- Time:
- 2:00pm - 3:30pm
- Location:
- Room No. 215 Department of Mathematics
- Description:
- Commutative Algebra seminar.

Speaker: R V Gurjar.

Affiliation: IIT Bombay.

Date and Time: Wednesday 04 September, 2:00 pm - 3:30 pm.

Venue: Room 215, Department of Mathematics.

Title: Shephard-Todd Theorem.

Abstract: We will present Chevalley's proof of this important result. As

applications, we will state several results from the paper of L. Avramov.

Proofs of some of these will be indicated.

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

Speaker: Tanmay Deshpande.

Affiliation: TIFR Mumbai.

Date and Time: Wednesday 04 September, 4:00 pm - 5:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: The Springer Correspondence and Character Sheaves.

Abstract: Using the Jordan normal form, the conjugacy classes of nilpotent

n x n matrices can be parametrized by partitions of n. On the other hand,

partitions of n also parametrize irreducible representations of the

permutation group S_n. In this talk, I will describe the Springer

correspondence which provides a deeper geometric understanding of the

above coincidence. Towards the end, I will sketch the ideas involved in

the proof of the Springer correspondence and their relationship with the

theory of character sheaves on reductive groups.

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

Speaker: Rudra P Sarkar.

Affiliation: ISI Kolkata.

Date and Time: Thursday 05 September, 4:00 pm - 5:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Asymptotic mean value property, a theorem of Plancherel and Polya.

Abstract: In rank one Riemannian symmetric spaces of noncompact type, we

shall characterize the eigenfunctions of the Laplace--Beltrami operator

with arbitrary eigenvalues through an asymptotic version of the ball mean

value property. This is joint work with Muna Naik and Swagato K Ray.

- Time:
- 4:30pm - 5:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG seminar.

Speaker: Maria Mathew.

Affiliation: IIT Bombay.

Date and Time: Friday 06 September, 4:30 pm - 5:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Gubeladze's geometric proof of Anderson's conjecture.

Abstract: Let M be a finitely generated seminormal submonoid of the free

monoid \mathbb Z_+^n and let k be a field. Then Anderson conjectured that

all finitely generated projective modules over the monoid algebra k[M] is

free. He proved this in case n=2. Gubeladze proved this for all n using

the geometry of polytopes. In a series of 3 lectures, we will outline a

proof of this theorem.

- Time:
- 11:30am - 1:00pm
- Location:
- Room No. 215 Department of Mathematics
- Description:
- Commutative Algebra seminar I.

Speaker: R V Gurjar.

Affiliation: IIT Bombay.

Date and Time: Monday 09 September, 11:30 am - 1:00 pm.

Venue: Room 215, Department of Mathematics.

Title: Invariant rings of pseudo-reflection groups.

Abstract: We will indicate proofs (based on L. Avramov's paper) of some of

the descent properties of rings of invariants of a finite

pseudo-reflection group acting on a local ring.

- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Combinatorics seminar.

Speaker: Venkata Raghu Tej Pantangi.

Affiliation: University of Florida and SUSTech, Shenzen, China.

Date and Time: Monday 09 September, 11:30 am - 12:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Critical groups of graphs.

Abstract: The critical group of a graph is an interesting isomorphic

invariant. It is a finite abelian group whose order is equal to the number

of spanning forests in the graph. The Smith normal form of the graph's

Laplacian determines the structure of its critical group. In this

presentation, we will consider a family of strongly regular graphs. We

will apply representation theory of groups of automorphisms to determine

the critical groups of graphs in this family

- Time:
- 2:30pm - 3:30pm
- Location:
- Room No. 215 Department of Mathematics
- Description:
- Speaker: Dilip Patil.

Affiliation: IISc, Bangalore.

Date and Time: Wednesday 11 September, 2:30 pm - 3:30 pm.

Venue: Room 215, Department of Mathematics.

Title: Formal Smoothness and Cohen Structure Theorems.

Abstract: We shall introduce smooth and formally smooth morphisms and

study their basic properties. We shall complete the proof of CST (Cohen’s

structure theorem for complete local rings).

- Time:
- 3:30pm - 4:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Analysis seminar.

Speaker: Jaikrishnan Janardhanan.

