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Max Planck Institute for Mathematics in the Sciences

The aim of the course is to learn how tools from algebraic geometry (in particular, from computational and real algebraic geometry) can be used to analyze standard models in molecular biology. Particularly, these models are key ingredients in the development of Systems and Synthetic biology, two active research areas focusing on understanding, modifying, and implementing the design principles of living systems. We will focus on the mathematical aspects of the methods, and exemplify and apply the theory to real networks, thereby introducing the participants to relevant problems and mechanisms in molecular biology. As a counterpart, however, the participants will also see how this field has in the past challenged current methods, mainly in the realm of real algebraic geometry, and has given rise to new general and purely theoretical results on polynomial equations. We will end our lectures with an overview of open questions in both fields.

Komplexe Netzwerke,    Geometrie und Topologie

Hausdorff Center for Mathematics – hcm (Universität Bonn)

TQFTs (Topological quantum field theories) are of central importance in several areas of mathematics and physics. From a mathematical point of view (going back to Atiyah), a TQFT is a symmetric monoidal functor from the cobordism category to some symmetric monoidal category. It can thus be seen as a representation of a fundamental geometric category on a target category and thereby organizes interesting algebraic structures, e.g. representations of mapping class groups, in terms of cobordism categories. In recent years, TQFTs have appeared in many more mathematical areas such as algebraic topology (the study of 4-manifolds) or algebraic geometry (the study of moduli spaces). In this Hausdorff school we would like to explore various facets of TQFTs related to representation theory and mathematical physics. The interplay of representation theory and TQFT is, at least, two-fold: on the one hand side, representation theory provides input data to construct TQFTs. The most famous example is given by the quantum groups Uq(sl(2)) from which a modular tensor category and thus a Chern-Simons type TQFT can be constructed. On the other hand, TQFTs explain and organize structures appearing in representation categories, for example character varieties and their quantizations.

Teilchenphysik und Felder,    Kurse und Veranstaltungen für Physikstudenten

The school aims at introducing PhD students and young researchers to some among the recent developments in mathematical physics, with an emphasis on many-body problems, quantum mechanics and quantum field theory. In recent years new analytical and probabilistic methods have been developed within these fields, allowing the mathematical physics community to advance in the understanding of the statistical mechanics properties of many-body and field-particle systems. The goal of the school is on the one hand to present such methods and on the other hand to provide an environment for the exchange of ideas among researchers with different mathematical background and research focus.

Kurse und Veranstaltungen für Physikstudenten,    Quantenmechanik und Quanteninformation

Hausdorff Center for Mathematics – hcm (Universität Bonn)

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.

MPI f. Mathematik, Bonn

The aim of the conference is to bring together early-stage career researchers in number theory (PhD students and postdocs who have obtained their PhD in 2021 or later). We hope that the friendly and engaging atmosphere will encourage the participants to ask questions and discuss their research freely, talk about future job applications and other important aspects of a career in academia. Furthermore, participants will be able to apply to give talks to describe the problems they are working on.

Hausdorff Center for Mathematics – hcm (Universität Bonn)

The last decade has witnessed tremendous advances in both interactive and automated theorem proving, and we are arguably on the doorstep of a new era, in which interactive theorem provers validate ground-breaking mathematical research in a reasonably short time, as shown in Peter Scholze's Liquid Tensor Experiment. This new area is driven both by new software and by a growing community of users. In addition, we have seen the advent of new software that guides mathematicians in finding proofs, helps them develop new conjectures or even generates a proof or part of a proof with minimal human input. This HSM will highlight both these developments.

The Active Training Course "Advanced Deep Learning" is hosted by the community organization DIG-UM with support from the BMBF-funded ErUM-Data-Hub.

The intensive course on Graph Neural Networks, Transformers, Normalizing Flows and Autoencoders will be held from Monday 25.9.23 to Thursday 28.9.23. The course includes a challenge to be worked out and presented by participant subgroups. The workshop is aimed at deep-learning enthusiasts from all ErUM communities (Research on Universe and Matter) who have prior knowledge of neural networks and applied basic concepts of deep learning. 

Kurse und Veranstaltungen für Physikstudenten,    Neuronale Netze und Künstliche Intelligenz, Maschinelles Lernen

Hausdorff Research Institute for Mathematics (HIM)

Hausdorff Research Institute for Mathematics (HIM)

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,    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)

Hausdorff Research Institute for Mathematics (HIM)