Master
2024/2025
Research Seminar "Representations and Probability 2"
Type:
Elective course (Mathematics)
Area of studies:
Mathematics
Delivered by:
Faculty of Mathematics
Where:
Faculty of Mathematics
When:
1 year, 3, 4 module
Mode of studies:
offline
Open to:
students of all HSE University campuses
Instructors:
Grigori Olshanski
Master’s programme:
Mathematics
Language:
English
ECTS credits:
3
Course Syllabus
Abstract
The seminar is mostly aimed to 3–4th year bachelor students, as well as master and PhD students. Senior participants are expected to deliver a talk on the seminar. The seminar topics are the mix of modern results in areas related to probability theory, random processes, dynamical systems, representations, and older areas, which are prerequisites to the former, as well as keep their own value.
Course Contents
- Random dynamical systems and their large time behaviour
- Wiener chaos and normal approximation
- Determinantal random point processes
- Potential theory for Markov chains on generic spaces: representation formulas and applications
- Exponentially growing groups: free, hyperbolic, Markov, Fuchsian, etc. Ergodic theory of their actions
- Classical representation theory
- Representations of infinite-dimensional groups and operator algebras
- Сonnections with algebraic combinatorics (symmetric functions), quantum groups, classical analysis, and probability theory
Interim Assessment
- 2024/2025 4th moduleParticipants can make a talk during the semester (this is usually graded with a mark 6-8) and/or solve the problems of the final exam. The problems list is given to the students approximately a week before the exam, and on the exam a student discusses the solutions that he/she obtained. Formula for calculating the final grade for the exam is provided along with the problems list.
