- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Special Seminar on Mathematical Modelling

============================

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.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
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.

- Time:
- 3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**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.

- Time:
- 4:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
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.

- Time:
- 5:30pm
- Location:
- Gmeet link: meet.google.com/sfo-vekm-yxz
- Description:
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: ------ [1] http://meet.google.com/sfo-vekm-yxz [2] https://sites.google.com/view/virtual-comm-algebra-seminar

- Time:
- 4:00pm - 4:45pm
- Location:
- Room No. A1A2, CDEEP, Department of Mathematics
- Description:
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.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Title : Group Testing Designs : A Combinatorial Marvel Speaker: Bikas K Sinha Retired Professor of Statistics Indian Statistical Institute, Kolkata Abstract : Group Testing is a technique to test a collection of units in several groups, rather than in isolation (i.e., one-at-a-time), in order to ascertain the 'status' of each individual unit in the collection in respect of a well-deﬁned 'feature'. The problem is to plan the testing procedure so as to be able to do so without any ambiguity and with a minimum number of such tests [called Group Tests (GTs)]. The response to be extracted from each unit is on the same 'feature' and it is 'binary' in nature. It is tacitly assumed that 'possession' of the feature by at least one unit within a group [so formed] would render the group 'identiﬁable' as 'possessed'. When this happens, we need to 'open up' the group and go for further exploration of the status of individual units of the group, possibly by sub-group(s) testing or by other means. Other possibility is that the group would be declared as 'passed', and consequently, it would mean that all constituent units within the group would be declared as 'passed' and 'at one go'! This interpretation is accepted for Group Testing schemes to work. When this latter phenomenon happens, the merit of Group Testing prevails over testing individual units in terms of reduction in the required number of tests. For a given collection of units, we may adopt one-at-a-time testing or Group Testing with formation of suitable groups, or even a combination of the two strategies. As is mentioned above, the sole purpose is to minimize the number of GTs in such situations for a given collection of test items. The above formulation looks deceptively simple! Hidden are probabilistic and combinatorial challenges. In this talk, we will discuss some issues related to combinatorial challenges only. Key Words.... Group tests; Hypergeometric group tests, Sequential group tests, t-completeness, Detecting power of order t, Group Divisible Designs, Petersen graphs.

- Time:
- 11:00am - 12:30pm
- Location:
- Room No 215, Department of Mathematics
- Description:
We will have *Basudev Pattanayak* speaking in the RTAG seminar from *11:00 to 12:30 AM* on *Thursday(tomorrow)*. Here are the necessary details for his talk: Time: Thursday, 10 November, 11:00 – 12:30 AM. Venue: Room 215, Department of Mathematics. Title: A Visit to the Local Langlands Conjecture.

- Time:
- 12:00pm - 1:00pm
- Location:
- Video call link: https://meet.google.com/rps-gagj-wtb
- Description:
Speaker: Prajakta Sahasrabuddhe Title: Minimal dilations for commuting contractions and Q-commutant lifting Date and time: Thursday, November 10· 12:00 pm – 1:00pm Google Meet joining info Video call link:

- Time:
- 2:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Commutative algebra seminars Please note the unusual time for the seminars this week. Thursday, 10 Nov. @ 2.30 pm Speaker: R. V. Gurjar Venue: Ramanujan Hall Title : Positively Graded Domains Abstract : We will discuss positively graded affine domains over complex field from algebraic, geometric, and topological viewpoints. Important results by M. Demazure, I. Dolgachev, H. Flenner, S. Goto, A. Grothendieck, S. Mori, W. Neumann, P. Orlik- P. Wagreich, H. Pinkham, Keiichi Watanabe will be mentioned. A very general result "conjectured" by me in 1990 and proved by O. Mathieu around 2003 will be discussed. It has important consequences for rings of invariants of reductive algebraic groups. Many naturally occurring examples of positively graded domains will be discussed. If time permits, I will mention closely related results proved recently by A. Pramanik-S. Thandar-R.V. Gurjar about affine surfaces with finite fundamental group at infinity.

