A rigorous introduction to the statistical analysis of random functions and associated random operators. Viewing random functions either as random Hilbert vectors or as stochastic processes, we will see the interplay between nonparametrics and multivariate ...
We propose an introduction to homotopy theory for topological spaces. We define higher homotopy groups and relate them to homology groups. We introduce (co)fibration sequences, loop spaces, and suspensions. We study long exact sequences. We construct Eilen ...
The theme of the working group varies from year to year. Examples of recent topics studied include: Galois theory of ring spectra, duality in algebra and topology, and topological algebraic geometry. ...
This course will provide an introduction to model category theory, which is an abstract framework for generalizing homotopy theory beyond topological spaces and continuous maps. We will study numerous examples of model categories and their applications in ...
The theme of the working group varies from year to year. Examples of recent topics studied include: Galois theory of ring spectra, duality in algebra and topology, topological algebraic geometry and twisted K-theory ...
We expect these mini-courses to equip junior researchers with new tools, techniques, and perspectives for attacking a broad range of questions in their own areas of research while also inspiring students to learn more about ground-breaking advances in pure ...
This course introduces the elementary topological concepts and tools that recently spread from condensed matter physics to various quantum and classical wave systems. ...
The goal of this course is to present an overview on the solvability and the regularity of relevant models of physical, technological and economical systems, which may be formulated as minimization problems of suitable integral functionals. ...
Quantum mechanics is one of the most successful physical theories. This course presents the mathematical formalism (functional analysis and spectral theory) that underlies quantum mechanics. It is simultaneously an introduction to mathematical physics and ...