Conferences  >  Mathematics  >  Courses and Events for Math Students and Early Career Researchers  >  Germany

Hausdorff Research Institute for Mathematics (HIM)

The goal of this program is to bring together experts of Formal Mathematics, exploit their interactions, foster future collaborations, and interface them better with the mathematical mainstream. At the same time the goal is to provide a platform for junior researchers to enter Formal Mathematics. A central, unifying theme is to break down adoption barriers of formal methods in Mathematics.

Mathematical Logic and Foundations,    Automated Theorem Proving

Hausdorff Research Institute for Mathematics (HIM)

SFB 1085 Higher Invariants at the Faculty of Mathematics at the Universität Regensburg

Analysis,    Algebra

Hausdorff Research Institute for Mathematics (HIM)

Because of the ubiquity of Fourier analysis, oscillatory integrals are present in many techniques in both harmonic analysis and analytic number theory. Current state-of-the-art methods in both fields are pushing beyond classical methods because of increased importance of understanding the uniformity and stability of the estimates. In addition, researchers are uncovering unifying ideas that span the (traditionally somewhat separated areas) of oscillatory integrals in the setting of analysis, and character sums in number theory. Recent work on estimating oscillatory integrals have even applied model theory, from logic. This summer school will give participants an introduction on the classical methods for estimating oscillatory integrals and explain current cutting-edge developments. Throughout, the lectures will view these problems through a lens of understanding the uniformity and stability of the estimates.

Analysis,    Calculus, Differential Equations and Integration

Hausdorff Research Institute for Mathematics (HIM)

This summer school will give participants an introduction to contemporary methods for studying maximal operators, with a particular focus on using maximal operators as a tool to understand other phenomena in analysis.

Hausdorff Research Institute for Mathematics (HIM)

Hausdorff Research Institute for Mathematics (HIM)

Many physical processes in materials science or geophysics are characterised by inherently complex interactions on a multitude of inseparable scales in space and time. The resolution of all features on all scales in a computer simulation easily exceeds today's computing resources. Observation and prediction of physical phenomena therefore requires insightful computational multi-scale models and methods for adaptive selection of relevant scales and effective representation of unresolved scales. This workshop will discuss the latest algorithms and models for this purpose, as well as the mathematics behind them, which enable reliable and efficient numerical simulation of challenging multiscale problems in modern high-performance computing environments.

Follow-Up Workshop to TP "Multiscale Problems: Algorithms, Numerical Analysis and Computation"

Hausdorff Research Institute for Mathematics (HIM)

Disordered systems emerge from physical models by incorporating additional random effects. They also appear as models for complex systems in various contexts, such as computer science or biology. Understanding these models rigorously has been a great challenge for several decades, but the mathematical research in disordered systems and related fields has seen tremendous progress in recent years and benefits from a fruitful interplay of techniques from probability theory, mathematical analysis, combinatorics and mathematical physics. The aim of the school is to present to PhD students and young researchers some of the most fascinating developments in disordered systems and related fields in recent years.

Systems theory, Control and Automation,    Complex Systems, Chaos and Self-Organisation

Hausdorff Research Institute for Mathematics (HIM)

The trimester program aims to bring together experts, postdocs, and students in computer science and certain areas in mathematics (analysis, probability, and combinatorics) in order to learn about some challenging open problems recently raised in computer science, to use and invent necessary new tools and techniques in mathematics to solve these challenging problems, and vice versa to learn and further extend methods developed in computer science to develop new directions in mathematics motivated by questions in computer science. The core topics of the trimester program would be: learning theory, complexity of classical and quantum algorithms, vector valued functions on the hypercube, complex Hypercontractivity, polynomial inequalities on the hypercube, and discrete approximation theory on the hamming cube.

Analysis,    Information Theory, Foundations of Computer Science

Hausdorff Research Institute for Mathematics (HIM)

The “classical” way of learning (Boolean) functions comes from very sophisticated extensions of theorems of Kahn—Kalai—Linial type. In those results the interplay between maximal influence and heavy Fourier tails is the main technique. Maximal influence should be large if the `tail’ is small. However, recently another approach that is hinged on Bohnenblust—Hille inequality appeared. The school will cover the classical maximal influence approach to `probably approximately correct' (PAC) learning as well as the recent achievements using Bohnenblust—Hille inequality and its quantum counterpart.

SFB 1085 Higher Invariants at the Faculty of Mathematics at the Universität Regensburg

Algebra,    Analysis