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Regular version of the site
2018/2019

Research Seminar "Representations and Probability 2"

Category 'Best Course for Broadening Horizons and Diversity of Knowledge and Skills'
Category 'Best Course for New Knowledge and Skills'
Type: Optional course (faculty)
When: 3, 4 module
Instructors: Grigori Olshanski
Language: English

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 representations and probability theory, and older areas, which are prerequisites to the former, as well as keep their own value.
Learning Objectives

Learning Objectives

  • The seminar is intended to introduce the subject area to the students, and to offer them an opportunity to prepare and give a talk.
Expected Learning Outcomes

Expected Learning Outcomes

  • Successful participants imporve their presentation skills and prepare for participation in research projects in the subject area.
Course Contents

Course Contents

  • Classical representations theory.
  • Representations of infinite-dimensional groups
  • Their connections with algebraic combinatorics (symmetric functions), classical analysis (orthogonal polynomials) and probabilities theory (point processes and Markov dynamics).
Assessment Elements

Assessment Elements

  • non-blocking Cumulative grade
    cumulative grade is proportional to number of tasks solved
  • non-blocking Final exam
Interim Assessment

Interim Assessment

  • Interim assessment (4 module)
    0.3 * Cumulative grade + 0.7 * Final exam
Bibliography

Bibliography

Recommended Core Bibliography

  • Kuksin, S. B., & Shirikyan, A. (2012). Mathematics of Two-Dimensional Turbulence. Cambridge, [England]: Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=480318

Recommended Additional Bibliography

  • Meyn, S. P., & Tweedie, R. L. (2009). Markov Chains and Stochastic Stability (Vol. 2nd ed). Cambridge: Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=313161