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Autumn Semester 2026

Date / Time Speaker Title Location
24 August 2026
11:15-12:15 		Dr. Eric Ahlqvist
University of Stockholm
Details

Number Theory Seminar

Title Schur sigma-groups of type (3,3)
Speaker, Affiliation Dr. Eric Ahlqvist, University of Stockholm
Date, Time 24 August 2026, 11:15-12:15
Location HG G 43
Abstract Fix an odd prime $p$. For any imaginary quadratic field $K$, the Galois group $G_K$ of its maximal unramified pro-$p$-extension is a Schur $\sigma$-group. If the minimal number of generators of $G_K$ is at least two, then work of Golod–Shafarevich and many others implies that $G_K$ is infinite unless it has Zassenhaus type $(3,3)$, $(3,5)$, or $(3,7)$. In these three remaining cases, there is no characterization of the pairs $(K,p)$ for which $G_K$ is finite. In most cases when the Zassenhaus type is $(3,3)$, we already know that $G_K$ is $p$-adic analytic and should therefore be finite according to the Fontaine-Mazur conjecture. Regardless of that, it is an interesting problem to classify all Schur $\sigma$-groups of type $(3,3)$. In this talk, I will present recent and ongoing joint work with Richard Pink towards such a classification.
Schur sigma-groups of type (3,3)read_more
HG G 43
9 October 2026
14:15-15:15 		Prof. Dr. Johannes Sprang
Duisburg-Essen
Details

Number Theory Seminar

Title Bounded functions on the character variety for quadratic extensions
Speaker, Affiliation Prof. Dr. Johannes Sprang, Duisburg-Essen
Date, Time 9 October 2026, 14:15-15:15
Location HG G 43
Abstract For any finite extension L of the field of p-adic numbers, the character variety of Schneider and Teitelbaum parametrizes locally L-analytic characters. Such character varieties and their generalizations play an important role in locally analytic representation theory and in the construction of p-adic L-functions. Recently, the question of whether all bounded functions on the character variety come from p-adic measures has attracted a lot of attention. The goal of this talk is to provide a positive answer to this question for quadratic extensions of the field of p-adic numbers.
Bounded functions on the character variety for quadratic extensionsread_more
HG G 43
16 October 2026
14:15-15:15 		Dr. Romain Branchereau
MPIM, Bonn
Details

Number Theory Seminar

Title Theta lifts and modular symbols for SL_N
Speaker, Affiliation Dr. Romain Branchereau, MPIM, Bonn
Date, Time 16 October 2026, 14:15-15:15
Location HG G 43
Abstract In the 1980s, Kudla and Millson developed a general framework for constructing holomorphic modular forms whose Fourier coefficients are intersection numbers of cycles in locally symmetric spaces attached to orthogonal groups. I will present an analogous construction for the symmetric space of SL_N. If time permits, I will also discuss ongoing joint work with Marti Roset and Peter Xu relating this construction to the p-adic Kudla program of Darmon–Pozzi–Vonk.
Theta lifts and modular symbols for SL_Nread_more
HG G 43
23 October 2026
14:15-15:15 		Prof. Dr. Asbjørn Nordentoft
University of Copenhagen
Details

Number Theory Seminar

Title Around thin subgroups of Fuchsian groups
Speaker, Affiliation Prof. Dr. Asbjørn Nordentoft, University of Copenhagen
Date, Time 23 October 2026, 14:15-15:15
Location HG G 43
Abstract In a beautiful paper Duke, Imamoglu and Toth constructed for each (fundamental) closed geodesic on the modular curve a thin subgroup with boundary mapping to this geodesic. The construction relied on minus continued fractions. In this talk I will provide an alternative and more geometric construction and explain how it extends to more general cusped hyperbolic surfaces. This will show connections to more geometric topics such as Scott’s lifting theorem. This is joint work with Ser Peow Tan.
Around thin subgroups of Fuchsian groupsread_more
HG G 43
30 October 2026
Details

Number Theory Seminar

Title Arithmetica Transalpina
Speaker, Affiliation
Date, Time 30 October 2026,
Location
Arithmetica Transalpina
6 November 2026
14:15-15:15 		Dr. Eric Yen-Yo Chen
EPFL
Details

