Kurse und Veranstaltungen für Studenten der Mathematik in den Vereinigten Staaten (USA)

MRSI – Mathematical Sciences Research Institute, Berkeley

Holomorphic dynamics is a vibrant field of mathematics that has seen profound progress over the past 40 years. It has numerous interconnections to other fields of mathematics and beyond. Our semester will focus on three selected classes of dynamical systems: rational maps (postcritically finite and beyond); transcendental maps; and maps in several complex variables. We will put particular emphasis on the interactions between each these, and on connections with adjacent areas of mathematics.

Komplexe Systeme und Chaos ,    Allgemeine wissenschaftliche Mathematik und fachübergreifende Veranstaltungen

This program is devoted to the investigation of universal analytic and geometric objects that arise from natural probabilistic constructions, often motivated by models in mathematical physics. Prominent examples for recent developments are the Schramm-Loewner evolution, the continuum random tree, Bernoulli percolation on the integers, random surfaces produced by Liouville Quantum Gravity, and Jordan curves and dendrites obtained from random conformal weldings and laminations. The lack of regularity of these random structures often results in a failure of classical methods of analysis. One goal of this program is to enrich the analytic toolbox to better handle these rough structures.

Algebra,    Geometrie und Topologie

IPAM - Institute for Pure & Applied Mathematics, an NSF Math Institute at UCLA

Quantum mechanics has strong connections with probability theory and statistics. Quantum states are amenable to probabilistic interpretation based on laws of statistics. Many quantum problems can be reformulated in terms of Feynman’s path integral formulation, which amounts to computing quantum partition functions using statistical sampling techniques. In addition, new statistical learning approaches are emerging that aim to incorporate “quantumness” to ensure unitarity and long-range correlations that are so ubiquitous in quantum systems. Considering these recent developments, it appears timely to bring together the large community of people working on quantum systems and statistical techniques. This workshop will broadly address the reaches and limitations of statistics as applied to the modeling and understanding of quantum systems and highlight examples where quantum and statistical models enhance each other.

Kurse und Veranstaltungen für Physikstudenten,    Quantenmechanik und Quanteninformation

Mathematical Sciences Research Institute (MRSI)

The field of Integral Equations has a long and distinguished history, being the driving force behind many fundamental developments in various areas of mathematics including Harmonic Analysis, Partial Differential Equations, Potential Theory, Scattering Theory, Functional Analysis, Complex Analysis, Operator Theory, Mathematical Physics and Numerical Analysis.

Infinitesimalrechnung, Differentialgleichungen, Integralrechnung,    Angewandte Mathematik (allgem.)

Mathematical Sciences Research Institute (MRSI)

The MSRI Undergraduate Program (MSRI--UP) is a comprehensive summer program designed for undergraduate students who have completed two years of university-level mathematics courses and would like to conduct research in the mathematical sciences.

Systembiologie und mathematische Biologie,    Genomforschung und Bioinformatik

Mathematical Sciences Research Institute (MRSI)

The topic of random graphs is at the forefront of applied probability, and it is one of the central topics in multidisciplinary science where mathematical ideas are used to model and understand the real world. At the same time, random graphs pose challenging mathematical problems that have attracted the attention from probabilists and combinatorialists since the 1960, with the pioneering work of Erdös and Rényi. Around the turn of the millennium, very large data sets started to become available, and several applied disciplines started to realize that many real-world networks, even though they are from various different origins, share many fascinating features. In particular, many of such networks are small worlds, meaning that graph distances in them are typically quite small, and they are scalefree, in the sense that there are enormous differences in the number of connections that their elements make. In particular, such networks are quite different from the classical random graph models, such as proposed by Erdös and Rényi. Spurred by these findings, many novel models have been introduced and properties have been investigated.

Graphentheorie und Kombinatorik,    Komplexe Netzwerke

Mathematical Sciences Research Institute (MRSI)

Algebra,    Infinitesimalrechnung, Differentialgleichungen, Integralrechnung

The Institute for Computational and Experimental Research in Mathematics (ICERM)

At the ICERM workshop "Lean for the Curious Mathematician 2022", experts in the Lean theorem prover will explain how to do number theory, topology, geometry, analysis, and algebra in the Lean theorem prover. This will be accessible to mathematicians without a specific background in computer-proof systems. The material covered will range from undergraduate mathematics to modern research. Participants will be invited to begin formalizing mathematical objects from their own research.

University of Colorado Boulder

The goal of this summer school is to introduce participants to tools and ideas from algebraic topology and homotopy theory that are used in the study of fixed point theory. This will be a problem set focused summer school surrounding four mini-courses.

1) Fixed point theory and Nielsen theory 2) Categorical Approach to Duality 3) Spectra 4) Trace Methods

The PCMI graduate summer school program in 2022 will consist of a sequence of 11 minicourses. Each minicourse is accompanied by a problem session. The topics are arranged so that there is good material and opportunities for learning both for less experienced students as well as more advanced students. Beyond their attendance in these minicourse sessions, all graduate participants will be able to take part in the substantial other benefits of a PCMI session. This includes the opportunity to interact with the researchers in residence and take part in the research seminar component of PCMI. Many graduate students also interact in significant ways with the undergraduate cohort,,the undergraduate faculty cohort, and may also participate in the many pedagogically focused activities which form part of the K-12 Teacher Leadership Program and the Workshop for Equity in Mathematics Education. PCMI includes numerous cross-program activities to help members from all these groups interact with one another.

