- Time:
- 10:30am - 12:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Algebraic Groups Seminar.

Speaker: Anupam Kumar Singh.

Affiliation: IISER Pune.

Date and Time: Monday 01 April, 10:30 am - 12:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: On Shalev's conjecture for type A_n and {}^2A_n.

Abstract: Let G be a group and w a word map on G. Shalev and others

computed bounds for |w(G)|/|G| when G is a finite simple group of Lie type

and showed that the lower bound is c/n except for type A_n and {}^2A_n. He

further conjectured that the same bound is expected for these cases as

well. In this talk, we present our exploration in this direction

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

Speaker: Ujjwal Das.

Affiliation: IIM Udaipur, Rajasthan.

Date and Time: Tuesday 02 April, 3:30 pm - 4:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Inference on zero inflated ordinal models with semiparametric link.

Abstract: In socioeconomic and Biological studies, observations on

individuals are often observed longitudinally on a Likert-type scale with

substantially large proportion of zeros. This leads to a special case of

mixture structured data where extra-variation occurs. Obviously the

standard ordinal data analysis fails to provide appropriate statistical

inference. We propose a suitable zero inflated semi parametric ordinal

model that takes into account the non linear link between the ordinal

response and a covariate. A sieve maximum likelihood estimator(MLE) is

proposed for the regression parameter of interest. We also propose a test

for the zero proportion in this semi parametric model. A simulation study

has been carried out to investigate the performance of the estimator as

well as the test.

- Time:
- 3:00pm - 3:50pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Popular Talk.

Speaker: Harsha Hutridurga.

Date and Time: Wednesday 03 April, 3:00 pm - 3:50 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Intrigue of Invisibility cloaking.

Abstract: Rendering objects or oneself invisible to others has fascinated

us since the dawn of human civilization. Illustration of such vanishing

acts are often made in sci-fi movies. Even though this idea of making

oneself invisible to others sounds out of reach, lately it is gaining

traction in the scientific community. This has led to the emergence of a

fascinating field of meta-materials which deals with the design and study

of assemblies of ordinary materials such that the assembly as a whole

behaves in an exotic manner. This talk will try to present some elementary

ideas involved in the theory of invisibility cloaking. The talk is

intended for non-experts and will be accessible to people familiar with

basic notions in multivariable calculus.

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

Speaker: Rachel Kuske.

Affiliation: Georgia Tech.

Date and Time: Wednesday 03 April, 4:00 pm - 5:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Prevalence of heavy-tailed distributions in systems with multiple

scales: insights through stochastic averaging.

Abstract: Heavy tailed distributions have been shown to be consistent with

data in a variety of systems with multiple time scales. Recently,

increasing attention has appeared in different phenomena related to

climate. For example, correlated additive and multiplicative (CAM)

Gaussian noise, with infinite variance or heavy tails in certain parameter

regimes, has received increased attention in the context of atmosphere

and ocean dynamics. We discuss how CAM noise can appear generically in

many reduced models. Then we show how reduced models for systems driven by

fast linear CAM noise processes can be connected with the stochastic

averaging for multiple scales systems driven by alpha-stable processes. We

identify the conditions under which the approximation of a CAM noise

process is valid in the averaged system, and illustrate methods using

effectively equivalent fast, infinite-variance processes. These

applications motivate new stochastic averaging results for systems with

fast processes driven by heavy-tailed noise. We develop these results for

the case of alpha-stable noise, and discuss open problems for identifying

appropriate heavy tailed distributions for these multiple scale systems.

This is joint work with Prof. Adam Monahan (U Victoria) and Dr. Will

Thompson (UBC/NMi Metrology and Gaming).

- Time:
- 3:30pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Algebraic K-Theory Seminar.

Speaker: Manoj Keshari.

Date and Time: Friday 05 April, 3:30 pm - 5:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: K_0 of a ring (2nd lecture).

- Time:
- 5:15pm - 6:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG Seminar.

Speaker: Madhusudan Manjunath.

Date and Time: Friday 05 April, 5:15 pm - 6:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Lorenzini Zeta Function of a Graph.

Abstract: We will see a two variable zeta function associated with a graph

due to Dino Lorenzini. I will mainly spend time discussing divisor theory

on graphs that arises in the definition of this zeta function.

- Time:
- 7:30pm - 8:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- IITB Mathematics Colloquium via videoconference.

Speaker: Luke Oeding.

Affiliation: Auburn University.

Date and Time: Monday 08 April, 7:30 pm - 8:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Tensors and Syzygies.

Abstract: Tensors are higher dimensional analogues of matrices. But unlike

matrices, there is still so much we don't know about their fundamental

algebraic properties. For example, for rank-r matrices we know that the

determinants of all (r+1)-minors of the matrix furnish a generating set

for the ideal of all relations among the entries of such matrices, but for

general rank-r tensors we have almost no idea what polynomials generate

their ideals. Moreover the entire minimal free resolution of the ideal in

the matrix case is know in terms of representation theory (Lascoux,

Eagon-Northocott, Weyman, and others), but relatively little is known in

the tensor case, (not even the length of the resolution).

I'll present evidence toward a conjecture on arithmetic

Cohen-Macaulay-ness that would generalize the Eagon-Hochster result in the

matrix case. I'll also highlight recent work with Raicu and Sam where we

compute precise vanishing and non-vanishing of the syzygies of rank-1

tensors.

- Time:
- 11:30am - 12:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Combinatorics and Theoretical Computer Science seminar.

Speaker: Rahul Santhanam.

Affiliation: University of Oxford.

Date and Time: Tuesday 09 April, 11:30 am - 12:30pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Independence Results in Propositional Proof Complexity.

Abstract: Given the lack of progress on complexity lower bounds, it is

natural to ask whether they are hard to prove, in some formal sense. I

will begin by briefly describing the classical incompleteness results of

Godel and Chaitin, and posing the question for whether there are analogues

of these results in complexity theory.

I will then introduce the finitistic framework of propositional proof

complexity, where we are interested in the existence of polynomial size

proofs verifiable in polynomial time. I will explain what it means to

prove circuit complexity or proof complexity lower bounds in this

framework. Finally, I will describe a strong complexity conjecture for

which it can be shown unconditionally that there are no feasible

propositional proofs, in a certain technical sense.

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

Speaker: Shuddhodan.

Affiliation: Freie Universitat, Berlin.

Date and Time: Tuesday 09 April, 2:30 pm - 3:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Self maps of varieties over finite fields.

Abstract: Esnault and Srinivas proved that as in de Rham cohomology over

the complex numbers, the value of the entropy of an automorphism of a

smooth proper surface over a finite field $\F_q$ is taken in the span of

the Neron-Severi group inside of of $\ell$-adic cohomology. In this talk

we will discuss some analogous questions in higher dimensions motivated by

their results and techniques.

- Time:
- 3:30pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Algebraic K-Theory Seminar.

Speaker: Manoj Keshari.

Date and Time: Friday 12 April, 3:30 pm - 5:00 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: K_0 of an exact category (3rd lecture).

- Time:
- 5:15pm - 6:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG Seminar.

Speaker: Madhusudan Manjunath.

Date and Time: Friday 12 April, 5:15 pm - 6:30 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Lorenzini Zeta Function of a Graph.

Abstract: We will see a two variable zeta function associated with a graph

due to Dino Lorenzini. I will mainly spend time discussing divisor theory

on graphs that arises in the definition of this zeta function.

- Time:
- 10:30am - 12:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Lecture Series on Partial Differential Equations.

Speaker: Kirill Cherednichenko.

Affiliation: University of Bath.

Title: Periodic PDEs with micro-resonators: unified approach to

homogenisation and time-dispersive media.

Venue: Ramanujan Hall, Department of Mathematics.

Date and Time: Tuesday 16 April, 10.30 am - 12.30 pm

Lecture I:

An overview of the mathematical theory of homogenisation as a toolbox for the analysis of multiscale problems. Wave propagation: resonant and nonresonant regimes. Non-resolvent estimates, time dispersion, and metamaterials: amotivation for a novel homogenisation principle.

