BIMSA > The Shape of Complexity: Geometry, Topology, and Statistics in Complex Systems
The Shape of Complexity: Geometry, Topology, and Statistics in Complex Systems
Lectures explore the interplay of geometry, topology, and statistics in soft matter and complex systems. Topics include topological interactions in macromolecular systems, the emergence of unconventional rare-event statistics in random walks and polymers, relation between exactly solvable 1D models like ASEP and statistics of heaps of pieces, interplay between fractal dimension and topoogy of random walks, and collective behavior in complex networks with applications to identification of clusters and brain studies. Despite their apparent diversity, these phenomena are united by a common underlying theme: the profound influence of non-Euclidean geometry on the statistics of complex systems. This course could offer graduate fellows, postdocs, students, and young researchers modern theoretical approaches in topology and statistics of random walks and many-body systems with collective interactions (24 lectures in total, each lecture = 2 academic hours).
Lecturer
Sergei Nechaev
Date
1st March, 2027 ~ -
Syllabus
Part 1:Low-dimensional topology and non-Euclidean geometry in nature
(4 lectures)

Part 2: Stretching fractal polymer near convex shapes and Kardar-Parisi-Zhang-like
statistics
(5 lectures)

Part 4: ASEP, TASEP, braids and heaps of pieces
(4 lectures)

Part 5: Sparse graphs, modular geometry, and discrete maps
(3 lectures)

Part 6: Fractional Browinan motion meets topology: subdiffusion vs entaglements
(4 lectures)

Part 7: Collective phenomena in networks, graph Laplacians, and spectral statistics
(4 lectures)
Video Public
Yes
Notes Public
Yes
Lecturer Intro
I graduated in 1985 from the Department of Physics at Moscow State University. From 1991 to 2007, I was affiliated with the Landau Institute for Theoretical Physics. Since 2008, I have been working in France, where I currently hold the position of Director of Research at CNRS (National Center for Scientific Research, France). I am based at the LPTMS (Laboratory of Theoretical Physics and Statistical Models), a laboratory affiliated with both CNRS and the University of Paris-Saclay (https://www.lptms.universite-paris-saclay.fr/). From 2015 to 2022, I served as the Director of the Interdisciplinary Scientific Center Poncelet, an International Research Laboratory of CNRS, located at the Independent University of Moscow (Moscow, Russia). I have authored more than 140 scientific publications in Web of Science journals. My current scientific interests are systematized below, where the list of main publications is presented. These publications constitute the core of references related to the course “Statistics and Topology of Random Paths”.