- Time:
- 10:30am - 11:30am
- Location:
- Room 216, Mathematics Department
- Description:
Title: Totally positive field extensions and pythagorean closures of formally real fields. Day-Date: 11th November 2022, Friday Time: 10:30 am - 11:30 am Venue: Room no 216, Department of Mathematics

Tiltle and Abstract: https://www.math.iitb.ac.in/~seminar/Priyabrata_Mandal.pdf

- Time:
- 12:30pm - 1:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Speaker: Ramlal Debnath

Title: Dilations of W-hypercontractions

Abstract: Attached with this email

Date and Time: Friday, November 11· 12:30 pm – 1:30 pm

Venue: Ramanujan Hall

- Time:
- 2:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
There is a change in timing of Prof. Nitsure's talk tomorrow (11th). He will lecture at 2:30 pm in Ramanujan hall.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Mathematics Colloquium Date: 11 Nov 2022, 4 pm. Speaker: Haruzo Hida University of California, Los Angeles, CA, USA

Title: Background of modular p-adic deformation theory and a brief outline Abstract: The deformation theory of modular forms is increasingly attracting many researchers in arithmetic geometry as it has been an important step in the proof of Fermat's last theorem by Wiles (and Taylor) and supplied an effective tool for the study of the p-adic Birch and Swinnerton Dyer conjecture in the proof by Skinner-Urban of divisibility of the characteristic power series of the Selmer group of a rational elliptic curve by its p-adic L-function under appropriate assumptions. I try to give my background motivation of creating the theory and describe an outline of the theory.

- Time:
- 5:30pm
- Location:
- Gmeet link: meet.google.com/ezs-fiec-gxd
- Description:
**Virtual Commutative Algebra seminars****Speaker:**Ramakrishna Nanduri, IIT Kharagpur**Date/Time:**Friday 11 November 2022, 5:30pmGmeet link: meet.google.com/ezs-fiec-gxd

**Title:**On the regularity of (symbolic) Rees algebra and (symbolic) powers of edge & vertex cover ideals of graphs**Abstract:**In this talk, we discuss the Castelnuovo-Mumford regularity (or regularity) of Rees algebras and symbolic Rees algebras of certain ideals associated with finite simple graphs and we give various combinatorial upper bounds. Also, we study the upper bounds for symbolic and ordinary powers of edge and vertex cover ideals of simple graphs.For more information and links to previous seminars, visit the website of VCAS:

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

- Time:
- 12:00pm - 1:00pm
- Location:
- Video call link: meet.google.com/yhv-azxc-yvj
- Description:
Speaker: Tapendu Rana Title: Lp-Boundedness of Pseudo-Differential Operators on Symmetric Spaces of Noncompact Type and Homogeneous Trees Date and time: Saturday, November 12, 12:00 pm – 1:00pm Google Meet joining info Video call link: meet.google.com/yhv-azxc-yvj The abstract is attached with this email.

- Time:
- 4:00pm - 4:45pm
- Location:
- Room No. A1A2, CDEEP, Department of Mathematics
- Description:
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.

- Time:
- 3:30pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Commutative algebra and algebraic Geometry seminar Speaker: R. V. Gurjar Dates: Tuesday, 8 and 15 November 2022 Time: 3.30-5.00 pm Venue: Ramanujan Hall Title : Positively Graded Domains Abstract : We will discuss positively graded affine domains over complex field from algebraic, geometric, and topological viewpoints. Important results by M. Demazure, I. Dolgachev, H. Flenner, S. Goto, A. Grothendieck, S. Mori, W. Neumann, P. Orlik- P. Wagreich, H. Pinkham, Keiichi Watanabe will be mentioned. A very general result "conjectured" by me in 1990 and proved by O. Mathieu around 2003 will be discussed. It has important consequences for rings of invariants of reductive algebraic groups. Many naturally occurring examples of positively graded domains will be discussed. If time permits, I will mention closely related results proved recently by A. Pramanik-S. Thandar-R.V. Gurjar about affine surfaces with finite fundamental group at infinity.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Date 16 November at 4 pm.

Speaker: Michel Waldschmidt, University of Sorbonne, Paris

Title On the degree of hypersurfaces with given singularities Abstract Let $n$, $t$ be positive integers and $S$ be a finite set of points in $\C^n$. We denote by $\omega_t(S)$ the least degree of a nonzero polynomial vanishing with multiplicity at least $t$ at each point of $S$. The sequence $(\omega_t(S)/t)_{t\ge 0}$ has a limite $\Omega(S)$ as $t$ tends to infinity. This invariant was introduced in 1975 for the proof of a Schwarz Lemma in several variables which occurs in the solution by Bombieri in 1970 of a conjecture of Nagata dealing with a generalization of a transcendence result of Schneider and Lang. The same invariant occurs in connection with another conjecture that Nagata introduced in 1959 in his work on Hilbert's 14th problem. It is closely related with Seshadri's constant.

