Geometric Group Theory (2022)

Convener(s)

 
Name:  Dr. Abhijit Pal  Dr. Angom Tiken Singh
Mailing Address:

 Assistant Professor,
FB 551, Department of Mathematics and Statistics
Indian Institute of Technology, Kanpur
Kanpur 208016, Uttar Pradesh, India

 Assistant Professor,
Mathematics Department North-Eastern Hill University, Shillong,
Umshing Mawkynroh
Shillong 793022, Meghalaya, India.
Email: abhipal at iitk.ac.in angomtiken at gmail.com

 

Geometric Group Theory is the study of groups treated as geometric objects. The idea of visualizing groups as geometric objects is mainly due to Mikhael Gromov who has revolutionized the subject with his seminal work.

This school is intended towards PhD students and young researchers working in the field of Geometry & Topology. The topics which we aim to cover are: Basic Hyperbolic Geometry, Hyperbolic Groups & its algorithmic properties, Gromov Boundary, Relatively Hyperbolic Groups, Graph of Groups, Structure of a group acting on a tree , Small Cancellation theory, Mapping Class Groups. The participants should be familiar with basic Algebraic topology.

 

Dates: 

Monday, May 30, 2022 - 09:00 to Saturday, June 11, 2022 - 18:00

Venue: 

Venue Address: 

 

Mathematics Department, North-Eastern Hill University
Umshing Mawkynroh
Shillong 793022, Meghalaya

 

 

Venue State: 

Venue City: 

PIN: 

793022

Chrono Order: 

360

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
(ShP) IIT-Goa

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-Palakkad

 

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. 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
(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)

Sn ac ks

 

 

(name of the speaker
in abbreviated form)

 

(name of the speaker
+
tutors in abbreviated form)

 

 

(name of the speaker in abbreviate d form)

 

(name of the speaker

+
tutors in abbreviated form)

 

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

 

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

 

 

 

 

 

Selected Applicants: 

 

