Mathematik Termine Mathematical Colloquium

Mathematical Colloquium

The Mathematical Colloquium of the HHU Düsseldorf takes place on selected
Fridays from 4.45 pm to 5.45 pm in Lecture Hall 25.22 HS 5H.

Before the Colloquium (from 4.15 pm) all are welcome to have tea, coffee and biscuits in room

Programme (Winter Semester 2023/24)

10.11.2023 Rebecca Waldecker (Halle) and Volker Remmert (Wuppertal)
(Special session with two speakers.)
Big Mathematics? The Classification of Finite Simple Groups, 1950s to 1980
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8.12.2023 Franziska Jahnke (Universiteit van Amsterdam).
Transfer theorems between fields of different characteristic - a model-theoretic approach
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How much does modular arithmetic (i.e., calculating modulo $p$) tell us about the integers and the rational numbers? Under which circumstances can we use insights about fields of positive characteristic (e.g., finite fields, function fields over finite fields, or power series fields over finite fields) to understand fields of characteristic 0 (and conversely)?
Classical methods to transfer results between fields of different characteristics are the Lefschetz principle and the Ax-Kochen/Ershov Theorem which states that asymptotically, the theory of the $p$-adic numbers $\mathbb{Q}_p$ and of power series fields $\mathbb{F}_p((t))$ coincide. Tilting perfectoid fields, a recent approach developed by Scholze, gives a transfer principle between certain henselian fields of mixed characteristic and their positive characteristic counterparts and vice versa. In this talk, we survey various transfer principles and present a model-theoretic approach to tilting via ultraproducts, which allows us to transfer many first-order properties between a perfectoid field and its tilt. A key ingredient in our approach is an Ax-Kochen/Ershov principle for perfectoid fields (and generalizations thereof). This is joint work with Konstantinos Kartas (Sorbonne Université).

12.1.2024 Gregor Gassner (Universität zu Köln).
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19.1.2024 Helmut Abels (Universität Regensburg).
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