January |
Kevin Hughes (University of Bristol) Discrete restriction theory We will introduce “discrete restriction theory” and it’s applications in number theory and analysis. We will then discuss Trevor Wooley’s efficient congruencing method and a prove “discrete decoupling” result for the parabola. If time permits I will discuss new bounds for discrete restriction to the curve (x,x^3). This is an example which presently lies beyond the scope of efficient congruencing/decoupling. This is joint work with Trevor Wooley. |
28 January |
Johannes Sprang (Universität Regensburg) Eisenstein–Kronecker series via the Poincaré bundle A classical construction of Katz gives a purely algebraic construction of real-analytic Eisenstein series using the Gauss–Manin connection on the universal elliptic curve. This has many applications in number theory. We provide an alternative algebraic construction of Eisenstein–Kronecker series via the Poincaré bundle. This construction allows a new interpretation of Katz’ p-adic Eisenstein measure in terms of p-adic theta functions. If time permits, we will discuss applications to the study of the elliptic polylogarithm for families of elliptic curves. |
4 February |
Jack Shotton (Durham University) Shimura curves and Ihara's lemma Ihara's lemma is a statement about the structure of the mod l cohomology of modular curves that was the key ingredient in Ribet's results on level raising. I will motivate and explain its statement, and then describe joint work with Jeffrey Manning on its extension to Shimura curves. |
11 February |
TBA |
18 February |
Ariel Pacetti (Universidad de Cordoba) |
25 February |
TBA |
4 March |
Catherine Hsu (University of Bristol) |
11 March |
Francesca Bianchi (University of Oxford) |
2018-19 Term 1
Organiser: David Lowry-Duda
8 October |
Samir Siksek (University of Warwick) |
15 October |
Ariel Weiss (University of Sheffield) Irreducibility of Galois representations associated to low weight Siegel modular forms |
22 October |
Kim Logan (University if Minnesota) Zeros of $L$-functions and unbounded operators |
29 October |
Martin Orr (University of Warwick) Unlikely intersections and E x CM abelian surfaces |
5 November |
Olivia Beckwith (University of Bristol) Indivisibility and divisibility of class numbers of imaginary quadratic fields |
12 November |
Thomas Bloom (Cambridge University) Diophantine approximation, GCD sums, and the sum-product phenomenon |
19 November |
Alain Kraus (Université Pierre-et-Marie-Curie - Paris VI) Asymptotic Fermat's Last Theorem and cyclotomic Z_2-extensions |
26 November |
Kwok-Wing Tsoi (King's College) On higher special elements of p-adic representations |
3 December |
Nuno Freitas (University of Warwick) The modular method, Frey abelian varieties and Fermat-type equations |
7 December (Friday) |
Minhyong Kim (Oxford) Diophantine geometry and principal bundles |