Number Theory Seminar

Title Langlands dual pairs of automorphic periods
Speaker, Affiliation Dr. Eric Yen-Yo Chen, EPFL
Date, Time 6 November 2026, 14:15-15:15
Location HG G 43
Abstract The relative Langlands program implicitly predicts that automorphic period formulae ought to come in Langlands dual pairs, in which the automorphic and spectral sides are exchanged. In recent work with Venkatesh and Cauchi—Gutierrez-Terradillos, we have successfully applied this philosophy to study several classical integral representations, whose duality statements required a generalization of Langlands' L-functions. After recalling the relevant aspects of this theory, we will survey known examples of dual pairs and examine the limits of our approach.
Langlands dual pairs of automorphic periodsread_more
HG G 43
13 November 2026
14:15-15:15 		Dr. Lennart Gehrmann
Universität Bielefeld
Details

Number Theory Seminar

Title Real quadratic singular moduli revisited
Speaker, Affiliation Dr. Lennart Gehrmann, Universität Bielefeld
Date, Time 13 November 2026, 14:15-15:15
Location HG G 43
Abstract Using the theory of rigid meromorphic cocycles for orthogonal groups, we give a new construction of Darmon and Vonk's p-adic singular moduli for real quadratic number fields. These p-adic numbers are conjectured to be algebraic and satisfy prime factorizations similar to the factorizations of differences of singular moduli. Mysteriously, they are only defined up to multiplication by units of certain orders in real quadratic number fields. Our new approach sheds some light on this ambiguity up to units. Moreover, it immediately implies the antisymmetry conjecture of Darmon and Vonk. This is joint work with Mike Daas, Håvard Damm-Johnsen and Sören Sprehe.
Real quadratic singular moduli revisitedread_more
HG G 43
20 November 2026
14:15-15:15 		Agostino Di Leo
University of Bonn
Details

Number Theory Seminar

Title A new approach to regulators
Speaker, Affiliation Agostino Di Leo, University of Bonn
Date, Time 20 November 2026, 14:15-15:15
Location HG G 43
Abstract Regulators are fundamental in number theory, appearing in formulas such as Dirichlet's unit theorem. In this talk I will focus on the p-adic analogue of this story. Then, following Beilinson and Gros' ideas of generalising p-adic regulators using Chern classes in some p-adic cohomology theories, I will present a new integral cohomology theory which specialises to the previous p-adic cohomology theories while being computable and integral.
A new approach to regulatorsread_more
HG G 43
27 November 2026
14:15-15:15 		Prof. Dr. David Loeffler
FernUni Schweiz
Details

Number Theory Seminar

Title Title TBA: David Loeffler
Speaker, Affiliation Prof. Dr. David Loeffler, FernUni Schweiz
Date, Time 27 November 2026, 14:15-15:15
Location HG G 43
Title TBA: David Loeffler
HG G 43
4 December 2026
Details

Number Theory Seminar

Title Swiss Number Theory Days
Speaker, Affiliation
Date, Time 4 December 2026,
Location
Swiss Number Theory Days
11 December 2026
14:15-15:15 		Prof. Dr. François Loeser
IMJ-PRG
Details

Number Theory Seminar

Title From Serre's mass formula to the Fundamental Lemma: the ubiquity of the orbifold volume formula
Speaker, Affiliation Prof. Dr. François Loeser, IMJ-PRG
Date, Time 11 December 2026, 14:15-15:15
Location HG G 43
Abstract At the end of the 70's, McKay observed that, given a finite group G acting on a variety V, one can in some cases express invariants of the quotient in terms of the action of G on V. Integration on the quotient has shown to be a powerful tool to understand this phenomenom, via the so called orbifold volume formula of Denef and Loeser. Yasuda later showed that this formula is better expressed in the language of Deligne-Mumford stacks. He also discovered that a p-adic version of the formula allows to recover Serre's mass formula for the number of totally ramified field extensions of fixed degree of finite extensions of the p-adics. More recently, Groechenig, Wyss and Ziegler haved used the orbifold volume formula to give a new proof of Ngô's Fundamental Lemma. In joint work with Forey and Wyss, we recently extended the formula beyond the Deligne-Mumford case (i.e. when the group G is no longer finite). As an application we obtain a formula for the (stringy) Hodge polynomial of the moduli space of semi-stable vector bundles of fixed rank and degree on a smooth projective curve. We plan to provide a gentle overview of these questions, focusing on some key examples.
From Serre's mass formula to the Fundamental Lemma: the ubiquity of the orbifold volume formularead_more
HG G 43

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