2026/2027
Research Seminar "Basic and Advanced Topics in Probability and Analysis 1"
ID 1251680
Type:
Optional course (faculty)
Delivered by:
Faculty of Mathematics
Where:
Faculty of Mathematics
When:
1, 2 module
Open to:
students of all HSE University campuses
Language:
English
ECTS credits:
3
Contact hours:
30
Course Syllabus
Abstract
This seminar is intended for both undergraduate and graduate students with a broad interest in probability and analysis. Led primarily by participating students, the sessions will explore a wide spectrum of results—from classical foundations to recent developments—across topics such as probability theory, random processes, dynamical systems, analysis, mathematical physics, and both ordinary and partial differential equations. A key component of the seminar will be student presentations and discussions centered on their own research. The seminar also serves as preparation for a more advanced seminar in probability and analysis.
Learning Objectives
- The objective of this seminar is to deepen participants' theoretical understanding and research proficiency in probability theory, analysis, and their interdisciplinary applications by facilitating the critical study of foundational results and recent developments. Through student-led presentations and discussions centered on individual research projects, the course aims to develop advanced academic presentation skills, foster rigorous scientific discourse, and prepare students for more specialized graduate-level seminars in these fields.
Expected Learning Outcomes
- The ability to critically analyze and present cutting-edge concepts across probability theory, stochastic processes, dynamical systems, mathematical physics, and differential equations, while situating one's own research findings within the framework of established fundamentals and contemporary advances.
Course Contents
- Various aspects of the theory of Markov chains with discrete and continuous time
- Various aspects of the theory of stochastic differential equations
- Mixing in Markov dynamical systems
- Various aspects of the large deviations theory
- Mass transfer, the Monge – Kantorovich problem
- Miscellaneous
Interim Assessment
- 2026/2027 2nd modulemin(P+T,10), where is P grade for participation in the research seminar and T is grade for the talk
Bibliography
Recommended Core Bibliography
- Optimal transport : old and new, Villani, C., 2009
- Вероятность : учеб. пособие для вузов, Ширяев, А. Н., 1989
- Вероятность. Кн. 2: Вероятность - 2: суммы и последовательности случайных величин - стационарные мартингалы, марковск..., Ширяев, А. Н., 2004
- Курс теории случайных процессов, Вентцель, А. Д., 1996
- Основы теории случайных процессов, Карлин, С., 1971
Recommended Additional Bibliography
- Основы теории случайных процессов, Карлин, С., 1971