Morse Theory
In this course, we introduce Morse theory and discuss several applications: Bott periodicity theorem, equivariant localization and Picard-Lefschetz theory.

Lecturer
Date
19th February ~ 29th May, 2025
Location
Weekday | Time | Venue | Online | ID | Password |
---|---|---|---|---|---|
Wednesday,Thursday | 10:40 - 12:15 | A3-1-103 | Zoom 16 | 468 248 1222 | BIMSA |
Syllabus
Part 1: Introduction to Morse Theory
Part 2: Bott periodicity theorem
Part 3: Applications in Symplectic Geometry
Part 4: Elements of Picard-Lefschetz theory
Part 2: Bott periodicity theorem
Part 3: Applications in Symplectic Geometry
Part 4: Elements of Picard-Lefschetz theory
Audience
Advanced Undergraduate
, Graduate
Video Public
Yes
Notes Public
Yes
Language
English
Lecturer Intro
Guillaume Tahar obtained his Ph.D from Université Paris Diderot, under the supervision of Anton Zorich. He was a senior postdoctoral fellow at the Weizmann Institute of Science and joined BIMSA as an Assistant Professor in 2022. His research focuses on geometric structures on surfaces, with applications to moduli spaces and dynamical systems. He contributed to the study of various flavours of geometric structures, including translation surfaces, polyhedral metrics, cone spherical metrics and complex affine structures. His approach typically involves a mix of complex analysis, geometric constructions, and combinatorial reasoning.
His key results include the proof of the existence of closed geodesics in dilation surfaces, the complete characterization of configurations of local invariants realized by a differential on a Riemann surface and the establishment of Grünbaum's asymptotic classification for simplicial line arrangements with few double points.
His recent research interests include the topological interpretation of quantum invariants of knots, the counting of BPS states in quantum field theory and holomorphic dynamics in higher dimensions.
His key results include the proof of the existence of closed geodesics in dilation surfaces, the complete characterization of configurations of local invariants realized by a differential on a Riemann surface and the establishment of Grünbaum's asymptotic classification for simplicial line arrangements with few double points.
His recent research interests include the topological interpretation of quantum invariants of knots, the counting of BPS states in quantum field theory and holomorphic dynamics in higher dimensions.