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Spring Semester 2024

Date / Time Speaker Title Location
23 February 2024
14:15-15:15 		Dr. Francesco Lemma
Université Paris Cité
Details

Number Theory Seminar

Title Kato explicit reciprocity law for Siegel modular forms of weight 3,3
Speaker, Affiliation Dr. Francesco Lemma, Université Paris Cité
Date, Time 23 February 2024, 14:15-15:15
Location 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 (CANCELLED)
HG G 43
1 March 2024
14:15-15:15 		Dr. Yuan Liu
University of Illinois Urbana-Champaign
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Number Theory Seminar

Title On the distribution of class groups — beyond Cohen-Lenstra and Gerth
Speaker, Affiliation Dr. Yuan Liu, University of Illinois Urbana-Champaign
Date, Time 1 March 2024, 14:15-15:15
Location 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 March 2024
14:15-15:15 		Dr. Efthymios Sofos
University of Glasgow
Details

Number Theory Seminar

Title Multiplicative functions and applications
Speaker, Affiliation Dr. Efthymios Sofos, University of Glasgow
Date, Time 8 March 2024, 14:15-15:15
Location 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 March 2024
14:15-15:15 		Dr. Rosa Winter
King's College London
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Number Theory Seminar

Title Weak weak approximation for del Pezzo surfaces of degree 2
Speaker, Affiliation Dr. Rosa Winter, King's College London
Date, Time 15 March 2024, 14:15-15:15
Location 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 March 2024
Details

Number Theory Seminar

Title Easter break - no seminar
Speaker, Affiliation
Date, Time 29 March 2024,
Location
Easter break - no seminar
5 April 2024
Details

Number Theory Seminar

Title Easter break - no seminar
Speaker, Affiliation
Date, Time 5 April 2024,
Location
Easter break - no seminar
12 April 2024
14:15-15:15 		Ingmar Metzler
Technische Universität Darmstadt
Details

Number Theory Seminar

Title Theta lifts, special cycles and Rankin–Selberg convolutions
Speaker, Affiliation Ingmar Metzler, Technische Universität Darmstadt
Date, Time 12 April 2024, 14:15-15:15
Location 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

Title On the Geometry of the Eigencurve
Speaker, Affiliation Prof. Dr. Mladen Dimitrov, Université de Lille
Date, Time 19 April 2024, 14:15-15:15
Location 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

Title The Grunwald Problem for solvable groups
Speaker, Affiliation Dr. Julian Demeio, University of Bath
Date, Time 26 April 2024, 14:15-15:15
Location 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 May 2024
Details

Number Theory Seminar

Title Auffahrt - no seminar
Speaker, Affiliation
Date, Time 10 May 2024,
Location
Auffahrt - no seminar
17 May 2024
Details

Number Theory Seminar

Title Arithmetica Transalpina
Speaker, Affiliation
Date, Time 17 May 2024,
Location UniDistance Suisse, Schinerstrasse 18, 3900 Brig
More information https://people.math.ethz.ch/~zerbess/ArithmeticaTransalpina.html
Arithmetica Transalpinaread_more
UniDistance Suisse, Schinerstrasse 18, 3900 Brig
24 May 2024
14:15-15:15 		Prof. Dr. Otmar Venjakob
Universität Heidelberg
Details

Number Theory Seminar

Title Explicit Reciprocity Laws in Number Theory
Speaker, Affiliation Prof. Dr. Otmar Venjakob, Universität Heidelberg
Date, Time 24 May 2024, 14:15-15:15
Location 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

Archive: AS 24 SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 SS 21 AS 20 SS 20 AS 19 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11 SS 11 AS 10 SS 10 AS 09

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