Organizers: Anders Södergren,
Christian Johansson.
12.02.2020 - Kevin Hughes (University of Bristol): Discrete restriction to the curve (x,x^3)
Abstract: In this talk I will motivate the problem of discrete restriction to the curve (x,x^3). This is one of the simplest cases outside the recently introduced and powerful machinery of decoupling and efficient congruencing. While the expected 10th decoupling inequality fails, we show that the nigh-optimal discrete restriction estimate holds. This is work with Trevor Wooley.
19.02.2020 - Nils Matthes (University of Oxford): Motivic periods
Abstract: A period is a complex number which can be written as the integral of an algebraic differential form over a semialgebraic set. This is a classical notion whose roots can be traced back at least to Euler and which conjecturally contains all special values of L-functions of algebraic varieties. Beginning in the 1960s it was realized that the study of periods may be viewed as part of Grothendieck's vision of motives which very recently lead to the notion of "motivic period". Although progress has been made, many fundamental questions about (motivic) periods remain.
26.02.2020 - Kirsti Biggs (Chalmers/GU): TBA
Abstract: TBA
04.03.2020 - Jasmin Matz (University of Copenhagen): TBA
Abstract: TBA
12.03.2020 - Jörg Brüdern (University of Göttingen): TBA
Abstract: TBA
18.03.2020 - Jakob Palmkvist (Chalmers/GU): TBA
Abstract: TBA
20.05.2020 - Valentijn Karemaker (Stockholm University/Utrecht University): TBA
Abstract: TBA
Past seminars
05.02.2020 - Pankaj Vishe (Durham University): Rational points on complete intersections over global fields
Abstract: The quantitative arithmetic of the set of rational points on a smooth complete intersection of two quadrics over the function field F_q(t) is obtained, under the assumption that q is odd and n≥9. The main ingredient here is the development of a Kloosterman refinement over global fields.
28.01.2020 - Jonas Bergström (Stockholm University): Traces of Hecke operators on spaces of Siegel modular forms modulo prime powers
Abstract: I will report on ongoing work, where I apply the Lefschetz fixed point theorem to local systems on the moduli space of abelian varieties of dimension at most 3, and use simple equalities in modular arithmetic, to study traces of Hecke operators on spaces of Siegel modular forms (of degree at most 3) modulo prime powers.
15.01.2020 - Dennis Eriksson (Chalmers/GU): Genus one mirror symmetry
Abstract: Mirror symmetry, in a crude formulation, is usually presented as a correspondence between curve counting on a Calabi--Yau variety X, and some invariants extracted from a mirror family of Calabi--Yau varieties. After the physicists Bershadsky--Cecotti--Ooguri--Vafa (henceforth BCOV), this is organised according to the genus of the curves in X we wish to enumerate, and gives rise to an infinite recurrence of differential equations. In this talk, I will give a general introduction to these problems, and present a rigorous mathematical formulation of the BCOV conjecture at genus one, in terms of a lifting of the Grothendieck--Riemann--Roch. I will explain a proof of the conjecture for Calabi--Yau hypersurfaces in projective space, based on the Riemann--Roch theorem in Arakelov geometry. Our results generalise from dimension 3 to arbitrary dimensions previous work of Fang--Lu--Yoshikawa.
This is joint work with G. Freixas and C. Mourougane.