AIS - Geometric Group Theory (2022)
Speakers and Syllabus
|
Name of the Speaker with affiliation
|
No. of Lectures (each 1.5 hrs)
|
Detailed Syllabus |
|
Dr. Sreekrishna Palaparthi (SKP) IIT-Guwahati
|
4 |
Groups and Presentations, Surfaces and their Fundamental Groups, Dehn’s Problems, Cayley Graphs, Group Actions, Covering Spaces and Deck Transformations, Quasi-Isometries, Svarc-Milnor Lemma. Basic Hyperbolic Geometry, Geodesics and Isometries of the Hyperbolic plane. |
|
Dr. Shiv Prasad |
4 |
Hyperbolic Surfaces, and Geodesics in it, Intersection Number, Dehn Twists, (M)apping (C)lass (G)roup, Alexander Trick, MCG of Torus, Relation between Dehn Twists, Center of MCG |
|
Dr. Pranab Sardar (PS) |
4 |
Free Groups, Trees and Amalgams, Bass-Serre Tree, Graph of Groups and its fundamental group, Structure of a group acting on a tree, Fixed Point Theory a group acting on a tree, Combination Theorems. |
|
Dr. Abhijit Pal (AP) |
4 |
Hyperbolic Metric spaces, Exponential divergence of Geodesics, Hyperbolic Groups and its Algorithmic properties , quasiconvex subgroups of Hyperbolic groups, Gromov Boundary of Hyperbolic spaces, Relatively Hyperbolic groups. |
|
Dr. Arpan Kabiraj (AK)
|
4 |
Curve complex, Birman exact sequence and finite generation and presentation of Mapping class group, Teichmuller space as the space of all discrete, faithful representations of fundamental group into PSL(2,R) quotiented by conjugation action, Dehn-Nielsen-Baer Theorem. |
|
Dr, Shubabrata Das (SD) |
4 |
Small Cancellation Theory: Definition of pieces, Small Cancellation (SC) Conditions: C'(\lambda), C(p) and T(q). Examples of SC groups. Van Kampen diagrams: construction and reduction, examples. Dehn's algorithm for solving word problem. Linear isoperimetric inequality. Proof of hyperbolicity for finitely presented groups satisfying SC conditions: C'(1/6) or C'(1/4) and T(4). Proof of Rips' theorem showing a finitely presented group as quotient of an SC group. SC conditions over hyperbolic and relatively hyperbolic groups. |
References:
- Fuchsian Groups, Svetlana Katok, Chicago Lectures in Mathematics
- Lectures on Hyperbolic Geometry, Beneditti-Petronio, Springer
- Metric Spaces of Non-positive curvature, M.Bridson & A.Haefliger, Springer.
- A Primer on Mapping Class Groups, Benson Farb & Dan Margalit, Princeton University Press.
- Trees, Jean-Pierre Serre, Springer
- Combinatorial group Theory, Paul E. Schupp & Roger Lyndon, Springer
- On Hyperbolic Groups after Mikhael Gromov, Etienne Ghys & Pierre de la Harpe, Springer.
Tutorial Assistants:
|
S. No. |
Name |
Affiliation |
|
1 |
Dr. Shiv Prasad (ShP) |
IIT-Goa |
|
2 |
Dr. Tiken Singh (TS) |
NEHU-Shillong |
|
3 |
Ms. Kuwari Mahanta (KM) |
IIT-Guwhati |
|
4 |
Dr. Suman Paul (SP) |
IISER-Bhopal |
|
5 |
Dr. Rahul Pandey (RP) |
M.A. Govt. Degree College, Gorakhpur |
Time Table
Tentative Time-Table (with names of speakers and course associates/tutors in abbreviated form):
|
Day |
Date |
Lecture 1 (9.30–11.00) |
Tea |
Tutorial |
|
Lunch |
Lecture 2 (2.00-3.30) |
Tea |
Tutorial |
Sn ac ks |
|
|
|
|
(name of the speaker |
|
(name of the speaker |
|
|
(name of the speaker in abbreviate d form) |
|
(name of the speaker + |
|
|
|
Mon |
30/5 |
SKP |
|
SKP,KM |
|
|
ShP |
|
ShP,TS |
|
|
|
Tues |
31/5 |
SKP |
|
SKP,KM |
|
|
ShP |
|
ShP,TS |
|
|
|
Wed |
1/6 |
SKP |
|
SKP,KM |
|
|
AP |
|
AP, SP |
|
|
|
Thu |
2/6 |
SKP |
|
SKP,KM |
|
|
AP |
|
AP, SP |
|
|
|
Fri |
3/6 |
ShP |
|
ShP,TS |
|
|
AP |
|
AP, SP |
|
|
|
Sat |
4/6 |
ShP |
|
ShP,TS |
|
|
AP |
|
AP,SP |
|
|
|
SUNDAY OFF |
|
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|
Mon |
6/6 |
PS |
|
PS,RP |
|
|
SD |
|
SD,SP |
|
|
|
Tues |
7/6 |
PS |
|
PS,RP |
|
|
SD |
|
SD,SP |
|
|
|
Wed |
8/6 |
PS |
|
PS,RP |
|
|
AK |
|
AK,RP |
|
|
|
Thu |
9/6 |
PS |
|
PS,RP |
|
|
AK |
|
AK,RP |
|
|
|
Fri |
10/6 |
SD |
|
SD,,SP |
|
|
AK |
|
AK,RP |
|
|
|
Sat |
11/6 |
SD |
|
SD,SP |
|
|
AK |
|
AK,RP |
|
|
|
|
|
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