# Seminars Calendar

**Friday May 3, 2024 - **Bruno Kahn (Institut de Mathématiques de Jussieu)

**TBA**

Abstract: TBA.

**Friday January 12, 2024 - 14:30 - 2AB40 - **Michel Waldschmidt (Institut de Mathématiques de Jussieu)

**Questions of transcendence related to periods of elliptical functions**

Abstract: TBA.

**Friday December 15, 2024 - 14:30 - 2AB40 - **Luca Terenzi

**TBA**

Abstract: TBA.

**Wednesday November 29, 2023 - 11:00 - 4DA2 - **Roberto Villaflor (Pontificia Universidad Católica de Chile)

**Periods of algebraic cycles and applications to Hodge loci**

Abstract: In this talk we will explain some methods for computing periods of algebraic cycles inside hypersurfaces of projective simplicial toric varieties, and show how this data can be used to study components of the Hodge loci. As one of the main ingredients we will introduce an Artinian Gorenstein ideal associated to each Hodge cycle. If time permits we will also discuss relations between this ideal and the (variational) Hodge conjecture.

**Tuesday November 21, 2023 - 11:00 - 4DA2 - **Jorge Duque (Universidad de Chile)

**Unveiling Fake Algebraic Cycles**

Abstract: In this talk, we will take a brief trip that will take us to fake linear cycles inside Fermat varieties. We will see some of their properties and why they are pathological. We will explore a systematic approach to obtain fake (non-linear) algebraic cycles in any dimension and degree inside non-Fermat hypersurfaces.

**Friday November 17, 2023 - 2BC30 - **Arithmetica Transalpina

**Speakers:**

- Özlem Imamoglu (ETH Zürich)

- Vincent Pilloni (Orsay)

- Alice Pozzi (Bristol)

- Joaquin Rodrigues (Marseille)

**Tuesday October 31, 2023 - 9:00 - 2AB45 - **Dino Festi (University of Padova)

**Black holes and unirationality**

Abstract: Physicists interested in high energy physics often encounter Feynman integrals presenting square roots in their argument. Exact solutions of these integrals are normally out of reach and so they are usually solved numerically. In order to achieve higher precision in the numeric evaluation, it is necessary to find a change of the variables of the integral that makes the square root disappear. Deciding the existence of such a change of variable is an algebraic problem that can be naturally translated into investigating the unirationality of a variety. The original problem can be generalized to sets of square roots and to algebraic extensions of function fields We will finally present a case coming from the study of two black holes, treated also using modularity results. The content of this talk is the fruit of a series of joint works with Marco Besier, Andreas Hochenegger, and Bert van Geemen.

**Friday October 27, 2023 - 14:30 - 2BC30 - **Yukako Kezuka (Institut de Mathématiques de Jussieu)

**On the L-values of families of quadratic twists of elliptic curves**

Abstract: For the elliptic curves E introduced by B. Gross, we show that the number of twists of E by quadratic extensions of discriminants up to X whose central L-value does not vanish satisfies >> X/log^{3/4}X. In particular, we obtain the finiteness of the Tate-Shafarevich groups for these curves.

**Friday October 13, 2023 - 14:00 - 2AB40 - **Federica Galluzzi (Università di Torino)

**Invariants of Brauer classes**

Abstract: The first part of the talk will be an introduction to Brauer groups. Then I will speak of Brauer groups of K3 surfaces and I will introduce some invariants of order two classes discussing examples related to cubic hypersurfaces in P^5 containing a plane. This is a joint work with Bert van Geemen.

**Monday September 25, 2023 - 11:00 - 2AB40 - **Masato Wakayama (Kyushu University)

**Number theory behind quantum interactions**

Abstract: We discuss number theoretic structure including e.g., modular forms, Eichler integrals, elliptic curves, “Apéry-like numbers”, behind certain quantum interaction models. These are arising from the special values of the spectral zeta functions via respective heat kernel/partition functions. Models where we treat are the (symmetric and asymmetric) quantum Rabi models and non-commutative harmonic oscillators. The former models are the most fundamental models in quantum optics and quantum information theory which describe the light-matter interaction. There is also an interesting connection between former and latter via the confluent process at their respective Heun ODE pictures. If the time allows, we will mention various number theoretic and geometric questions which are open

**Monday September 18, 2023 - 15:00 - 2AB40 - **Sophie Marques (Stellenbosch University)

**The Geometry of Moduli Spaces: Classification of Field Extensions up to Isomorphism (Joint with Jacob Ward, Mpendulo Cele, Elizabeth Merma, Chad Brache) **

Abstract: In this presentation, we focus on the classification of field extensions up to isomorphism, a task that requires the development of a robust classification system. The goal is to gain a better understanding of the structure of field extensions by studying associated families of polynomials. The analysis deepens by examining specific cases of cubic, quartic, and radical extensions, including those that may not necessarily be Galois extensions. Concepts such as radical closure and Artin-Schreier are introduced. Special attention is given to cyclotomic extensions in this context.

# Working Seminars

Condensed mathematics 2022

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