2021/2022
Research Seminar "Representations and Probability 2"
Category 'Best Course for Career Development'
Category 'Best Course for Broadening Horizons and Diversity of Knowledge and Skills'
Category 'Best Course for New Knowledge and Skills'
Type:
Optional course (faculty)
Delivered by:
Faculty of Mathematics
Where:
Faculty of Mathematics
When:
3, 4 module
Open to:
students of all HSE University campuses
Language:
English
ECTS credits:
3
Contact hours:
36
Course Syllabus
Abstract
In recent decades several areas of mathematics were developed where constructions from the probability theory, the representations theory, or both play the central role. The seminar is focused on various topics in these domains, especially emphasizing connections between them.
Learning Objectives
- Knowledge of key notions and results in asymptotic representations theory
- Knowledge of key notions and results in theory of random point fields, including determinantal processes.
Expected Learning Outcomes
- Knowledge of key results and methods in asymptotic representations theory, including asymptotic theory of characters.
- Knowledge of key results in theory of determinantal processes. Ability to use them to study properties of simple DPs.
- Knowledge of main results in theory of othogonal polynomials (Christoffel-Darboux kernels, etc.) Familiarity with asymtotic results for orthogonal polynomial ensembles.
Course Contents
- Orthogonal polynomials and random point processes
- Determinantal processes
- Asymptotic representations theory
Interim Assessment
- 2021/2022 4th moduleThe final grade is the maximum of the grades for the exam and the talk
Bibliography
Recommended Core Bibliography
- Fulton, W. (1997). Young Tableaux : With Applications to Representation Theory and Geometry. Cambridge [England]: Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=570403
Recommended Additional Bibliography
- Fuad Aleskerov, & Andrey Subochev. (2013). Modeling optimal social choice: matrix-vector representation of various solution concepts based on majority rule. Journal of Global Optimization, (2), 737. https://doi.org/10.1007/s10898-012-9907-2