Departement Mathematik

Number theory seminar

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Frühjahrssemester 2024

Datum / Zeit Referent:in Titel Ort
23. Februar 2024
14:15-15:15 		Dr. Francesco Lemma
Université Paris Cité
Details

Number Theory Seminar

Titel Kato explicit reciprocity law for Siegel modular forms of weight 3,3
Referent:in, Affiliation Dr. Francesco Lemma, Université Paris Cité
Datum, Zeit 23. Februar 2024, 14:15-15:15
Ort HG G 43
Abstract In a series of papers, Loeffler-Zerbes and their collaborators constructed a non-zero Euler system for Siegel modular forms, providing the first evidence for the BSD conjecture for abelian surfaces of rank 0. I will present a proof of the non-triviality of the Euler system for the minimal cohomological weight by the generalized explicit reciprocity law for the critical twist, following Kato. This is a joint work with Tadashi Ochiai (Tokyo Institute of Technology).
Kato explicit reciprocity law for Siegel modular forms of weight 3,3read_more (ABGESAGT)
HG G 43
1. März 2024
14:15-15:15 		Dr. Yuan Liu
University of Illinois Urbana-Champaign
Details

Number Theory Seminar

Titel On the distribution of class groups — beyond Cohen-Lenstra and Gerth
Referent:in, Affiliation Dr. Yuan Liu, University of Illinois Urbana-Champaign
Datum, Zeit 1. März 2024, 14:15-15:15
Ort HG G 43
Abstract The Cohen-Lenstra heuristic studies the distribution of the p-part of the class group of quadratic number fields for odd prime p, and Gerth’s conjecture regards the distribution of the 2-part of the class group of quadratic fields. The main difference between these two conjectures is that while the (odd) p-part of class group behaves completely “randomly”, the 2-part of class group does not since the 2-torsion of the class group is controlled by the genus field. In this talk, we will discuss a new conjecture generalizing Cohen-Lenstra and Gerth’s conjectures. The techniques involve Galois cohomology and embedding problems of global fields. If time permits, we will also discuss how to prove a function field analog of this new conjecture, by counting points on the Hurwitz spaces.
On the distribution of class groups — beyond Cohen-Lenstra and Gerthread_more
HG G 43
8. März 2024
14:15-15:15 		Dr. Efthymios Sofos
University of Glasgow
Details

Number Theory Seminar

Titel Multiplicative functions and applications
Referent:in, Affiliation Dr. Efthymios Sofos, University of Glasgow
Datum, Zeit 8. März 2024, 14:15-15:15
Ort HG G 43
Abstract I will discuss some new results on averages of multiplicative functions over integer sequences from arXiv:2402.08710. We will then give applications to Cohen-Lenstra and Manin's conjecture. Joint work with Chan, Koymans and Pagano.
Multiplicative functions and applicationsread_more
HG G 43
15. März 2024
14:15-15:15 		Dr. Rosa Winter
King's College London
Details

Number Theory Seminar

Titel Weak weak approximation for del Pezzo surfaces of degree 2
Referent:in, Affiliation Dr. Rosa Winter, King's College London
Datum, Zeit 15. März 2024, 14:15-15:15
Ort HG G 43
Abstract Del Pezzo surfaces are classified by their degree d, and integer between 1and 9. The lower the degree, the more arithmetically complex these surfaces are. It is generally believed that, if a del Pezzo surface has one rational point, then it has many, and that they are well-distributed. After giving an overview of different notions of ‘many’ rational points and what is known so far for del Pezzo surfaces, I will focus on joint work with Julian Demeio and Sam Streeter where we prove weak weak approximation for del Pezzo surfaces of degree 2 with a general point.
Weak weak approximation for del Pezzo surfaces of degree 2read_more
HG G 43
29. März 2024
Details

Number Theory Seminar

Titel Easter break - no seminar
Referent:in, Affiliation
Datum, Zeit 29. März 2024,
Ort
Easter break - no seminar
5. April 2024
Details

Number Theory Seminar

Titel Easter break - no seminar
Referent:in, Affiliation
Datum, Zeit 5. April 2024,
Ort
Easter break - no seminar
12. April 2024
14:15-15:15 		Ingmar Metzler
Technische Universität Darmstadt
Details