Zahlentheorie, Arithmetik,    Numerische Analysis

Georgia Institute of Technology

Topology Students Workshop is a biennial conference at Georgia Insitute of Technology that started in 2012. The first three were funded by a National Science Foundation Career Award and the fourth is funded by an independent grant from the National Science Foundation. The workshop serves as both a research conference and a professional development workshop for graduate students in the fields of geometric group theory, geometry, and topology. Each workshop has included approximately 50 participants and 10 mentors at various career stages. The Topology Students Workshop is unique in its emphasis on community building, professional development, and communication skills.

Texas A&M University

The topic of this concentration week is metric geometry, to be held in-person at Texas A&M University in College Station, Texas. The conference will feature a variety of short research talks by participants as well as three mini-courses. Talks in any area broadly construed as metric geometry are welcome. Such areas include, but are not limited to, random geometries, metric graph theory, geometric group theory, and geometric functional analysis. The main goals of the conference are to provide a platform for participants to circulate their research achievements, expose them to new research topics, and open doors for future collaborations.

Part of the 2022 Texas A&M Workshop in Analysis and Probability

Mathematical Sciences Research Institute (MRSI)

The summer school will lead participants from appealing, simple-to-state problems at confluence of combinatorics, geometry, and topology to sophisticated topological methods that are required for their resolution. In recent years topological methods have found numerous novel applications in mathematics and beyond, such as in data science, machine learning, economics, the social sciences, and biology. The problems we will discuss are particularly well-suited to rapidly put students in a position to approach related research questions.

Mathematical Sciences Research Institute (MRSI)

The goal of this summer school is to give students crash courses in tropical and logarithmic geometry, with a particular focus on the applications in enumerative geometry and moduli theory.

Geometrie und Topologie,    Algebra

University of California Davis

Each day will be dedicated to a specific topic. Mornings will consist of three research talks on this topic, focusing on recent developments and useful techniques for doing research. The first talk will be given by one of the leading mentors, the other two talks will be given by participants. Afternoons will consist of research working groups, where participants break into groups to do research on open problems.

University of California Davis

Each day will be dedicated to a specific topic. Mornings will consist of three research talks on this topic, focusing on recent developments and useful techniques for doing research. The first talk will be given by one of the leading mentors, the other two talks will be given by participants. Afternoons will consist of research working groups, where participants break into groups to do research on open problems.

The University of Texas at Austin

This summer program provides 5 days of concentrated study of topics in Analysis of Partial Differential Equations at the graduate level, followed by a two days workshop. The school will offer 4 courses on topics at the forefront of current research in Partial Differential Equations. Lectures will be followed by daily discussion sessions. During discussion sessions students will be divided in small groups and work on sets of problems related to the courses topics. The workshop will include talks by senior mathematicians and posters and short talks by junior researchers.

The mathematics and physics around gauge theory have, since their first interaction in the mid 1970's, prompted tremendous developments in both mathematics and physics. Deep and fundamental tools in partial differential equations have been developed to provide rigorous foundations for the mathematical study of gauge theories. This led to ongoing revolutions in the understanding of manifolds of dimensions 3 and 4 and presaged the development of symplectic topology. Ideas from quantum field theory have provided deep insights into new directions and conjectures on the structure of gauge theories and suggested many potential applications. The focus of this program will be those parts of gauge theory which hold promise for new applications to geometry and topology and require development of new analytic tools for their study.

Mathematische Physik,    Computerphysik und Numerische Simulation

Mathematical Sciences Research Institute (MRSI)

Over the last decade, there has been a wealth of new applications of homotopy-theoretic techniques to Floer homology in low-dimensional topology and symplectic geometry, including Manolescu’s disproof of the high-dimensional Triangulation Conjecture and Abouzaid-Blumberg’s proof of the Arnol’d Conjecture in finite characteristic. Conversely, results in Floer theory and categorification have opened new directions of research in homotopy theory, from string topology to S-Lie algebras. The goal of this workshop is to introduce researchers in Floer theory to modern techniques and questions in homotopy theory and, conversely, introduce researchers in homotopy theory to ideas underlying Floer theory and its applications.

Mathematical Sciences Research Institute (MRSI)

The Introductory Workshop aims to provide a coherent overview of current research in algebraic cycles, L-values, Euler systems, and the many connections between them. This includes the study of special cycles on Shimura varieties and moduli spaces of shtukas, integral representations of L-values and the construction of p-adic L-functions, and the construction of Euler systems from special elements in Chow groups or higher Chow groups of Shimura varieties. Workshop lectures will be organized into short lecture series, so as to allow each series to begin with expository lectures on foundational results before moving on to current research.