- Time:
- 5:00pm
- Location:
- Video call link: https://meet.google.com/jmv-jpox-fcr
- Description:
Speaker: Mitul Islam (Heidelberg University)

Time: November 17, Thursday, 5 pm (Indian Standard Time)

Title: Understanding linear groups via real convex projective structures

Abstract: In recent years, real convex projective geometric structures

(which are a generalization of hyperbolic structures) have played an

important role in understanding discrete subgroups of projective general

linear groups. This has connections with several other areas like (higher)

Teichmüller theory and Anosov representations. In this talk, I will

discuss the notion of real convex projective structures and convex

co-compact groups and then study them from the perspective of geometric

group theory. In particular, I will discuss results (joint work with A.

Zimmer) that provide a complete geometric characterization of relatively

hyperbolic convex co-compact groups (with respect to any peripheral

subgroups).

Google Meet joining info

Video call link: https://meet.google.com/jmv-jpox-fcr

Or dial: (US) +1 208-715-5833 PIN: 835 386 658#

- Time:
- 3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Seminar on Linear Algebra Friday,18 November 2022 at 3.30 pm Venue: Ramanujan Hall Speaker: Rajesh Sharma, Himachal Pradesh University, Shimla Title: On some inequalities related to the Cauchy-Schwarz inequality in matrix algebra Abstract: We focus on the non-commutative versions of some inequalities related to the Cauchy-Schwarz inequality in matrix algebra. We discuss some inequalities involving positive unital linear maps on matrix algebra and demonstrate how positive linear maps can be used to obtain bounds for the spreads of matrices. The particular cases provide inequalities of statistical interest involving moments of discrete and continuous random variables.

- Time:
- 4:35pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Date: Friday, 18th November 2022 @4:35 pm

Venue: Ramanujan Hall

Speaker: T. N. Venkataramana, TIFR Mumbai

Title: Unipotent Generators for Higher Rank arithmetic Groups.

Abstract: Old results of Tits, Vaserstein, Raghunathan and myself say that the subgroup generated by elementary matrices, in any arithmetic higher rank group - namely the G(Z) of integer points of a simple algebraic group G defined over Q, is also arithmetic. The proofs rely on constructing a suitable completion of the group G(Q) of rational points and showing that this completion is a central extension of the (finite) adelic completion of G(Q). The other main ingredient of the proof relies on "Moore's uniqueness of reciprocity laws", which is used to deduce that

this extension is finite.In this talk I describe a modification of the proof which shows that only the centrality is enough; the technically complicated second step may be avoided.

- Time:
- 5:30pm
- Location:
- Gmeet link: meet.google.com/nrf-fugo-xzp
- Description:
Virtual Commutative algebra seminar Date and Time: Friday, 18 November 2022, 5:30pm Gmeet link: meet.google.com/nrf-fugo-xzp [1] Speaker: Mina Bigdeli, IPM, Tehran, Iran Title: Quadratic monomial ideals with almost linear free resolutions For more information and links to previous seminars, visit the website of VCAS: https://sites.google.com/view/virtual-comm-algebra-seminar [2]

- Time:
- 4:00pm - 4:45pm
- Location:
- Room No. A1A2, CDEEP, Department of Mathematics
- Description:
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.

- Time:
- 3:00pm - 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
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.

- Time:
- 9:30am - 10:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
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

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Mathematics Colloquium

Speaker: Antareep Mandal, IIT Madras

Venue: Ramanujan Hall

Date: 4 pm, 23 November 2022

Title: Uniform sup-norm bounds for Siegel cusp forms

Abstract: Obtaining sup-norm bounds for automorphic forms is a classical problem related to fundamental problems in analytic number theory as well as in arithmetic geometry, as, for example, the Lindelöf hypothesis for automorphic L-functions, quantum ergodicity and entropy bounds, or the study of Arakelov invariants of modular curves. This talk is about obtaining uniform sup-norm bounds of Siegel cusp forms on average over an orthonormal basis using the heat kernel on Siegel upper half-space. We employ various techniques from the theory of harmonic analysis on symmetric spaces and classical as well as spectral theories of automorphic forms.

First, we relate Siegel cusp forms to the bottom of the spectrum of the respective weighted Siegel-Maass Laplacian. Then we construct and analyze the corresponding heat kernel to arrive at the conjectured optimal bounds for both cocompact and cofinite arithmetic subgroups of the symplectic group. Further, we show that these bounds are uniform over a tower of arithmetic subgroups of finite index.

- Time:
- 2:30pm - 3:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
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.

