Group Theory Sangam 

What's next?

We plan to continue hosting various activities related to Group Theory and keep this page updated with information on related activities being organised by others. 

Conference on "Group Theory and related topics" 

February 27, 2023 - March 04, 2023 at NISER Bhubaneswar

The School of Mathematical Sciences, NISER Bhubaneswar, is organizing a conference on "Group Theory and related topics" during February 27, 2023 - March 04, 2023. The objective of the conference is to discuss various topics related to group theory and its applications. Leading mathematicians working on different aspects of group theory are invited to give lectures and participate in discussion meetings. Young researchers including Ph.D. students and Post-Doctoral Fellows will also have the opportunity to contribute talks on their research work.

For details and time-to-time updates about the conference, please visit the following website: https://www.niser.ac.in/GTConf/

The link for the conference is also available on the main pages of NISER Bhubaneswar (https://www.niser.ac.in/) and the School of Mathematical Sciences (https://www.niser.ac.in/sms/).

You can write to the organiser: gtconf [at] niser [dot] ac [dot] in

Lecture Series

Compact Lie groups and their representations 

Speaker: Prof MS Raghunathan 

(October - December 2022)

First talk: Monday 17th October at 4 pm at the IIT Bombay maths department and will be available over zoom (to get the zoom details please write to grouptheory21@gmail.com). Each lecture will be of 90 minutes. The course will run roughly through the middle of December, so about 8 lectures.  

Since Monday 24th October is  Deepawali, the lecture will be organized on the 26th afternoon for which the precise timing will be communicated later.

Hosts: Prof D. Prasad and Prof J. K Verma at IIT Bombay

Prof MS Raghunathan will give a course of lectures aimed at beginning Ph.D. students on a topic of basic importance to all of mathematics. 

Abstract: In this course I will first talk about the structure theory of compact Lie groups, beginning with the fact that a compact connected Lie group is an almost direct product of the identity connected component of its centre and its commutator subgroup (which is closed subgroup) conjugacy of maximal tori and the fact that every element is contained in a maximal torus. In the course of proving these results, some results on the topology of compact Lie groups which will also be proved. I will then establish Weyl's theorem which asserts that if G is a compact connected Lie group and [G,G]=G, π1(G,e) is finite (and hence the universal covering of a compact group whose abelianisation is trivial is a compact. Then I will introduce roots and weights and the Dynkin diagram of the compact group and sketch a proof of the fact that the Dynkin diagram determines the group locally. The remaining lectures will be devoted to representation theory. I will establish the bijective correspondence between 'Dominant Weights' and irreducible representations. The course will end with the Weyl Character Formula for the character of an irreducible representation corresponding to a 'dominant' weight. The entire theory is essentially  the same as the representation theory of reductive algebraic groups. I will off and on indicate how the two are related.  

I will be assuming some familiarity with basic theory of Lie groups such as the correspondence between Lie sub-algebras of the Lie group and Lie subgroups of the Lie groups; also with some basic results from algebraic topology. 

About the speaker: see wiki page , an article by Prof Dani, Bhavan article

Link to the website

Lectures are available on YouTube

Lecture Series November 2021

Witt vectors, arithmetic jet spaces, and algebraic groups

by Prof. James Borger, Australian National University (ANU, Australia)

Speaker:  Prof. James Borger (ANU, Australia)

Dates: 2nd, 9th, 16th, 23rd November 2021 

Time: 11.30 am IST - 1.00 pm IST

Abstract: We will take the following question as our motivation: In what sense can a matrix group with entries in Z/p^nZ, with p prime, be thought of as an algebraic group? In the first two or three lectures, I'll develop the general theory of Witt vectors and arithmetic jet spaces (or Greenberg transforms). I'll do this from the point of view of p-derivations, arithmetic differential operators, and δ-rings, which allows for a clean development parallel to the geometric theory of usual jet spaces. It is due mainly to André Joyal and Alexandru Buium. In the remaining time, I'll turn to algebraic groups and discuss specific structures and properties that arise with them. I'll conclude with some applications and questions.

Please visit  https://www.imsc.res.in/~amri/witt/ for the registration and other details. 

July 2021

Lecture series July 2021 (3, 10, 17, 24, 31 July 2021)

A COURSE ON EXCEPTIONAL GROUPS

by Maneesh Thakur, Indian statistical institute, Bangalore India. 

Host: Shripad Garge, IIT Bombay, Mumbai India

(for the lecture notes and videos go to the course webpage above)

January to May 2021

During the period January to May 2021, we organized a seminar series. The seminar met every Tuesday at 4 PM Indian Standard Time. This was attended regularly by 40-50 participants, included international audiences. We thank all our speakers and the audience for their enthusiastic response. All talks are available on our YouTube channel.

Abstract of all talks

Schedule of Talks

Expected Audience

Poster

YouTube Channel

This is a semester long seminar series, starting from 5th January 2021, on wide ranging topics in  Group Theory, including  Algebraic Groups, Finite Groups, Geometric Group Theory, Representation Theory, Probabilistic Group Theory, Group Algebras, Group Cohomology etc.

As the name suggests, the activity aims at bringing Indian group theorists, working in diverse areas, at one platform,  keeping abreast everyone of the latest developments and fostering collaboration through interaction.  

The organisers of this seminar series are:

• Manoj Kumar Yadav, HRI, Pryagraj, India

• Anupam Kumar Singh, IISER Pune, India

This seminar will meet online each Tuesday at 16:00 hours Indian Standard Time (IST) which is 10:30 AM GMT.

To receive updates, you can get in touch with one of us or write to us at grouptheory21@gmail.com

Links to some ongoing seminars