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

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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. 

Special Seminar on Mathematical Modelling

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Date & Time: 1st November 2022, Tuesday; 4-5 pm Venue: Ramanujan Hall

Mathematical modelling in infectious disease epidemiology: a highly selective overview

Mathematical modelling has played an increasingly important role in public health responses to infectious diseases. As with any modelling efforts, the development and use of models always need to be accompanied by a careful understanding of the strengths and limitations of models. In this talk, I will give an entirely personal view of how mathematical modelling has developed in recent years, with a focus on its applied use in public health decision-making. As well as a rapid introduction to modern modelling techniques, topics will include HIV, human tuberculosis and COVID-19.

About the Speaker:

Nim Arinaminpathy is a Professor of Mathematical Epidemiology at Imperial College London. In his research, he applies mathematical modelling to study the spread and control of infectious diseases, with a focus on human tuberculosis (TB). He works closely with national TB programmes in high-burden countries, particularly India. He also works with the WHO South-East Asian Regional Office (SEAR) on TB control priorities for the region and serves on the WHO Strategic and Technical Advisory Group for TB. Additionally, since 2020 he has worked closely with the Indian Council of Medical Research, providing advice in support of the COVID-19 response in India.

Title: Computing the Hausdorff dimension of Dynamical and Diophantine sets: some examples.

Abstract: I will introduce the notion of Hausdorff measure and dimension. I will then explain via examples, some joint work with Debanjan Nandi (Weizmann Institute) which estimates, and in many cases computes, the dimension of many sets which occur naturally in the theory of dynamics on spaces of negative curvature. These objects in turn are connected to Diophantine analysis. I will also explain the connection. Most of the talk will be elementary.   

Analysis Seminar

Time: 3:30 pm, Thursday 3 November 2022

Venue: Ramanujan Hall, Department of Mathematics

Speaker: Sushil Singla, Indian Institute of Science (IISc), Bangalore, India.

Title: Interpolation Polynomials and Linear Algebra

Abstract: We reconsider the theory of Lagrange interpolation polynomials
with multiple interpolation points and apply it to linear algebra. In
particular, we show that one can evaluate a meromorphic function at a
matrix, using only an interpolation polynomial. As an application of
Lagrange interpolation polynomials, we also provide proof that all
complex matrices can be put into Jordan normal form.

Radhika Gupta (TIFR)  will be speaking in our Topology Seminar on 4th
November, 2022 at 4:30 PM in Ramanujan Hall.


Title: Stretch factors of graph maps and polynomial invariants of
free-by-cyclic groups

Abstract: In this talk we will associate two numbers, the geometric and
homological stretch factors, to a graph map and see under what conditions
they are equal. We will then upgrade these notions to free group
automorphisms. Finally, we will cast these numbers in terms of two
polynomial invariants, the Alexander polynomial and McMullen polynomial,
associated to a free-by-cyclic group and see how these polynomials are
related to each other.

Virtual Commutative algebra seminars

Speaker: Vivek Sadhu, IISER Bhopal
Date/Time: 4 November 2022, 5:30pm

Gmeet link: meet.google.com/sfo-vekm-yxz [1]

Title: Injectivity of Brauer groups for valuation rings
Abstract:  In the nonnoetherian situation, valuation rings often behave 
like regular rings. We will discuss several such results which are 
classically known to be true for regular rings, but also true for 
valuation rings. We then focus on Brauer groups. It is well known that 
Br(R) injects into Br(K) provided R is a regular domain and K=qt(R). We 
observe that the same is true for valuation rings. In fact, we will 
discuss a more general result in the setting of e'tale cohomology.

For more information and links to lecture notes and videos of previous 
seminars,

visit the website of VCAS:

  https://sites.google.com/view/virtual-comm-algebra-seminar [2]



Links:
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[1] http://meet.google.com/sfo-vekm-yxz
[2] https://sites.google.com/view/virtual-comm-algebra-seminar