- Time:
- 4:00pm
- Location:
- Video call link: https://meet.google.com/rmq-ijfz-edh
- Description:
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#

- Time:
- 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Algebraic geometry seminar Date and time: Thursday, 24 Nov. 2022, 5 pm Venue: Ramanujan Hall Speaker: Nitin Nitsure Title: Stacks and moduli

- Time:
- 5:30pm
- Location:
- Gmeet link: meet.google.com/gcb-evfu-wtu
- Description:
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

- Time:
- 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Number theory seminar****Date and time:**Monday, 28th November 2022, 4 pm**Venue:**Ramanujan Hall**Speaker:**Anatareep Mandal, IIT Madras**Title:**Heat kernel analysis and the sup-norm bound problem - A deeper dive**Abstract:**This is in continuation of the earlier talk on 'Uniform sup-norm bounds for Siegel cusp forms' last week. We elaborate on Flensted-Jensen's complex reduction technique for calculating spherical functions on real groups by reducing it to the complex case and then take a deeper dive into the estimation of sup-norm bound problem for cusp forms via analysis of heat kernels constructed using Flensted-Jensen's method.

- Time:
- 2:30pm
- Location:
- Room No 215, Department of Mathematics
- Description:
Date and time: Tuesday, 29 November at 2.30 pm Venue: Room 215 Speaker: Arindam Banerjee, IIT Kharagpur Title: A binomial type formula for integral closures of powers of monomial ideals. Abstract: Let I and J be two ideals in two polynomial rings A=K[x_1,....,x_m] and B=[y_1,...,y_n] respectively. Tai Ha et al. proved a binomial formula for $(I+J)^(n)$ in (A \tensor B) in terms of symbolic powers I^(t) and J^(t') where t and t' are less than or equal to n. A similar formula fails for integral closures of powers of ideals, even for monomial ideals. It has been shown in a recent joint work with Tai Ha that for monomial ideals some binomial type formula holds for integral closures of powers of (I+J). Using this formula we have also shown some formulas for regularity (and depth) of integral closures of powers of (I+J) in terms of regularity (and depth) of integral closures of lower powers of I and J. In this talk, we plan to discuss this work and some potential problems.

- Time:
- 3:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
**Statistics seminar****Date and time:**Tuesday, 29th November at 3:00 pm**Venue:**Ramanujan Hall.**Speaker:**Subrata Kundu, George Washington University (USA),**Title:**Some remarks on generalizations of the likelihood function and the likelihood principle**Abstract:**The sufficiency principle (SP), the weak conditionality principle (WCP), the likelihood function (LF), and the likelihood principle (LP) for a general statistical inference problem are discussed. It is argued that a general statistical problem can be regarded as a prediction problem by treating the quantity (z) of inferential interest as the realized but unobserved value of a random vector Z. The LF is defined as the density of the data given z and the unknown fixed parameters of the model, considered as a function of z and θ. The SP and WCP are modified such that they are equivalent to the LP based on the proposed LF.(Joint work with Tapan K. Nayak)

- Time:
- 2:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Mathematics Colloquium

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Speaker: Arindam Banerjee, IIT Kharagpur

Date: 30 November, 2022 at 2.30 pm

Venue: Ramanujan HallTitle: Castelnuovo-Mumford regularity of edge Ideals of graphs and their powers

Abstract: Regularity of edge ideals of graphs and their powers have been a very popular area of research in commutative algebra for the last one decade.

Edge ideals are one of the rare classes of ideals where linear resolution of the ideal implies linear resolution for higher powers i.e minimum possible regularity

for an edge ideal implies minimum possible regularity for all its higher powers(proved by Herzog, Hibi and Zheng). It was also characterised (by Froberg)

that an edge ideal has linear resolution (or minimum possible regularity) if and only if the underlying graph is chordal.This motivated people to

take up various projects for finding sharp upper bounds for regularity for various powers of edge ideals. Two questions largely guided this research:1. The Nevo-Peeva Question: Is it true that all higher powers (greater than equal to 2) have linear resolutions for edge ideals with

a. linear presentation (that is edge ideals whose first differential matrix of minimal free resolution has linear entries) and

b. regularity less than equal to $3$?2. The sharp upper bound Conjecture for regularity of powers in terms of the regularity of the ideal: It is believed that

regularity of an edge ideal is r implies for the s th power the regularity is bounded above by 2s+r-1.There has been much progress towards both of these but both remain open so far. Recently the second question has been

solved for all bipartite graphs. Also for all graphs the bound has been proven for the second power (r+2).

There has been some effort to study how regularity behaves "on an average for all graphs" using some probabilistic methods.In this talk we plan to discuss the history and current state of research in this area.

- Time:
- 4:00pm - 5:15pm
- Location:
- Room No. A1A2, CDEEP, Department of Mathematics
- Description:
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.

Hope to see you there!

Best wishes, Dipendra

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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.