Affiliation: IIT Madras.

Date and Time: Wednesday 11 September, 3:30 pm - 4:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Holomorphic mappings into the symmetric product of a Riemann surface.

Abstract: The symmetric product is an interesting and important

construction that is studied in Algebraic Geometry, Complex Geometry,

Topology and Theoretical Physics. The symmetric product of a complex

manifold is, in general, only a complex space. However, in the case of a

one-dimensional complex manifold (i.e., a Riemann surface), it turns out

that the symmetric product is always a complex manifold. The study of the

symmetric product of planar domains and Riemann surfaces has recently

become very important and popular.

In this talk, we present two of our recent contributions to this study.

The first work (joint with Divakaran, Bharali and Biswas) gives a precise

description of the space of proper holomorphic mappings from a product of

Riemann surfaces into the symmetric product of a bordered Riemann

surface. Our work extends the classical results of Remmert and Stein. Our

second result gives a Schwarz lemma for mappings from the unit disk into

the symmetric product of a Riemann surface. Our result holds for all

Riemann surfaces and yet our proof is simpler and more geometric than

earlier proved special cases where the underlying Riemann surface was the

unit disk or, more generally, a bounded planar domain. This simplification

was achieved by using the pluricomplex Green's function. We will also

highlight how the use of this function can simplify several well-know and

classical results.

- Time:
- 4:30pm - 5:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Mathematics Colloquium.

Speaker: Parthanil Roy.

Affiliation: ISI Bangalore.

Date and Time: Wednesday 11 September, 4:30 pm - 5:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: How to tell a tale of two tails?

Abstract: We study the extremes of branching random walks under the

assumption that underlying Galton-Watson tree has infinite progeny mean.

It is assumed that the displacements are either regularly varying or have

lighter tails. In the regularly varying case, it is shown that the point

process sequence of normalized extremes converges to a Poisson random

measure. In the lighter-tailed case, however, the behaviour is much more

subtle, and the scaling of the position of the rightmost particle in the

n-th generation depends on the family of stepsize distribution, not just

its parameter(s). In all of these cases, we discuss the convergence in

probability of the scaled maxima sequence. Our results and methodology are

applied to study the almost sure convergence in the context of cloud speed

for branching random walks with infinite progeny mean. The exact cloud

speed constants are calculated for regularly varying displacements and

also for stepsize distributions having a nice exponential decay.

This talk is based on a joint work with Souvik Ray (Stanford University),

Rajat Subhra Hazra (ISI Kolkata) and Philippe Soulier (Univ of Paris

Nanterre). We will first review the literature (mainly, the PhD thesis

work of Ayan Bhattacharya) and then talk about the current work. Special

care will be taken so that a significant portion of the talk remains

accessible to everyone.

- Time:
- 2:00pm - 3:30pm
- Location:
- Room 215, Department of Mathematics
- Description:
- Commutative Algebra seminar III.

Speaker: Dilip Patil.

Affiliation: IISc, Bangalore.

Date and Time: Thursday 12 September, 2:00 pm - 3:30 pm.

Venue: Room 215, Department of Mathematics.

Title: Formal Smoothness and Cohen Structure Theorems.

Abstract: We shall introduce smooth and formally smooth morphisms and

study their basic properties. We shall complete the proof of CST (Cohen’s

structure theorem for complete local rings).

- Time:
- 11:00am - 12:00pm
- Location:
- Room No.215, Department of Mathematics
- Description:
- Combinatorics seminar.

Speaker: Niranjan Balachandran.

Affiliation: IIT Bombay.

Date and Time: Friday 13 September, 11:00 am - 12:00 pm.

Venue: Room No.215, Department of Mathematics.

Title: Equiangular lines in R^d.

Abstract: Suppose $0<\alpha<1$. The problem of determining the size of a

maximum set of lines (through the origin) in R^d s.t. the angle between

any two of them is arccos(\alpha) has been one of interest in

combinatorial geometry for a while now (since the mid 60s). Recently,

Yufei Zhao and some of his students settled this in a strong form. We will

see a proof of this result. The proof is a linear algebraic argument and

should be accessible to all grad students.

- Time:
- 4:30pm - 5:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG seminar.

Speaker: Maria Mathew.

