- 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.