Abstracts

1. Model theory and Brunn-Minkowski inequalities - Assist. Prof.Trần Chiêu Minh, National University of Singapore 

Abstract: Model theory is a subfield of mathematical logic arising from efforts to understand when a structure admits a relatively simple axiomatization in various senses. These questions led logician to import ideas from algebraic geometry and in turn develop more flexible geometries which are applicable in many contexts.
In this talk, I would like to explain how the topic came about, and how ideas from model theory help us to generalize Brunn-Minkowski inequalities to nonabelian locally compact groups.

2. VF-convolution - Assoc. Prof. Lê Quý Thường, VNU University of Science 

Abstract: We define convolution products on the Grothendieck ring KVF* of proper invariant VF-definable sets and on the Grothendieck ring KRV* of doubly bounded RV-definable sets. The latter one induces convolution products on a certain quotient KRV*/I and on !KRES. In Fichou-Yin’s work (2022), improving Hrushovski-Loeser’s work (2015), there is a natural ring homomorphism from KVF* to the monodromic Grothendieck ring of complex algebraic varieties which factors through KRV*/I and !KRES. We prove that all three morphisms in the composition are compatible with the convolution products.

3. Transfer principle - Dr. Đỗ Việt Cường, VNU University of Science 

Abstract: Transfer principles in model theory are results that transfer theorems from one field to another. In this talk we will focus on a result that transfers theorem about identities of p-adic integrals from one collection of fields to others and its application to various fundamental lemmas.

4. Non-Archimedean seminorms - Dr. Cristhian Emmanuel Garay Lopez, Centro de Investigación en Matemáticas, Mexico

Abstract: The concept of Krull valuation is very useful in many areas of mathematics, such as algebra, order theory, singularity theory, non-Archimedean geometry and non-Archimedean analysis.
Non-Archimedean seminorms are a generalization of Krull valuations that appeared naturally in applications from tropical algebraic and non-Archimedean geometry.
In this talk we will introduce the necessary background to define them, and we will give some concrete applications of non-Archimedean seminorms which are not Krull valuations.