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

Institute for Pure and Applied Mathematics (IPAM), UCLA

Applications that involve HJ PDEs in a high-dimensional (and possibly infinite-dimensional) setting lead to challenging computational problems. Although a large literature is available on HJ PDEs, many challenges remain both from a mathematical and computational point of view. The program will open with one week of tutorials, presented by some of the main organizers. These tutorials will provide an introduction to the major themes of the entire program and connect the themes of the four workshops. The goal is to introduce a common language and build a foundation for the participants of this program who have diverse scientific backgrounds. During the weeks between workshops, participants in residence will develop collaborations; we expect fruitful discussions especially between domain scientists, algorithm developers and pure and applied mathematicians.

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

Institute for Pure and Applied Mathematics (IPAM), UCLA

Ideas to be explored in the workshop include different computational methodologies for efficient real-time solution of nonlinear HJ equations in reachability, optimal control, and differential games. Ideas such as efficient reduced-complexity computation of optimal control solutions, exploiting structure to decompose the solution space to scalable computations and reduced-complexity feedback structures for efficient implementation of optimal controllers based on available data will be considered.

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

Institute for Pure and Applied Mathematics (IPAM), UCLA

This workshop will bring together researchers with background in PDEs, Inverse Problems, and Scientific Computing who are already working in machine learning, along with researchers who are interested in these approaches.

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

Institute for Pure and Applied Mathematics (IPAM), UCLA

This week-long workshop on Mean Field Games (MFG) and Applications for has a number of goals: (i) to gather together leading researchers in MFG and certain cognate areas (economics, optimal transportation, finite dimensional Hamilton-Jacobi equations, Stochastic equations, applied control, numerics). (ii) to expose new researchers to the promise of the field and its array of challenges, while grounding them in its basic techniques; (iv) to make available to the wider community a series of broad interest talks on MFG.

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

Institute for Pure and Applied Mathematics (IPAM), UCLA

In spite of its flexibility, computing nonlinear problems in random media is very expensive. Hence, in practice, it is needed to consider environments which are small random perturbations of periodic ones, and then to obtain some asymptotic expansion for the ergodic constants. Concrete examples of such phenomena that relate to Hamilton-Jacobi equations are large deviations, front propagation and random walks in random media. The latter strengthens the connection with probability.

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

The application of topology to physics has become an integral part of a second quantum revolution in the sciences. The discovery of topological insulators and progress towards topological superconductors realizing non-abelian statistics has moved topological phases of matter onto the center stage in the interaction of topology and physics beyond the quantum Hall effect. While topological physics has been intensively investigated by physicists for the last few decades, the mathematical theory lags far behind. One challenge is formulating the right definition of topological phases of matter, which is closely related to the notoriously difficult problem of finding a rigorous mathematical formulation of quantum field theory. In this summer school, we will focus on two relatively mature foundational topics, and two new directions in the mathematics of topological phases of matter.

Kurse und Veranstaltungen für Physikstudenten,    Mathematische Physik

College of Liberal and Professional Studies | University of Pennsylvania

The Mathematics Academy is a unique opportunity for students interested in examining mathematical concepts rarely offered at the high school level. This rigorous, proof-oriented program will fuse lectures, problem sessions, demonstrations, and exploratory research to engage students.

Mathematical Sciences Research Institute – MSRI

The Illustrating Mathematics program brings together mathematicians, makers, and artists who share a common interest in illustrating mathematical ideas via computational tools.

The program includes week-long workshops in Geometry and Topology, Algebra and Number Theory, and Dynamics and Probability, as well as master courses, seminars, and an art exhibition.

moduli spaces of geometric structures, hyperbolic geometry, configuration spaces, sphere eversions, apollonian packings, kleinian groups, sandpiles and tropical geometry, analytic number theory, supercharacters, complex dynamics, billiards, random walks, and Schramm–Loewner evolution