NCM workshop on
Finite groups of Lie type
A follow up of Algebraic Group Workshop held in 2019 at IIT Bombay, Mumbai
Host Institute: IISER Pune, India
Organisers: Dr. Anupam Kumar Singh, IISER Pune, Dr. Shripad M Garge, IIT Bombay, Mumbai
Contact us: algebraicgroups19@gmail.com
Duration : 31 July - 3 October 2021 (online)
Registration: It has to be done through NCM website. Please follow the link below.
https://www.atmschools.org/school/2021/NCMW/fglt
Selected Applicants: see the list here
In case you haven't recieved the link to the lectures, please write at the email id algebraicgroups19@gmail.com
Topics for the workshop:
The details of the courses are as follows:
Course 1 - Finite Groups of Lie type: This topic would be a natural follow up of the 2019 AIS on Algebraic groups where the theory over algebraically closed fields was considered. This topic intends to expose the participants to the structure of reductive groups defined over a finite field and their representations with emphasis on Deligne-Lusztig theory.
Course 2 - Word maps and linear groups: It was a conjecture of Oystein Ore, from 1951, that every element of a non-abelian finite simple group G is a commutator. After almost 60 years, this conjecture was settled in affirmative in the celebrated paper of Liebeck, O’Brien, Shalev, and Tiep, well-known in the community as LOST. Ore’s conjecture asserts that the function, not a group homomorphism, from G x G to G which sends a pair (g, h) to the element ghg^{-1}h^{-1} is surjective. It was then natural to consider various such maps, called word maps, and investigate their properties.
The theory of word maps on groups and their applications has developed significantly in the past two decades, with emphasis on finite simple groups, infinite linear groups, profinite groups and related objects. Word width was studied, leading to solutions to a question of Serre (by Nikolov and Segal) and the conjecture of Ore, stated above. Probabilistic aspects of word maps were also explored, leading to a probabilistic Tits alternative for linear groups, characterizations of probabilistically nilpotent groups, as well as recent solutions to probabilistic Waring problems. This series of lectures will describe these developments, related results, and tools used in the proofs.
Speakers:
Course 1:
(DP) Dipendra Prasad, IIT Bombay, Mumbai, India (Representations of finite groups of Lie type)
(SMG) Shripad Garge, IIT Bombay, Mumbai, India (Structure of finite groups of Lie type)
(MM) Manish Mishra, IISER Pune, India (Supercuspidal representations for finite and p-adic groups)
(CRV) C. R. Vinroot, College of William and Mary, VA, USA (Real representations of finite groups of Lie type)
Course 2:
(AK) Amit Kulshrestha, IISER Mohali, India (Images of word maps and chirality)
(BK) Boris Kunyavskii, Bar Ilan University, Israel (Word maps on linear algebraic groups)
(AKS) Anupam Singh, IISER Pune, India (Power maps on finite groups of Lie type)
(BS) B. Sury, ISI Bengaluru, India (Combinatorial theory of arithmetic groups)
Tutors:
(AB) Anirban Bose, IISER Mohali
(SB) Sushil Bhunia, IISER Mohali
(PC) Pratyusha Chattopadhyay, BITS Pilani, Hyderabad
(SPP) Shiv Prakash Patel, IIT Delhi
Title & Abstracts in pdf
Time Table and weekly material (all times are Indian Standard Time -- IST = +5:30 GMT)
July 31, 2021, Saturday 18 IST-19:30 DP --- Notes Video
August 01, 20021, Sunday 16 IST -17:30 AKS --- Notes Video
August 5, 2021, Thursday, 17:30 IST -18:30 Tutorial --- Assignment0508
August 6, 2021 , Friday, 17:30 IST -18:30 Tutorial --- Assignment0608
August 7, 2021 Saturday 18 IST -19:30 DP Video
August 8, 2021 Sunday 16 IST -17:30 AK Notes Video
August 12, 2021 Thursday, 17:30 IST -18:30 Tutorial (we will continue discussing the last assignment)
August 13, 2021 Friday, 17:30 IST -18:30 Tutorial --- Assignment1308
August 14, 2021 Saturday 18 IST -19:30 MM Notes Video
August 15, 2021 Sunday 16 IST -17:30 AK Notes Video
August 19, 2021 Thursday, 17:30 IST -18:30 Tutorial --- Assignment1908
August 20, 2021 Friday, 17:30 IST -18:30 Tutorial --- Assignment2008
August 21, 2021 Saturday 1800 IST -19:30 MM Notes Video
August 22, 2021 Sunday 1600 IST -17:30 BK Notes Video
August 26, 2021 Thursday, 17:30 IST -18:30 Tutorial --- Assignment2608
August 27, 2021 Friday, 17:30 IST -18:30 Tutorial --- Assignment2708
August 28, 2021 Saturday 1800 IST -19:30 MM Notes Video
August 29, 2021 Sunday 1600 IST -17:30 BK Notes Video
September 2, 2021 Thursday, 17:30 IST -18:30 Tutorial --- Assignment0209
September 3, 2021 Friday, 17:30 IST -18:30 Tutorial --- Assignment0309
September 4, 2021 Saturday 1800 IST-19:30 SMG Notes Video
September 5, 2021 Sunday 1600 IST -17:30 BK Notes Video
September 9, 2021 Thursday, 17:30 IST -18:30 Tutorial --- Assignment0909
September 10, 2021 Friday, 17:30 IST -18:30 Tutorial --- Assignment1009
September 11, 2021 Saturday 1800 IST -19:30 SMG Notes Video
September 12, 2021 Sunday 1600 IST -17:30 BK Notes Video
September 16, 2021 Thursday, 17:30 IST -18:30 Tutorial Assignment1609
September 17, 2021 Friday, 17:30 IST -18:30 Tutorial Assignment1709
September 18, 2021 Saturday 1800 IST -19:30 CRV Notes Video
September 19, 2021 Sunday 1600 IST -17:30 AKS Notes Video
September 23, 2021 Thursday, 17:30 IST -18:30 Tutorial Assignment2309
September 24, 2021 Friday, 17:30 IST -18:30 Tutorial Assignment2409
September 25, 2021 Saturday 1800 IST -19:30 CRV Notes Video
September 26, 2021 Sunday 1600 IST -17:30 AKS Notes Video
October 2, 2021 Saturday 1800 IST -19:30 Sury Notes (both lecture combined) Video
October 3, 2021 Sunday 1600 IST -17:30 Sury Video