Prof MS Raghunathan will give a course of lectures aimed at beginning PhD students

on a topic of basic importance to all of mathematics. Title and abstract are given below.

The course will begin on Monday 17th October at 4pm in the room A1-A2 of CDEEP on the ground floor of the Math building. 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 26th afternoon for which I will separately announce the precise timing.

It will be a lecture course in hybrid mode so that others not in IIT can also benifit from this course. Feel free to tell your friends in case it may interest them. Here is the zoom link in case you cannot attend in person:

Hope to see you there!

Best wishes, Dipendra

-------------------------------------------------------------------

Title: Compact Lie groups and their representations

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. 

Date and Time: Tuesday, 22 Nov. 2022,  3-4 pm.

Venue: Ramanujan Hall

Speaker: Rama Mishra (IISER Pune)

Title: State Sum Models for Quantum Invariants of Knots and Links

Abstract. This talk will be expository in nature. I will introduce the 
notion of quantum invariants of knots and links and explain what it 
means to have a state sum model for a given quantum invariant. I will 
discuss two-state sum models coming from two directed graphs namely the 
part-arc graph denoted by PK and the arc graph denoted by G_K associated 
with a knot diagram. Flows on these respective graphs are the states. We 
prove that there is a bijection between the flows on P_K and the flows 
on G_K.

Speaker: Wasim Akram

Title: Feedback stabilization of parabolic equations and its numerical 
study

Date: 23rd November 2022 (Wednesday)

Time: 09:30 AM - 10:30 AM

Venue: Ramanujan Hall, Dept. of Mathematics

Mathematics Colloquiumm

Date and time: Thursday, 24 November 2022, 2.30 pm

Venue: Ramanujan Hall

Speaker: Parimala Raman, Emory University, Atlanta, GA, USA

Title: Quadratic forms over function fields

Abstract: A classical theorem of Hasse-Minkowski leads to the fact that 
every quadratic form in at least five variables over a totally imaginary 
number field represents zero nontrivially. One is naturally led to 
similar questions concerning function fields of curves over totally 
imaginary number fields. Do quadratic forms in a sufficiently large 
number of variables represent zero nontrivially over these fields? This 
is a big open question even for the rational function field in one 
variable over a totally imaginary number field. The expectation is that 
every quadratic form in at least nine variables over such a field 
represents zero nontrivially; over function fields of p-adic curves, 
every form in nine variables admits a nontrivial zero. We shall explain 
some recent progress in this direction.

Speaker: Jérôme Vétois (McGill University)
Time: November 24, Thursday, 4 pm (Indian Standard Time)

Title: Sign-changing blowing-up solutions to the Yamabe equation on a
closed Riemannian manifold

Abstract: In this talk, I will discuss the question of existence of
families of sign-changing solutions to the Yamabe equation, which blow up
in the sense that their maximum values tend to infinity. It is known that
in the case of positive solutions, there does not exist any blowing-up
families of solutions to this problem in dimensions less than 25, except
in the case of manifolds conformally equivalent to the round sphere
(Khuri, Marques and Schoen, 2009). I will present a construction showing
the existence of a non-round metric on spherical space forms of dimensions
greater than 10 for which there exist families of sign-changing blowing-up
solutions to this problem. Moreover, the solutions we construct have the
lowest possible limit energy level. As a counterpart, we will see that
such solutions do not exist at this energy level in dimensions less than
10. This is a joint work with Bruno Premoselli (Université Libre de
Bruxelles).


Google Meet joining info:
Video call link: https://meet.google.com/rmq-ijfz-edh
Or dial: ‪(US) +1 269-224-0185‬ PIN: ‪997 320 446‬#

Algebraic geometry seminar

Date and time: Thursday, 24 Nov. 2022, 5 pm

Venue: Ramanujan Hall

Speaker: Nitin Nitsure

Title: Stacks and moduli

 Virtual Commutative Algebra seminar

Date and Time: 25 November 2022, 5:30 pm

Gmeet link: meet.google.com/gcb-evfu-wtu [1]

Speaker: Kohsuke Shibata, Okayama University, Okayama, Japan

Title: Bounds of the multiplicity of abelian quotient complete 
intersection singularities\

Abstract:  K. I. Watanabe classified all abelian quotient complete 
intersection singularities. Watanabe defined a special datum in order to 
classify abelian quotient complete intersection singularities. In this 
talk, I investigate the multiplicities and the log canonical thresholds 
of abelian quotient complete intersection singularities in terms of the 
special datum. Moreover, I give bounds of the multiplicity of abelian 
quotient complete intersection singularities.\

For more  information and links to previous seminars, visit the website 
of VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar