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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.

Kurse und Veranstaltungen für Studenten der Mathematik,    Infinitesimalrechnung, Differentialgleichungen, Integralrechnung

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.

Dynamics Days Europe is a series of major international conferences founded in the 1980’s that provides a European forum for developments in the theory and applications of dynamics. For more than 40 years, it has been bringing together researchers from a wide range of backgrounds including physics, mathematics, biology, and engineering for interdisciplinary research in nonlinear science.

Ergodic theory, topological and homogeneous dynamics Network dynamics Machine Learning Bifurcation theory Dynamics and geometry Nonlinear waves Fluids and turbulence Computational methods Medical and neuro-dynamics Quantum Chaos Multibody dynamics

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.

Kurse und Veranstaltungen für Studenten der Mathematik,    Informationstheorie und Grundlagen der Informatik

The Hausdorff Research Institute for Mathematics (HIM)

The interaction between learning theory and harmonic analysis was emphasized by mathematics of quantum computing. One of the outstanding open problems in this area concerns the sharp estimates in Bohnenblust-Hille inequality that generalizes a celebrated Littlewood’s lemma. How to learn (with small error and with large probability) a complicated function or a very large matrix in a relatively small number of random (quantum) queries? Of course, there should be some Fourier type restrictions on a function (a matrix) to have a reasonable answer to this. 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.

Neuronale Netze und Künstliche Intelligenz, Maschinelles Lernen,    Kurse und Veranstaltungen für Studenten der Mathematik

The Hausdorff Research Institute for Mathematics (HIM)

This workshop aims at bringing together young and talented mathematicians which work on subjects related to Calculus of Variations and its applications. Examples of interesting topics covered in the conference include regularity in PDEs, machine learning, mechanics, geometric flows, optimal transportation, Riemannian geometry, and quantum mechanics.

The general idea of the workshop is to not limit the interaction between speakers and participants to the bare scientific presentations, but to provide enough space and time between the talks to leave space to potential collaborations and fruitful discussions. We in particular encourage researchers in a young stage of career (Master and PhD students) to participate to the Workshop.

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

Algebra,    Kurse und Veranstaltungen für Studenten der Mathematik

The Hausdorff Research Institute for Mathematics (HIM)

Analytic questions of a discrete nature are ubiquitous in many areas of mathematics and theoretical computer science. The purpose of this conference is to bring together a diverse group of experts working, broadly, on Discrete Analysis with particular emphasis on questions having a geometric component. The topics will include Boolean analysis, vector-valued harmonic analysis, metric embeddings, geometry of graphs and groups, and aspects of discrete probability and theoretical computer science.

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

The Hausdorff Research Institute for Mathematics (HIM)

Harmonic analysis on the hypercube has long found exciting applications in theoretical computer science, in areas as diverse as learning theory, voting theory, and computational complexity theory. And TCS has also inspired challenging new questions in analysis, often leading to new perspectives on familiar topics. Indeed, this connection is only deepening as quantum computing, machine learning, and other areas of TCS expand to spaces beyond the hypercube. Talks in this workshop will focus on such connections recently uncovered, techniques in use today, and conjectures old and new. We hope it can also be an invitation to the topic for a harmonic analysis audience, thanks to additional introductory talks scheduled.

Hausdorff Research Institute for Mathematics (HIM)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)