James Wright (University of Edingburgh, Schottland): "Recent progress in pointwise ergodic theory"

We survey recent results establishing pointwise almost everywhere convergence of ergodic averages. We will make connections between these developments and advances in quantitative bounds for polynomial progressions in dense sets of integers.

Michael Alexis (MI) "Calculus teachers hate him because of this one weird trick, find out why!!"

I’ll present the concept of dyadic decomposition, a simple but stupidly effective technique for quickly estimating various sums and integrals, all without computing a single anti-derivative. We’ll discuss topics ranging from the p-test in Calculus to the Calderon-Zygmund decomposition for estimating averaging operators and the Hardy-Littlewood maximal function.

Mario Ohlberger (University of Münster, Germany): "Reduced Order Surrogate Models for PDE-Constrained Optimization and Inverse Problems"

Classically, model order reduction for parameterized systems is based on a so-called offline phase, where reduced approximation spaces are constructed and the reduced parameterized
system is built, followed by an online phase, where the reduced system can be cheaply evaluated in a multi-query context. In this contribution, instead, we follow an active learning or
enrichment approach where a multi-fidelity hierarchy of reduced order models is constructed on-the-fly while exploring a parameterized system. To this end we focus on learning based
reduction methods in the context of PDE constrained optimization and inverse problems and evaluate their overall efficiency. We discuss learning strategies, such as adaptive enrichment
within a trust region optimization framework as well as a combination of reduced order models with machine learning approaches. Concepts of rigorous certification and convergence will be
presented, as well as numerical experiments that demonstrate the efficiency of the proposed approaches.

María Inés de Frutos Fernández (MI) "What is... mathematical formalization"

Mathematical formalization is the process of digitizing mathematical definitions and results using a "proof assistant" (e.g. Lean), that is, a computer program capable of checking logical statements against a set of inference rules and some basic axioms. In recent years, the community of mathematicians working on formalization has grown rapidly and has reached milestones that demonstrate the ability to formalize results at the frontier of knowledge. In this talk, I will give an introduction to formalization, survey recent formalization projects, and discuss applications to mathematical research, teaching, and communication. No previous knowledge in this area will be assumed.

Bjorn Poonen (MIT, USA): "Cohomological obstructions to rational points"

It is almost a true statement that the only known way to prove that a variety over a number field has no rational point is to exhibit a cohomological obstruction. I will briefly survey a few things that are known about the Brauer-Manin obstruction, the descent obstruction, and related obstructions.

David Aretz (MPIM): "A Brief History of Going in Circles: From Belts to Bott"

This talk explains why rotating yourself twice is more mathematically respectable than rotating once, why vector bundles repeat every 8 dimensions like a bad sitcom plot, and what all of this has to do with electrons being antisocial. There will be K -theory, Bott periodicity, and a belt. It will all make sense in the end. Probably.

Helge Holden (NTNU, Norway): What are the compact sets in Lebesgue spaces?

Compactness in Lebesgue spaces is fully characterized by the classical Kolomogorov–Riesz theorem.
We present how this theorem and the classical Arzelà–Ascoli theorem can be derived from a very elementary
lemma. Furthermore, we show that one of the conditions of the Kolomogorov–Riesz theorem is redundant. 
Finally, we discuss how we can derive the Aubin–Lions–Dubinskii theorem on compactness in Bochner spaces in this setting.

Annabell Gros (IAM): "Extrema of branching Brownian motion"

Branching Brownian motion is a classical model from probability theory that describes the random motion and branching of particles over time. In this talk, we give an introduction to the study of its extreme values. We explore the connection to a particular PDE (the F-KPP equation), discuss the maxima of random variables, and encounter several biologically motivated models. Basic knowledge of probability theory is sufficient to follow the talk.

Speaker TBA: "TBA"

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Eva-Maria Hekkelman (MPIM): "TBA"

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