Affiliation: IIT Bombay.

Date and Time: Friday 13 September, 4:30 pm - 5:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Gubeladze's geometric proof of Anderson's conjecture (Lecture II).

Abstract: Let M be a finitely generated seminormal submonoid of the free

monoid \mathbb Z_+^n and let k be a field. Then Anderson conjectured that

all finitely generated projective modules over the monoid algebra k[M] is

free. He proved this in case n=2. Gubeladze proved this for all n using

the geometry of polytopes. In a series of 3 lectures, we will outline a

proof of this theorem.

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

Speaker: Ayan Bhattacharya.

Affiliation: CWI, Amsterdam.

Date and Time: Tuesday 17 September, 4:00 pm - 5:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: PLFit estimation procedure and its consistency.

Abstract: In Clauset et. al. (2009), PLFit estimation procedure has been

proposed for the power-law index and became popular immediately for its

versatile applicability. This has been used in many areas including

scale-free networks, energy networks, preferential attachment model,

teletrafic data etc. But the theoretical support for this estimation

procedure is still lacking. In this talk, consistency of PLFit procedure

will be addressed under semiparametric assumption. This is an ongoing

joint work with Bohan Chen, Remco van der Hofstad and Bert Zwart.

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

Speaker: Rishabh Gvalani.

Affiliation: Imperial College London, United Kingdom.

Date and Time: Thursday 19 September, 3:00 pm - 4:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: A mountain pass theorem in the space of probability measures and

applications.

Abstract: We prove a version of the mountain pass theorem for lower

semicontinuous and lambda-geodesically convex functionals on the space of

probability measures P(M) equipped with the W_2 Wasserstein metric,

where M is a compact Riemannian manifold or R^d. As an application of this

result, we show that the empirical process associated to a system of

weakly interacting diffusion processes exhibits a form of noise-induced

metastability. The result is based on an analysis of the associated

McKean–Vlasov free energy, which for suitable attractive interaction

potentials has at least two distinct global minima at the critical

parameter value b = b_c. Joint work with Andre Schlichting.

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

Speaker: Rekha Biswal.

Affiliation: Max Planck Institute for Mathematics, Bonn, Germany.

Date and Time: Thursday 19 September, 4:00 pm - 5:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Macdonald polynomials and level two Demazure modules for affine

sl_{n+1}.

Abstract:- Macdonald polynomials are a remarkable family of orthogonal

symmetric polynomials in several variables. An enormous amount of

combinatorics, group theory, algebraic geometry and representation theory

is encoded in these polynomials. It is known that the characters of level

one Demazure modules are non-symmetric Macdonald polynomials specialized

at t=0. In this talk, I will define a class of polynomials in terms of

symmetric Macdonald polynomials and using representation theory we will

see that these polynomials are Schur-positive and are equal to the graded

character of level two Demazure modules for affine sl_{n+1}. As an

application we will see how this gives rise to an explicit formula for the

graded multiplicities of level two Demazure modules in the excellent

filtration of Weyl modules. This is based on joint work with Vyjayanthi

Chari, Peri Shereen and Jeffrey Wand.

- Time:
- 3:30pm - 5:00pm
- Location:
- Room 215, Department of Mathematics
- Description:
- Commutative Algebra seminar.

Speaker: R V Gurjar.

Affiliation: IIT Bombay.

Date and Time: Monday 23 September, 3:30 pm - 5:00 pm.

Venue: Room 215, Department of Mathematics.

Title: Paul Robert's Theorem.

Abstract: Let a finite abelian group G act on a normal local domain R

with residue field of R of char. 0. Assume that R^G is a UFD. Then R is a

free R^G- module. In particular, if R^G is regular then R is Cohen

Macaulay.

We will start preparation for P. Samuel's descent theory.

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

Speaker: Agnid Banerjee.

Affiliation: TIFR-CAM, Bangalore.

Date and Time: Monday 23 September, 4:00 pm - 5:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: The structure of the regular and the singular set of the free

boundary in the obstacle problem for fractional heat equation.

Abstract: In this talk, I will discuss the structure of the free boundary

in the obstacle problem for fractional powers of the heat operator. Our

results are derived from the study of a lower dimensional obstacle problem

for a class of local, but degenerate, parabolic equations. The analysis

will be based on new Almgren, Weiss and Monneau type monotonicity formulas

and the associated blow-up analysis. This is a joint work with D.

