Speaker: Charlotte Bartnick (Univ. Freiburg)
Time: 10:50-11:40
Location: Hörsaal 114, Kollegienhaus

Title: Differentially closed fields of positive characteristic

Abstact: Differentially closed fields are the differential equivalent to algebraically closed fields. They provide a setting for model theorists to study differential algebraic questions.

In this talk, we will introduce the properties of differentially closed fields in positive characteristic from a model theoretic point of view. In particular, we will describe definable groups. No prior model theoretic knowledge is required.

Speaker: Seoyoung Kim (Univ. Basel)
Time: 13:50-14:40
Location: Hörsaal 114, Kollegienhaus

Title: An application of Stepanov's method and its implication on multiplicative Sarkozy's conjecture

Abstract: We investigate the multiplicative structure of a shifted multiplicative subgroup and its connections with additive combinatorics and the theory of Diophantine equations. We show that if a nontrivial shift of a multiplicative subgroup G contains a product set AB, then the size of the set |A||B| is essentially bounded by |G|, refining a well-known consequence of a classical result by Vinogradov, and a recent result of Hanson-Petridis based on Stepanov’s method. Using this, we make progress towards a conjecture of Sarkozy on the multiplicative decompositions of shifted multiplicative subgroups. In particular, we prove that for almost all primes p, the set {x^2-1: x in F_p*} \{0} cannot be decomposed as the product of two sets in F_p non-trivially. If time permits, we discuss recent progress on Sarkozy’s conjecture and the Lev-Sonn conjecture. This is a joint work with K. Yip and S. Yoo.

Speaker: Kenza Memlouk (Univ. Strasbourg)
Time: 15:10-16:00
Location: Hörsaal 114, Kollegienhaus

Title: Multiple zeta values and quiver representations

Abstract: In this talk, we are interested in multiple zeta values. They are periods associated to the category MTM(Z) of mixed Tate motives over the ring of integers. Recently, A.Huber and M.Kalck have shown that some subcategories of MTM(Z) are equivalent to representations of some quivers. We will see the implications of this result on motivic multiple zeta values. More precisely, we will compare this point of view with a construction of Goncharov and we will explore this new perspective on formal multiple zeta values.

More information on the website:

https://rhine-transcendence.github.io/meeting8