2020/2021![Learning Objectives](/f/src/global/i/edu/objectives.svg)
![Expected Learning Outcomes](/f/src/global/i/edu/results.svg)
![Course Contents](/f/src/global/i/edu/sections.svg)
![Interim Assessment](/f/src/global/i/edu/intermediate_certification.svg)
![Bibliography](/f/src/global/i/edu/library.svg)
Research Seminar "Representations and Probability 1"
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:
1, 2 module
Language:
English
ECTS credits:
3
Contact hours:
30
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
- 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
- Successful participants imporve their presentation skills and prepare for participation in research projects in the subject area.
Course Contents
- Continuous-time Markov chains and their asymptotical behavior.
- Empirical and invariant measures for Markov chains. Potential theory for Markov chains
- Determinantal point processes. Results connecting them with Markov chains.
- Large-time behavior of diffusion process. Applications to non-equilibrium statistical mechanics.
Interim Assessment
- Interim assessment (2 module)The final grade is the maximum of the two grades: the grade for the talk (if the student gave it) and the exam grade.
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