At its core, it is a functional analysis course for physicists and covers the basics of measure theory, function spaces and linear operators.
Section of Physics
Teachers: Aru Juhan
Language: french
Academic term: 2023-2024
Introduction to the theory of martingales in discrete time, in particular convergence and optional sampling theorems. Application to branching processes. Introduction to Brownian motion and its main properties.
Section of Mathematics
Teachers: Jego Antoine Pierre François
Language: french
Academic term: 2023-2024
Previous Courses:
Spring 2019 : MATH-654 Topics in 2D continiuum random geometry
This course was about 2D continuum random geometry. We overviewed the recent progress in describing and studying natural families of random curves (SLE), random height functions (GFF) and random metrics (LQG), emphasising the intimate connections between these objects.
Previous teaching & supervision
University level teaching and supervision
- Autumn 2018: Reading seminar in Probability: Yang-Mills measures (together with E. Powell)
- Spring 2018: Supervision of a Master’s project on “Nodal sets of Gaussian functions”
- Autumn 2017: Reading seminar in Probability: Zeros of Gaussian analytic functions (together with V. Tassion)
- Spring 2017: Master’s level course on concentration of measure (together with T. Lupu)
- Autumn 2016: Reading seminar in Probability: Gaussian multiplicative chaos
- Spring 2016: Exercise classes for a Master class on “Schramm-Loewner Evolution and Gaussian free field” by W. Werner (together with A. Kassel and T. Lupu)
- Spring 2016: Co-supervision of a Master’s thesis on “Ciesielski-Taylor identities” (together with T. Lupu and W. Werner)
Popularisation
With co-authors we wrote a book on high-school mathematics “The evening textbook of mathematics”. It tries to make sometimes seemingly difficult and dry mathematics more lively and warm — more like it actually is. The book is freely available here (in Estonian). I occasionly write about mathematics in Estonian; and have also had the opportunity to share my passion in mathematics at several general audience talks, including a TEDx talk on “Structures of randomness” here (in Estonian).