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Autumn Semester 2025

Date / Time Speaker Title Location
19 September 2025
14:15-15:15 		Prof. Dr. Adam Morgan
Cambridge
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Number Theory Seminar

Title On the Hasse principle for degree 4 del Pezzo surfaces
Speaker, Affiliation Prof. Dr. Adam Morgan, Cambridge
Date, Time 19 September 2025, 14:15-15:15
Location HG G 43
Abstract I will discuss recent work with Skorobogatov, and work in progress with Lyczak, establishing the Hasse principle for classes of degree 4 del Pezzo surfaces, conditional on finiteness of certain Tate--Shafarevich groups. Key to the method is the study of an auxiliary family of Kummer surfaces.
On the Hasse principle for degree 4 del Pezzo surfaces read_more
HG G 43
3 October 2025
14:15-15:15 		Prof. Dr. Emmanuel Kowalski
ETH Zurich, Switzerland
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Number Theory Seminar

Title Equidistribution and Wasserstein distance
Speaker, Affiliation Prof. Dr. Emmanuel Kowalski, ETH Zurich, Switzerland
Date, Time 3 October 2025, 14:15-15:15
Location HG G 43
Abstract (joint work with T. Untrau) The talk will explain how Wasserstein distances provide a natural and flexible way to quantify equidistribution theorems in number theory. As an illustration, we will present a quantitative version of Deligne's Equidistribution Theorem.
Equidistribution and Wasserstein distanceread_more
HG G 43
10 October 2025
14:15-15:15 		Prof. Dr. Sebastian Herrero
University of Santiago de Chile
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Number Theory Seminar

Title A Lyapunov exponent associated to modular functions
Speaker, Affiliation Prof. Dr. Sebastian Herrero, University of Santiago de Chile
Date, Time 10 October 2025, 14:15-15:15
Location HG G 43
Abstract We define and prove properties of a GL(2, Z)-invariant function, a Lyapunov exponent associated to the modular function j, generalizing a function defined by Spalding and Veselov in the case of the constant function 1. Our results were motivated by conjectures of Kaneko about the "values" of j at real quadratic irrationalities. This is joint work with Paloma Bengoechea and Özlem Imamoglu.
A Lyapunov exponent associated to modular functionsread_more
HG G 43
17 October 2025
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Number Theory Seminar

Title Arithmetica transalpina
Speaker, Affiliation
Date, Time 17 October 2025,
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 October 2025
14:15-15:15 		Dr. Amina Abdurrahman
IHÉS
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Number Theory Seminar

Title A cohomological formula for symplectic L-functions and applications
Speaker, Affiliation Dr. Amina Abdurrahman, IHÉS
Date, Time 24 October 2025, 14:15-15:15
Location HG G 43
Abstract I will present a topological perspective on the order of the Tate-Shafarevich group up to squares as an application of a formula established in previous joint work with A. Venkatesh which gives a cohomological expression for the central value of symplectic L-functions on curves. I will sketch ideas of the proofs, and in particular the analogous picture in topology that is crucial in the arithmetic proofs.
A cohomological formula for symplectic L-functions and applicationsread_more
HG G 43
31 October 2025
14:15-15:15 		Dr. Peter Jossen
King's College London
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Number Theory Seminar

Title Exponential integrals and period numbers
Speaker, Affiliation Dr. Peter Jossen, King's College London
Date, Time 31 October 2025, 14:15-15:15
Location HG G 43
Abstract Definite integrals where the integrand contains an exponential function are a common sight in mathematics and mathematical physics. In particular cases, the values of these integrals turn out to be expressible as definite integrals with an algebraic integrand, that means, they are classical periods. A very well known example for this is the identity $$\int_0^\infty t^{-1} \sin(t) dt = \pi/2 = \int_{-1}^1 \sqrt{1- t^2}dt.$$ Another example is given by moment integrals of Bessel functions, which turn out to be multiples of pi by an algebraic number in the simplest cases. In more elaborate cases however, the formulas for Bessel moments start to involve special values of L-functions, elliptic integrals and values of hypergeometric functions, all of which are classical periods associated with algebraic varieties defined over number fields. I will explain why it is no accident that Bessel moments, and indeed many other similar definite integrals produce period numbers, and which algebraic varieties they come from.
Exponential integrals and period numbersread_more
HG G 43
7 November 2025
14:15-15:15 		Prof. Dr. Stefan Wewers
Universität Ulm
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Number Theory Seminar

Title Semistable reduction of smooth quartics
Speaker, Affiliation Prof. Dr. Stefan Wewers, Universität Ulm
Date, Time 7 November 2025, 14:15-15:15
Location HG G 43
Abstract Let K be a local field with residue characteristic p>0 and X a smooth projective curve over K of genus g>=2. The general problem I want to address in this talk is the explicit computation of the semistable reduction of X. If the gonality n of X is strictly less than p, then there is a well-understood method using the theory of admissible reduction. Recently, a lot of effort has been spent on the case n=p, in particular n=p=2 (hyperelliptic curves with residue characteristic p=2). In my talk I will address the first case where n>p, namely smooth plane quartics (non-hyperelliptic curves of genus g=3) and residue characteristic p=2. This is joint work with Kletus Stern and Max Schwegele.
Semistable reduction of smooth quarticsread_more
HG G 43
14 November 2025
14:15-15:15 		Prof. Dr. Kęstutis Česnavičius
Sorbonne Université
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Number Theory Seminar

