TEW - Groups and Geometry (2023)
Speakers and Syllabus
Syllabus:
|
Name of the Speaker with affiliation |
No. of Lectures |
Detailed Syllabus |
|
Dr. Chandan Maity (CM), IISER Mohali |
3 |
Symmetries: Group action, Stabilizer subgroup, transitive group action, Discontinuous group action, Presentation of groups, Free groups.
|
|
Dr. Krishnendu Gongopadhyay (KG)
|
4
|
Euclidean Geometry-I: Euclidean plane, Isometries of the Euclidean plane, Similarity, Subgroups of Euclidean isometries.
Hyperbolic Geometry- I Several models of the hyperbolic space: the upper-half space model and the Poincaré disc model. Isometries of the hyperbolic plane, Classification of isometries, Geodesics. |
|
Dr. Soumya Dey (SD), KREA University, Sri City |
6 |
Surfaces: Covering Spaces of a Topological Space. Fundamental groups. Riemann Surfaces. Uniformization theorem. Classification of surfaces.
|
|
Dr. Kuntal Banerjee (KB), Presidency University, Kolkata |
4
|
Euclidean Geometry-II:
Triangle group. Regular tessellations of the Euclidean plane. Discontinuous groups of Euclidean motions. Symmetries of regular polyhedron.
|
|
Dr. Abhishek Mukherjee, Kalna College, Burdwan
|
3
|
Hyperbolic Geometry- II
Gauss-Bonnet theorem. Hyperbolic trigonometry. Finite subgroups of the isometry group, Simplicity of the isometry group. |
|
Dr. Subhabrata Das (SDA), Presidency University, Kolkata
|
4 |
Fuchsian groups: Fuchsian groups. Fundamental domains and Dirichlet regions. Poincaré's theorem and groups generated by side-pairing transformations.
|
References:
- S. Katok,Fuchsian Groups, Chicago Lectures in Mathematics, University of Chicago Press.
- R. C. Lyndon, Groups and Geometry, London Mathematical Society Lecture Notes Series 101, LMS.
- John G. Ratcliffe, Foundation Of Hyperbolic manifolds, Graduate Texts in Mathematics 149, Springer-Verlag, 1994.
(Lecture notes from the speakers, if available)
Time Table
Time-table (with names of speakers and tutors):
|
Day |
Date |
Lecture 1 (9.30–10.30) |
Tea (10.35-10.55) |
Lecturer 2 (11.00–12.00) |
Lecture 3 (12.00–1.00) |
Lunch (1.00 |
Lecture 4 (2.30-3.30) |
Tea (3.35 |
(4.00-5:00) |
Snacks (5.00 |
|
|
|
(Speaker’s name) |
|
(Speaker’s name) |
(Speaker’s name) |
|
(Speaker’s name) |
|
|
|
|
Mon |
05/06 |
CM-1 |
|
SD-1 |
KG-1 |
|
KG-2 |
|
Discussions |
|
|
Tue |
06/06 |
CM-2 |
|
SD-2 |
KG-3 |
|
CM-3 |
|
Discussions |
|
|
Wed |
07/06 |
KG-4 |
|
SD-3 |
KB-1 |
|
SDA-1 |
|
Discussions |
|
|
Thu |
08/06 |
AM-1 |
|
SD-4 |
KB-2 |
|
SDA-2 |
|
Discussions |
|
|
Fri |
09/06 |
AM-2 |
|
SD-5 |
KB-3 |
|
SDA-3 |
|
Discussions |
|
|
Sat |
10/06 |
AM-3 |
|
SD-6 |
KB-4 |
|
SDA-4 |
|
Discussions |
|