


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 A1A2 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 subalgebras 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, 34 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 twostate sum models coming from two directed graphs namely the partarc 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 HasseMinkowski 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 padic 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: Signchanging blowingup solutions to the Yamabe equation on a closed Riemannian manifold Abstract: In this talk, I will discuss the question of existence of families of signchanging 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 blowingup 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 nonround metric on spherical space forms of dimensions greater than 10 for which there exist families of signchanging blowingup 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/rmqijfzedh Or dial: (US) +1 2692240185 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/gcbevfuwtu [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/virtualcommalgebraseminar