Title The Manin constant and the modular degree
Speaker, Affiliation Prof. Dr. Kęstutis Česnavičius, Sorbonne Université
Date, Time 14 November 2025, 14:15-15:15
Location HG G 43
Abstract The Manin constant c of an elliptic curve E over Q is the nonzero integer that scales the differential ω determined by the normalized newform f associated to E into the pullback of a Néron differential under a minimal parametrization \phi : X_0(N) ---> E. Manin conjectured that c = ±1 for optimal parametrizations. We show that in general c | deg(\phi), under a minor assumption at 2 and 3, which improves the status of the Manin conjecture for many E. Our core result that gives this divisibility is the containment ω ∈ H^0(X_0(N), Ω), which we establish by combining automorphic methods with techniques from arithmetic geometry (here the modular curve X_0(N) is considered over Z and Ω is its relative dualizing sheaf over Z). To overcome obstacles at 2 and 3, we analyze nondihedral supercuspidal representations of GL_2(Q_2) and exhibit new cases in which X_0(N) has rational singularities over Z. The talk is based on joint work with Abhishek Saha and Michalis Neururer.
The Manin constant and the modular degreeread_more
HG G 43
21 November 2025
14:15-15:15 		Prof. Dr. Pierre Charollois
Sorbonne Université
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Number Theory Seminar

Title On Eisenstein Jugendtraum for complex cubic fields
Speaker, Affiliation Prof. Dr. Pierre Charollois, Sorbonne Université
Date, Time 21 November 2025, 14:15-15:15
Location HG G 43
Abstract In the early 2000s Giovanni Felder and his collaborators began the group-theoretic study of the elliptic gamma function, a remarkable multivariable meromorphic q-series arising from mathematical physics. In particular they obtained a collection of modular functional equations under the group SL3(Z) which make it a higher-dimensional analogue of the Jacobi theta function. In this work, we unveil the significance that this function and its variants have in number theory. Our main thesis is that these functions play the role of modular units in extending the theory of complex multiplication to complex cubic fields. In other words we propose a conjectural solution to Hilbert’s 12th problem for complex cubic fields, following a line of research actually initiated by G. Eisenstein. We give substantial numerical evidence that support this conjecture, and relate it to the Stark conjecture by proving an analogue of the Kronecker limit formula in this cubic setting. If times permits, I will also mention ongoing generalizations to SLn(Z), n>3, as part of Pierre Morain's PhD work at Sorbonne Université. This is joint work with Nicolas Bergeron and Luis Garcia.
On Eisenstein Jugendtraum for complex cubic fieldsread_more
HG G 43
28 November 2025
14:15-15:15 		Dr. Rena Chu
University of Goettingen
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Number Theory Seminar

Title Short character sums evaluated at homogeneous polynomials
Speaker, Affiliation Dr. Rena Chu, University of Goettingen
Date, Time 28 November 2025, 14:15-15:15
Location
Abstract Let $p$ be a prime. Bounding short Dirichlet character sums is a classical problem in analytic number theory, and the celebrated work of Burgess provides nontrivial bounds for sums as short as $p^{1/4+\varepsilon}$ for all $\varepsilon>0$. In this talk, we will first survey known bounds in the original and generalized settings. Then we discuss the so-called ``Burgess method'' and present new results that rely on bounds on the multiplicative energy of certain sets in products of finite fields.
Short character sums evaluated at homogeneous polynomialsread_more
5 December 2025
Details

Number Theory Seminar

Title Swiss Number Theory Days 2025
Speaker, Affiliation
Date, Time 5 December 2025,
Location
Swiss Number Theory Days 2025
12 December 2025
14:15-15:15 		Dr. Noam Kimmel
University of Bonn
Details

Number Theory Seminar

Title Zeros of Poincaré series
Speaker, Affiliation Dr. Noam Kimmel, University of Bonn
Date, Time 12 December 2025, 14:15-15:15
Location
Abstract We explore the zeros of certain Poincaré series P(k,m) of weight k and index m for the full modular group. These are distinguished modular forms, which have played a key role in the analytic theory of modular forms. We study the zeros of P(k,m) when the weight k tends to infinity. The case where the index m is constant was considered by Rankin who showed that in this case almost all of the zeros lie on the unit arc |z|=1. In this talk we will explore the location of the zeros when the index m grows with the weight k, finding a range of different limit laws. Along the way, we also establish a version of Quantum Unique Ergodicity for some ranges.
Zeros of Poincaré seriesread_more

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