AIS - Geometric Group Theory (2020)

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. Bidyut Sanki (BS)
IIT-Kanpur

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)
IISER-Mohali

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)
IIT-Kanpur

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)
IIT-Bhubaneswar

 

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)
Presidency University, Kolkata

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:

  1. Fuchsian Groups, Svetlana Katok, Chicago Lectures in Mathematics
  2. Lectures on Hyperbolic Geometry, Beneditti-Petronio, Springer
  3. Metric Spaces of Non-positive curvature, M.Bridson & A.Haefliger, Springer.
  4. A Primer on Mapping Class Groups, Benson Farb & Dan Margalit, Princeton University Press.
  5. Trees, Jean-Pierre Serre, Springer
  6. Combinatorial group Theory, Paul E. Schupp & Roger Lyndon, Springer
  7. On Hyperbolic Groups after Mikhael Gromov, Etienne Ghys & Pierre de la Harpe, Springer. 

Tutorial Assistants:

S. No.

Name

Affiliation

1

Dr. Suraj Krishna (SK)

TIFR

2

Dr. Shiv Prasad (ShP)

IIT-Goa

3

Dr. Tiken Singh (TS)

NEHU-Shillong

4

Ms. Kuwari Mahanta (KM)

IIT-Guwhati

5

Mr. Suman Paul (SP)

IIT-Kanpur

6

Ms. Swathi Krishna (SwK)

IISER-Mohali


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

(11.05 –11.25)

Tutorial

(11.30-12.30)

 

Lunch

(12.35–1.55)

Lecture 2

(2.00-3.30)

Tea

(3.35-3.55)

Tutorial

(4.00-5.00)

Snacks

 

 

 

(name of the speaker in abbreviated form)

 

(name of the speaker + tutors in abbreviated form)

 

 

(name of the speaker in abbreviated form)

 

(name of the speaker + tutors in abbreviated form)

 

Mon

15

SKP

 

SKP,TS, KM

 

 

BS

 

BS,KM,TS

 

Tues

16

SKP

 

SKP,TS,KM

 

 

BS

 

BS,KM,TS

 

Wed

17

SKP

 

SKP,TS,KM

 

 

AP

 

AP,ShP, SP

 

Thu

18

SKP

 

SKP,TS,KM

 

 

AP

 

AP,ShP, SP

 

Fri

19

BS

 

BS,KM,TS

 

 

AP

 

AP,ShP, SP

 

Sat

20

BS

 

BS,KM,TS

 

 

AP

 

AP,ShP, SP

 

SUNDAY OFF

 

Mon

22

PS

 

PS,SK,SwK

 

 

SD

 

SD,SK,SP

 

Tues

23

PS

 

PS,SK,SwK

 

 

SD

 

SD,SK,SP

 

Wed

24

PS

 

PS,SK,SwK

 

 

AK

 

AK,SwK,ShP

 

Thu

25

PS

 

PS,SK,SwK

 

 

AK

 

AK,SwK,ShP

 

Fri

26

SD

 

SD,SK,SP

 

 

AK

 

AK,SwK,ShP

 

Sat

27

SD

 

SD,SK,SP

 

 

AK

 

AK,SwK,ShP

 

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