Number Theory Seminar

Titel Theta lifts, special cycles and Rankin–Selberg convolutions
Referent:in, Affiliation Ingmar Metzler, Technische Universität Darmstadt
Datum, Zeit 12. April 2024, 14:15-15:15
Ort HG G 43
Abstract Theta lifts have long been known for constructing examples of automorphic forms in different settings. The Borcherds lift, for instance, gives rise to remarkable product expansions in the orthogonal context and allows to derive relations for special divisors. It is closely related to the Kudla–Millson lift and both have played a significant role in studying special divisors of Shimura varieties of orthogonal type. These lifts were related to each other by Bruinier and Funke who also proved surjectivity/injectivity in several cases. We present an approach to generalise these results, involving cycle integrals and Hecke theory, and discuss two new results, one of which was proven in collaboration with Riccardo Zuffetti.
Theta lifts, special cycles and Rankin–Selberg convolutionsread_more
HG G 43
19. April 2024
14:15-15:15 		Prof. Dr. Mladen Dimitrov
Université de Lille
Details

Number Theory Seminar

Titel On the Geometry of the Eigencurve
Referent:in, Affiliation Prof. Dr. Mladen Dimitrov, Université de Lille
Datum, Zeit 19. April 2024, 14:15-15:15
Ort HG G 43
Abstract We will give an overview of the local geometry of the Coleman-Mazur eigencurve at classical points. If time permits we will explain possible generalizations in higher dimension, namely in the Hilbert modular setting.
On the Geometry of the Eigencurveread_more
HG G 43
26. April 2024
14:15-15:15 		Dr. Julian Demeio
University of Bath
Details

Number Theory Seminar

Titel The Grunwald Problem for solvable groups
Referent:in, Affiliation Dr. Julian Demeio, University of Bath
Datum, Zeit 26. April 2024, 14:15-15:15
Ort HG G 43
Abstract Let $K$ be a number field. The Grunwald problem for a finite group (scheme) G/K asks what is the closure of the image of $H^1(K,G) \to \prod_{v \in M_K} H^1(K_v,G)$. For a general $G$, there is a Brauer—Manin obstruction to the problem, and this is conjectured to be the only one. In 2017, Harpaz and Wittenberg introduced a technique that managed to give a positive answer (BMO is the only one) for supersolvable groups. I will present a new fibration theorem over quasi-trivial tori that, combined with the approach of Harpaz and Wittenberg, gives a positive answer for all solvable groups. Partial results were also obtained independently by Harpaz and Wittenberg.
The Grunwald Problem for solvable groupsread_more
HG G 43
10. Mai 2024
Details

Number Theory Seminar

Titel Auffahrt - no seminar
Referent:in, Affiliation
Datum, Zeit 10. Mai 2024,
Ort
Auffahrt - no seminar
17. Mai 2024
Details

Number Theory Seminar

Titel Arithmetica Transalpina
Referent:in, Affiliation
Datum, Zeit 17. Mai 2024,
Ort UniDistance Suisse, Schinerstrasse 18, 3900 Brig
Mehr Informationen https://people.math.ethz.ch/~zerbess/ArithmeticaTransalpina.html
Arithmetica Transalpinaread_more
UniDistance Suisse, Schinerstrasse 18, 3900 Brig
24. Mai 2024
14:15-15:15 		Prof. Dr. Otmar Venjakob
Universität Heidelberg
Details

Number Theory Seminar

Titel Explicit Reciprocity Laws in Number Theory
Referent:in, Affiliation Prof. Dr. Otmar Venjakob, Universität Heidelberg
Datum, Zeit 24. Mai 2024, 14:15-15:15
Ort HG G 43
Abstract The quadratic Reciprocity Law for the Legendre or Jacobi-Symbol forms the starting point of all Reciprocity Laws as well as of class field theory. It is closely related to the product formula of the quadratic Hilbert-Symbol over local fields. Various mathematicians have established higher explicit formulae to compute higher Hilbert-Symbols. Analogs were found for formal (Lubin-Tate) groups. Eventually Perrin-Riou has formulated a Reciprocity Law, which allows the explicit computation of local cup product pairings by means of Iwasawa- and p-adic Hodge Theory. In this talk I shall try to give an overview of these topics, at the end I will explain recent developments in this regard.
Explicit Reciprocity Laws in Number Theoryread_more
HG G 43

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