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

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

Algebra,    Geometrie und Topologie

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

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

Infinitesimalrechnung, Differentialgleichungen, Integralrechnung,    Informations & Wissensmanagement, Big Data Computing

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

Kurse und Veranstaltungen für Studenten der Mathematik,    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.

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.

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

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,    Kurse und Veranstaltungen für Studenten der Mathematik

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)

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)

This workshop brings together leading experts in Boolean analysis, information theory, and lattices to explore the forefront of these disciplines through the talks and discussions about intriguing open problems, recent resolutions, and the evolution of innovative ideas, approaches, and techniques.

Hausdorff Research Institute for Mathematics (HIM)