Danielli, N. Garofalo and A. Petrosyan.

- Time:
- 2:45pm - 3:45pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Mathematics Colloquium Talk II.

Speaker: Amalendu Krishna.

Affiliation: TIFR, Mumbai.

Date and Time: Wednesday 25 September, 2:45 pm - 3:45 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Revisiting Bertini theorems.

Abstract: The classical Bertini theorem in algebraic geometry says that a

general hyperplane section of a smooth quasi-projective subvariety of a

projective space over an algebraically closed field is also smooth. It was

already known long time ago that such a result holds over any infinite

field. However, this turned out to be false over finite field, as Katz

showed. Poonen then showed that Bertini theorem can be salvaged over

finite fields by allowing hypersurfaces of large degree rather than just

hyperplanes. In this talk, we shall revisit these Bertini theorems. In

particular, we shall prove new Bertini theorems for normal and integral

schemes over finite fields. This is based on a joint work with Mainak

Ghosh.

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

Speaker: Omprokash Das.

Affiliation: TIFR, Mumbai.

Date and Time: Wednesday 25 September, 4:00 pm - 5:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Birational classification of algebraic varieties.

Abstract: Algebraic varieties are common solutions of bunch of

multi-variable polynomials equations, for example, straight line, circle,

cuspidal curve, nodal curve, sphere, etc. Classifying all algebraic

varieties up to isomorphism is the ultimate goal of algebraic geometry. Of

course, this is nearly impossible achieve, so we consider various weaker

form of classification, and classifying varieties ‘Birationally’ is of

those tools. In this talk I will explain what it means to classify

varieties birationally, what are the difficulties in higher dimensions and

the role of Minimal Model Program (MMP) in birational classification.

- Time:
- 4:00pm - 5:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG seminar.

Speaker: Maria Mathew.

Affiliation: IIT Bombay.

Date and Time: Friday 27 September, 4:00 pm - 5:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Gubeladze's geometric proof of Anderson's conjecture, Lecture III.

Abstract: Let M be a finitely generated seminormal submonoid of the free

monoid \mathbb Z_+^n and let k be a field. Then Anderson conjectured that

all finitely generated projective modules over the monoid algebra k[M]

is free. He proved this in case n=2. Gubeladze proved this for all n using

the geometry of polytopes. In a series of 3 lectures, we will outline a

proof of this theorem.

- Time:
- 5:30pm - 6:30pm
- Location:
- Room No. 215 Department of Mathematics
- Description:
- Algebraic Groups seminar.

Speaker: Anupam Kumar Singh.

Affiliation: IISER Pune.

Date and Time: Friday 27 September, 5:30 pm - 6:30 pm.

Venue: Room 215, Department of Mathematics.

Title: z-classes in algebraic groups.

Abstract: Two elements of a group G are said to be z-equivalent if their

centralizers are conjugate within G. The z-equivalence is a weaker

relation than the conjugacy relation. Let G be an algebraic group defined

over a field k. Steinberg, proved that when G is a reductive group and k

is an algebraically closed field, G(k) has finitely many z-classes. This

result is generalised to more general base field k which are of type (F).

In this talk, we discuss the results on this problem.

- Time:
- 3:30pm - 5:00pm
- Location:
- Room No. 215 Department of Mathematics
- Description:
- Commutative Algebra seminar.

Speaker: R V Gurjar.

Affiliation: IIT Bombay.

Date and Time: Monday 30 September, 3:30 pm - 5:00 pm.

Venue: Room 215, Department of Mathematics.

Title: P. Samuel's descent theorem.

Abstract: Let R be a normal noetherian domain with a finite group of

automorphisms G. Samuel's result says that the kernel of the natural

homomorphism Cl(R^G)\to Cl(R) is a subgroup of H^1(G,U), where U is the

group of units in R.

If R is divisorially unramified over R^G then the kernel is isomorphic to

H^1(G,U). This enables us to find the divisor class groups of rings of

invariants of finite group actions on polynomial or power series rings. If

time permits two general constructions of cyclic unramified coverings of

normal varieties will be discussed.