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

Title : Grothendieck's theorem on algebraic de Rham cohomology of

varieties

Speaker: Saurav Bhaumik

Time & Date: 4-5pm, Tuesday 16th April.

Venue: Ramanujan Hall.

Abstract: Let X be a smooth scheme of finite type over C, and let X' be

the corresponding complex analytic variety. Grothendieck proved that the

complex cohomologies H^q(X') can be calculated as the hypercohomologyes of

the algebraic de Rham complex on X. We will present Grothendieck's proof.

- Time:
- 5:10pm - 6:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Popular Talk in Mathematics.

Speaker: Atharva Korde.

Date and Time: Tuesday, 16 April. 5.10 pm - 6.00 pm.

Refreshments will be served before the talk.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Secret avatars of two spaces.

Abstract: The spaces SL(2, R) and SL(2,R)/SL(2, Z) look quite difficult to

visualize at first glance. In this talk, we shall see that these two

spaces are actually homeomorphic to some nice-looking spaces.

- Time:
- 10:30am - 12:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Lecture Series on Partial Differential Equations.

Speaker: Kirill Cherednichenko.

Affiliation: University of Bath.

Title: Periodic PDEs with micro-resonators: unified approach to

homogenisation and time-dispersive media.

Venue: Ramanujan Hall, Department of Mathematics.

Wednesday 17 April, 10.30 am - 12.30 pm

Lecture II.

Spectral boundary-value problems: boundary triples and the corresponding M-operators (“Dirichlet-to-Neumann maps”). Their role in the quantitative analysis of degenerate problems. Krein formula for a generalised Robin problem.

- Time:
- 10:00am - 12:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Lecture Series on Partial Differential Equations.

Speaker: Kirill Cherednichenko.

Affiliation: University of Bath.

Title: Periodic PDEs with micro-resonators: unified approach to

homogenisation and time-dispersive media.

Venue: Ramanujan Hall, Department of Mathematics.

Thursday 18 April, 10.00 am - 12.00 pm

Lecture III:

Periodic media with resonant components (“high contrast composites”). Gelfand transform and direct integral: a reduction of the full-space problem

to a family of “transmission” problems on the period cell. A reformulation in terms

of the M-operator on the interface. Diagonalisation of the M-operator on the nonresonant component: Steklov eigenvalue problem.

- Time:
- 5:15pm - 6:15pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- CACAAG seminar.

Speaker: Priyamvad Srivastav.

Affiliation: IMSc, Chennai.

Date and Time: Thursday 18 April, 5.15 pm - 6.15 pm.

Venue: Ramanujan Hall, Department of Mathematics.

Title: Product of primes in arithmetic progression.

Abstract: Let $q$ be a positive integer and let $(a,q)=1$ be a given

residue class. Let $p(a,q)$ denote the least prime congruent to $a

\mod{q}$. Linnik's theorem tells us that there is a constant $L>0$, such

that the $p(a,q) \ll q^L$. The best known value today is $L = 5.18$.

A conjecture of Erdos asks if there exist primes $p_1$ and $p_2$, both

less than $q$, such that $p_1 p_2 \equiv a \mod{q}$. Recently, Ramar\'{e}

and Walker proved that for all $q \geq 2$, there are primes $p_1, p_2,

p_3$, each less than $q^{16/3}$, such that $p_1 p_2 p_3 \equiv a \mod{q}$.

Their proof combines additive combinatorics with sieve theoretic

techniques. We sketch the ideas involved in their proof and talk about a

joint work with Olivier Ramar\'{e}, where we refine this method and obtain

an improved exponent of $q$.

- Time:
- 10:30am - 12:30pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Lecture Series on Partial Differential Equations.

Speaker: Kirill Cherednichenko.

Affiliation: University of Bath.

Title: Periodic PDEs with micro-resonators: unified approach to

homogenisation and time-dispersive media.

Venue: Ramanujan Hall, Department of Mathematics.

Friday 19 April, 10.30 am - 12.30 pm.

Lecture IV.

