Classical Constructions in Geometric Topology
In this course, we will discuss several classical topics in Geometric Topology: Morse theory, De Rham theory (including the construction of characteristic classes) and Mostow rigidity theorem.
Lecturer
Date
11th March ~ 28th May, 2024
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Monday,Tuesday | 11:10 - 12:55 | A1-103 | ZOOM B | 462 110 5973 | BIMSA |
Prerequisite
Undergraduate topology
Syllabus
Part 1: Morse theory (including a proof of Bott periodicity theorem)
Part 2: De Rham theory (including an introduction to characteristic classes, rational homotopy theory and classification results of vector bundles)
Part 3: The various proofs of Mostow rigidity theorem
Part 2: De Rham theory (including an introduction to characteristic classes, rational homotopy theory and classification results of vector bundles)
Part 3: The various proofs of Mostow rigidity theorem
Video Public
Yes
Notes Public
No
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.