Panorama of Geometric structures on surfaces
In this course, we introduce the general notion of (G,X)-structures on manifolds. After providing the basic results on the topology of surfaces (including the topological classification theorem), we will give a general panorama of (G,X)-structures in dimension two. We will focus on two classes of geometric structures:
- metrics with constant curvature (possibly with singularities);
- geometric structures compatible with a structure of Riemann surface.
We will discuss fruitful interactions with combinatorics, dynamical systems and the general theory of moduli spaces.
- metrics with constant curvature (possibly with singularities);
- geometric structures compatible with a structure of Riemann surface.
We will discuss fruitful interactions with combinatorics, dynamical systems and the general theory of moduli spaces.
Lecturer
Date
11th October ~ 29th December, 2023
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Wednesday,Friday | 14:20 - 16:05 | A3-2a-201 | ZOOM 06 | 537 192 5549 | BIMSA |
Prerequisite
Undergraduate general topology and complex analysis
Syllabus
PART 1: Axiomatic topology of surfaces (Radò theorem, Invariance of domain, Brouwer fixed point theorem)
PART 2: Atlases and (G,X)-structures
PART 3: Combinatorial topology of bidimensional complexes
PART 4: Metrics with constant curvature
PART 5: Introduction to Riemann Surfaces
PART 6: Translation surfaces
PART 7: Complex projective and affine structures on surfaces
PART 2: Atlases and (G,X)-structures
PART 3: Combinatorial topology of bidimensional complexes
PART 4: Metrics with constant curvature
PART 5: Introduction to Riemann Surfaces
PART 6: Translation surfaces
PART 7: Complex projective and affine structures on surfaces
Video Public
Yes
Notes Public
Yes
Lecturer Intro
Guillaume Tahar obtained his Ph.D from Université Paris Diderot, under the supervision of Anton Zorich. He was a senior postdoctoral fellow in Weizmann Institute of Science and joined BIMSA as an assistant professor in 2022. He contributed to the study of moduli spaces of various flavours of geometric structures on surfaces. His results include proving the existence of closed geodesics in dilation surfaces and the complete characterization of configurations of local invariants realized by a differential on a Riemann surface. His recent research interests include linear differential operators, simplicial arrangements of lines and quantum invariants of knots.