Schur-Frobenius inversion formula the generalised resolvent on the

resonant inclusion. An effective description of the original family of transmission

problems. A time-dispersive effective formulation in the whole space. An example

of the effective formulae for a specific cell geometry. Band gaps and “metamaterial”

properties.

- Time:
- 2:30pm - 3:30pm
- Location:
- Room No. 113, Department of Mathematics
- Description:
- Commutative algebra:

Date, Time, Venue: Friday, 19th Apr, 2:30 - 3:30 p.m.,Commutative algebra Room 113.

Title: Pure modules and Cohen-Macaulay rings

Abstract: This is a talk in Boij-Soderberg theory, which involves the

study of Betti cones over quotients of polynomial rings. These were

introduced by Boij-Soderberg in 2008, and explored further by

Eisenbud-Schreyer in 2009. I will give a quick introduction to this theory

and the main problems.

Finally, I will point out how of a result of mine (joint with Rajiv

Kumar) on the construction of pure modules over Cohen-Macaulay rings

follows immediately from the work of Eisenbud-Schreyer using Noether

Normalization, and the Auslander-Buchsbaum Formula (which are two

important results the students proved in the reading course).

I will try to make the talk as self-contained as possible. All are welcome.

- Time:
- 9:00am - 10:15am
- Location:
- Room No. 114, Department of Mathematics
- Description:
- Time: 9.00 am - 10.15 am.

Speaker: R.V. Gurjar.

Title: Linquan Ma’s generalisations of Lech’s Conjecture

Abstract: The following two results will be considered. Let (A,M) ⊂ (R,N) be a local ﬂat homomorphism with A a regular local ring such that A contains its residue ﬁeld. Let I be an ideal in A. Then eR/IR ≥ eR, where e denotes the multiplicity. Ma has stated four conjectures related to Lech’s Conjecture. We will discuss the relationships between these conjectures. If time permits, I will indicate how we can understand C.P. Ramanujam’s geometric interpretation of multiplicity in a more intuitive manner.

- Time:
- 10:15am - 11:30am
- Location:
- Room No. 114, Department of Mathematics
- Description:
- Time:10.15 am - 11.30 am.

Speaker: Sudeshna Roy

Title: Linquan Ma’s solution of the cyclic generalised Lech’s conjecture for graded rings

Abstract: Let R be a standard graded K-algebra and I be a homogeneous ideal. In this talk we show that if pdRR/I < ∞, then eR | eR/I. In particular, eR ≤ eR/I.

- Time:
- 11:45am - 1:00pm
- Location:
- Room No. 114, Department of Mathematics
- Description:
- Time: 11.45 am - 01.00 pm.

Speaker: Kriti Goel.

Title: Numerically Robert rings.

- Time:
- 2:30pm - 3:45pm
- Location:
- Room No. 114, Department of Mathematics
- Description:
- Time: 02.30 pm - 03.45 pm.

Speaker: Mitra Koley.

Title: Lech’s conjecture for 3-dimensional Gorenstein rings

Abstract for (3) and (4): Ma formulated a weakened generalised Lech’s conjecture and proved it for a class of rings known as numerically Roberts rings, in equal characteristic p > 0. Using these results, combined with results on Hilbert-Kunz multiplicities, he proved the Lech’s conjecture for 3-dimensional Gorenstein rings of equal characteristic p > 0. In the ﬁrst part of the talk, we deﬁne numerically Roberts rings and prove a few results required for proving the main result, which will be proved in the second part of the talk.

- Time:
- 4:00pm - 5:15pm
- Location:
- Room No. 114, Department of Mathematics
- Description:
- Time: 4.00 pm - 5.15 pm.

Speaker: Shreedevi Masuti.

Title: The Stru¨ckrad-Vogel conjecture

Abstract: Let M be a ﬁnite module of dimension d over a Noetherian local ring (R,m). The set{`(M/IM)/e(I,M)}, where I varies over m-primary ideals, is bounded below by (1/d!)e(R/textannM). If ˆ M is equidimensional, this set is bounded above by a constant depending only on M. The lower bound extends an inequality of Lech and the upper bound answers a question of Stru¨ckrad-Vogel.