Serial SID Full Name Gender Affiliation University/Institute M.Sc./ M.A. Year of Passing M.Sc./ M.A Ph.D. Deg Date
1 32689 Mr. Promod Sharma Male Iit (Bhu) Assam university 2017  
2 32715 Mr. Sushil Bhunia Male IISER Mohali Jadavpur University 2010 28/08/2017
3 32718 Mr. Partha Sarathi Ghosh Male Presidency University PRESIDENCY UNIVERSITY 2018  
4 32748 Mr. Tejbir Lohan Male IISER Mohali IIT Kanpur 2018  
5 32768 Mr. Rakesh Halder Male IISER Mohali IIT Kanpur 2018  
6 32778 Ms Priyanka Tanaji Magar Female Department Of Mathematics, Iit Bombay Savitribai Phule Pune university 2017  
7 32816 Mr. Ravi Tomar Male Iiser Mohali Delhi University 2015  
8 32821 Mr. Somnath Maity Male Iiser, Mohali ISI, KOLKATA 2014  
9 32836 Mr. Swarup Bhowmik Male Iit Kharagpur UNIVERSITY 2018  
10 32859 Ms Poonam Ramnath Pokale Female IITB Savitribai Phule Pune University 2015  
11 32869 Mr. Uddhab Roy Male The University Of Burdwan THE UNIVERSITY OF BURDWAN 2018  
12 33078 Mr Nirmal Biswas Male University Of Kalyani University of Kalyani 2016  
13 33088 Mr. Gour Gopal Biswas Male University Of Kalyani University of Kalyani 2017  
14 33146 Mr Bhola Nath Saha Male IIT,Kanpur UNIVERSITY OF NORTH BENGAL 2017  
15 33150 Mr. Devender Singh Male IIT Kanpur IITROORKEE 2018  
16 33373 Mr. Anuj Kumar Sirohi Male Jawaharlal Nehru University Jawaharlal Nehru University 2018  
17 33640 Mr. Manas Mandal Male The Institute Of Mathematical Sciences University of Calcutta 2018  
18 33674 Ms. Oorna Mitra Female IMSC University of Calcutta 2015  
19 33686 Mr. George Shaji Male Iiser Mohali IISER Mohlai Appeared  
20 33690 Mr. Soumitra Das Male Mizoram University North-Eastern Hill University 2012  
21 33700 Mr Rahul Pandey Male IIT Kanpur Banaras Hindu University 2015  
22 33737 Dr. Sourav Sen Male Harish Chandra Research Institute (Hri) RAMAKRISHNA MISSION VIVEKANANDA UNIVERSITY 2013 14/02/2020
23 33761 Mr. Biswajit Nag Male School Of Mathematics, TIFR N/A    
24 33766 Ms. Priyanka Suryakant Bheske Female IIT Madras Indian Institute of Technology Madras Appeared  
25 33768 Mr Vinay Sipani Male IIT Madras Indian Institute of Technology, Madras (IIT Madras) 2019  
26 33790 Mr Shanborlang Bynnud Male North Eastern Hill University North Eastern Hill University, shillong 2016  
27 33798 Ms. Ramya Nair Female IISER Pune Mumbai University 2015  
28 33805 Ms Saniya Hari Wagh Female Tata Institue Of Fundamental Research Savitribai Phule Pune University 2018  
29 33806 Mr Raju Kumar Gupta Male IIT Delhi Banaras Hindu University 2019  
30 33822 Mr. Sagnik Jana Male Presidency University Presidency University 2020  
31 33829 Mr Ankur Sarkar Male The Institute Of Mathematical Sciences University of Kalyani 2016  
32 33834 Mr. Bhargab Das Male Indian Statistical Institute Indian Statistical Institute Appeared  
33 33849 Ms. Apeksha Sanghi Female Iiser Bhopal University of Delhi 2015  
34 33853 Dr. Puneet Kumar Gupt Male University Of Lucknow University of Lucknow 2012 03/04/2019
35 33855 Mr. Neeraj Kumar Dhanwani Male Iiser Bhopal Devi Ahiliya University, Indore 2015  
36 33859 Mr. Ritwik Chakraborty Male Indian Institute Of Technology      
37 38791 Mr. Rakesh Halder Male Indian Institute Of Science Education And Research Indian Institute of Technology, Kanpur 2018  
38 38813 Mr. Vikas Laxmikant Shukla Male Iim A IISER Pune 2020  
39 38827 Mr. Rana Sardar Male IIT Kanpur The University of Burdwan 2018  
40 38849 Mr. Pravin Kumar V Male IISER Mohali Indian Institute of Science Education and Research, Mohali 2021  
41 38867 Mr. Achintya Dey Male IIT Kanpur Banaras Hindu University 2019  
42 38902 Ms. Anusha Bhattacharya Female Indian Institute Of Science Education And Research, Mohali Chennai Mathematical Institute (M.Sc.) 2020  
43 38935 Mr. Utsav Dewan Male Indian Statistical Institute, Kolkata Indian Statistical Institute, Kolkata 2020  
44 38991 Mr Dibyendu Das Male Indian Statistical Institute Bangalore Indian Statistical Institute Bangalore 2021  
45 39024 Mr Harshul Khanna Male Indian Statistical Institute      
46 39030 Ms. Pragya Belwal Female IISER Mohali Malaviya National Institute of Technology Jaipur 2019  
47 39070 Ms Deepanshi Saraf Female IISER Mohali IISER Mohali 2022  
48 39071 Mr. Debattam Das Male IISER Mohali Banaras Hindu University 2020  
49 39073 Mr. Sayan Pal Male IIT Kanpur IIT Kharagpur 2021  
50 39103 Ms. Deblina Das Female IIT Palakkad University of Calcutta, Ballygunge Science College. 2019  
51 39124 Mr. Srigyan Nandi Male ISI      
52 39125 Mr Antareep Saud Male NISER National Institute of Science Education and Research Appeared  
53 39151 Mr Rahul Mondal Male IISER Mohali ISI Bangalore 2021  
54 39169 Mr. Prajwal Samal Male IIT Kanpur IIT Kanpur Appeared  
55 39209 Mr. Satyajit Maity Male IISER Bhopal CMI 2018  
56 39210 Mr. Kumar Sannidhya Shukla Male University Of Western Ontario National Institute of Science Education and Research (NISER), Bhubaneswar, India 2021  
57 39233 Ms. Lekha Das Female IIT, Guwahati Ramakrishna Mission Vivekananda Educational And Research Institute, Belur 2021  
58 39254 Mr Arnab Kundu Male Indian Institute Of Information Technology Ramakrishna Mission Vivekananda Educational and Research Institute 2021  
59 39291 Ms Shaivi Chavan Female Indian Institute Of Science Education And Research (Bhopal)   Appeared  
60 39298 Mr Sudip Dolai Male Indian Institute Of Technology Kanpur Indian institute of technology kanpur 2022  
61 39326 Ms Samraggi Ghosh Female Iiser Mohali      
62 39337 Ms Tithi Dwary Female Iit Guwahati Calcutta University 2020  
63 39351 Mr. Arkajit Pal Choudhury Male Indian Statistical Institute, Kolkata Indian Statistical Institute,. Kolkata 2020  
64 39363 Mr Nishith Mandal Male IIT Kanpur, India University of Delhi 2018  
65 39452 Ms Anuvertika Pandey Female NISER, Bhubaneswar Banaras Hindu University 2020  
66 39469 Ms. Ananya Gaur Female IISER Mohali IISER Mohali    

How to Reach: 

TBA

School Short Name: 

ggt

Last Date Application: 

Sunday, March 15, 2020

List of Conveners: 

  • Prof Jaydeb Sarkar
  • Prof Rajesh Sharma

 

School Type: 

AIS