


Lecture series on Lie groups.
Monday, 20 March at 4 pm
Tea: 3.50 pm
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Venue: A1A2, CDEEP, Mathematics Department
Host: Dipendra Prasad
Speaker: M. S. Raghunathan
Affiliation: CEBS, Mumbai
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 identityconnected component of its center and its commutator subgroup (which is a 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, π_1(G,e) is finite (and hence the universal covering of a compact group whose abelianization is trivial is compact.
Then I will introduce roots and weights and the Dynkin diagram of the compact group and sketch 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.
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PDE Seminar
Tuesday, 21 March at 4 pm
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Venue: 216, Mathematics Department
Host: Saikat Mazumdar
Speaker: Dr. Souptik Chakraborty
Affiliation: IIT Bombay
Title: Quantitative stability results of some functional inequalities
Abstract: In 1992, BianchiEgnell proved that the "Sobolev deficit" is bounded below by the distance of the function to the manifold of optimizers which gives a quantitative version of Lions result. In recent years, Figalli and other mathematicians obtained quantitative stability results for the critical exponent problem which is the EulerLagrange equation associated to Sobolev inequality. In this talk, I'm going to present recent developments in this direction. In particular, I will talk about some progress in the quantitative stability aspects of HardySobolev inequality. This is an ongoing joint project with Saikat Mazumdar.
Algebraic groups Seminar
Tuesday, 21 March at 4 pm
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Venue: 114, Mathematics Department
Host: Shripad Garge
Speaker: Shripad M. Garge
Affiliation: IIT Bombay
Title: Linear algebraic groups, basic themes. V
Abstract: We discuss the last section in Springer's second chapter. It is on determining a group by its representations.
Commutative Algebra Seminar
Thursday, 23 March 2023, 4 pm
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Venue: Ramanujan Hall
Host: Tony Puthenpurakal
Speaker: Tony Puthenpurakal
Affiliation: IIT Bombay
Title: Asymptotic primes and analytic spread
Abstract: We discuss two results of Brodmann. The first result shows that over a Noetherian ring, Ass M/I^nM stabilizes for n large. The second result shows that depth M/I^nM is constant for n large.
Algebraic Geometry Seminar
Friday 24 March 2023, 11.00am
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Venue: Ramanujan Hall, Department of Mathematics
Host: Sudarshan Gurjar
Speaker: Nitin Nitsure
Affiliation: TIFR, Mumbai (retd)
Title: Local Criterion of FlatnessII
GGT Seminar
Date and time: Friday 24 March, 2023 at 12:35 pm
Venue: Room No 114, Department of Mathematics
Host: Rekha Santhanam
Speaker: Ankit Rai
Affiliation: IIT Bombay
Title: The PingPong Lemma.
Abstract : The talk will be based on the chapter titled The PingPong Lemma from the book Office hours with a geometric group theorist. The chapter consists of pingpong lemma and it's application(s), a construction of Farey tree and a gentle introduction to hyperbolic upper half plane.
CACAAG seminar
4 PM Friday, 24 March 2023
Please note the deviation in the time from the previous seminars.
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Venue: Ramanujan Hall
Host: Madhusudan Manjunath
Speaker: Madhusudan Manjunath
Affiliation: IIT Bombay
Title: Unimodality and Log concavity in Algebra, Geometry, and Combinatorics: hvectors of Polytopes and Toric Geometry.
Abstract: We discuss unimodality questions on hvectors of polytopes and sketch an approach via toric geometry.
Virtual Commutative Algbera Seminar
Friday, 24 March 2023, 6.30 p.m.
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Venue: meet.google.com/upzrfxhuob
Host: J. K. Verma
Speaker: Takumi Maruyama
Affiliation: Purdue University, USA
Title: Uniform bounds on symbolic powers in regular rings via closure theory
Abstract: The containment problem asks: For a fixed ideal I, which symbolic powers of I are contained in an ordinary power of I? We present a closuretheoretic proof of the theorem which says that for ideals I in regular rings R, there is a uniform containment of symbolic powers of I in ordinary powers of I.