- Time:
- 9:30am - 11:00am
- Location:
- A1A2 hall, CDEEP, IIT Bombay
- Description:
- Name of the instructor: Prof. Eduard Feireisl.

Affiliation: Czech Academy of Sciences.

Mode of instruction: via videoconference.

Title of the mini-course: Mathematical Aspects of Euler Equations.

Venue: A1A2 hall, CDEEP, IIT Bombay.

We consider the phenomenon of oscillations in the solution families to partial differential equations. To begin, we briefly discuss the mechanisms preventing oscillations/concentrations and make a short excursion in the theory of compensated compactness. Pursuing the philosophy "everything what is not forbidden is allowed" we show that certain problems in fluid dynamics admit oscillatory solutions. This fact gives rise to two rather unexpected and in a way contradictory results: (i) many problems describing inviscid fluid motion in several space dimensions admit global-in-time (weak solution); (ii) the solutions are not determined uniquely by their initial data. We examine the basic analytical tool behind these rather ground breaking results - the method of convex integration applied to problems in fluid mechanics and, in particular, to the Euler system.

- Time:
- 11:00am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Combinatorics Seminar

Speaker : Nishad Kothari.

Time: 11 AM, Friday, 1st February.

Venue: Ramanujan Hall.

Title : Pfaffian Orientations and Conformal Minors.

Abstract: See attachment.

- Time:
- 11:30am - 1:00pm
- Location:
- A1A2 hall, CDEEP, IIT Bombay
- Description:
- Name of the instructor: Prof. Eduard Feireisl.

Affiliation: Czech Academy of Sciences.

Mode of instruction: via videoconference.

Title of the mini-course: Mathematical Aspects of Euler Equations.

Venue: A1A2 hall, CDEEP, IIT Bombay.

We consider the phenomenon of oscillations in the solution families to partial differential equations. To begin, we briefly discuss the mechanisms preventing oscillations/concentrations and make a short excursion in the theory of compensated compactness. Pursuing the philosophy "everything what is not forbidden is allowed" we show that certain problems in fluid dynamics admit oscillatory solutions. This fact gives rise to two rather unexpected and in a way contradictory results: (i) many problems describing inviscid fluid motion in several space dimensions admit global-in-time (weak solution); (ii) the solutions are not determined uniquely by their initial data. We examine the basic analytical tool behind these rather ground breaking results - the method of convex integration applied to problems in fluid mechanics and, in particular, to the Euler system.

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

Speaker: Ramachandran Balasubramanian.

Time: 4:30-5:30 pm, Friday 1 February, 2018.

Venue: Ramanujan Hall.

Title: Zeta Functions Associated to Graphs.

Abstract: This series of talks will cover various notions of zeta

functions associated to graphs

- Time:
- 2:00pm - 3:30pm
- Location:
- Room No. 216 Department of Mathematics
- Description:
- Speaker: Dipendra Prasad.

Time: Wednesday 06 February, 2-3:30pm.

Venue: Room 216.

Title: "An introduction to Lie groups, Symmetric spaces, and Shimura

varieties based on examples".

Abstract: I will give an introductory course of 3-4 lectures on the topics

mentioned in the title to an audience without any prior knowledge of the

subject which is a meeting ground for Differential geometry, Algebraic

geometry, and Number theory.

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

Speaker: Lionel Levine, Cornell University.

Time: Wednesday, 06 February, 4pm.

Venue: Ramanujan Hall.

Title: Circles in the sand.

Abstract: I will describe the role played by an Apollonian circle packing

in the scaling limit of the abelian sandpile on the square grid Z^2. The

sandpile solves a certain integer optimization problem. Associated to each

circle in the packing is a locally optimal solution to that problem. Each

locally optimal solution can be described by an infinite periodic pattern

of sand, and the patterns associated to any four mutually tangent circles

obey an analogue of the Descartes Circle Theorem. Joint work with Wesley

Pegden and Charles Smart.

- Time:
- 11:30am
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Probability Statistics seminar

Speaker: Fabrice Gamboa, Toulouse Institute of Mathematics

Time: Thursday 07 February, 11:30 am-- 12:30 am.

Venue: Ramanujan Hall.

Title: Sum rules and large deviations,

Abstract: In a famous paper published in Annals of Mathematics (2003),

Killip and Simon gave a Szegö like theorem for the circular law (sum

rule). The proof of this sum rule relies on mathematical analysis. This

sum rule relates the Kullback-Leibler information with respect to the

semi-circular law to coefficients involved in the recursive construction

of the orthogonal polynomials. Using the theory of large deviations for

random matrices we recover easily this sum rules and provide a full

machinery to establish and prove new ones.

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

Speaker: Ramachandran Balasubramanian.

Time: 2:30-3:30 pm, Friday 08 February, 2018.

Venue: Ramanujan Hall.

Title: Zeta Functions Associated to Graphs.

Abstract: This series of talks will cover various notions of zeta

functions associated to graphs.

- Time:
- 3:45pm - 5:15pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- K-Theory Seminar.

Speaker: Sudarshan Gurjar.

Time: Friday 08 February, 3:45 - 5:15 pm.

Venue - Ramanujan Hall.

Title: Topological vector bundles.

- Time:
- 2:00pm - 3:30pm
- Location:
- Room No. 216 Department of Mathematics
- Description:
- Lecture Series.

Speaker: Dipendra Prasad.

Date and Time: Wednesday 13 February, 2.00pm - 3.30pm.

Venue: Room 216.

Title: An introduction to Lie groups, Symmetric spaces and Shimura

varieties based on examples.

Abstract: I will give an introductory course of 3-4 lectures on the topics

mentioned in the title to an audience without any prior knowledge of the

subject which is a meeting ground for Differential geometry, Algebraic

geometry, and Number theory.

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

Speaker: Tejas Kotwal.

Date and Time: Wednesday 13 February, 4.00pm - 5.00pm.

Venue: Ramanujan Hall.

Title: Dynamics in Linear Algebra.

Abstract: In this talk, I shall first give an introduction to the subject

of dynamical systems. After going through a few concepts that arise in

dynamical systems through examples, we see how similar ideas can be

interpreted in the context of linear algebra. In particular, we deal with

finite dimensional complex vector spaces and end by understanding a simple

proof of the Cayley-Hamilton theorem. An interesting aspect of this

approach is that we can avoid the machinery of determinants altogether.

- Time:
- 11:00am - 12:30pm
- Location:
- Room No. 105 Department of Mathematics
- Description:
- PDE Seminar.

Speaker: Harsha Hutridurga.

Date and Time: Thursday 14 February, 11.00am - 12.30pm.

Venue: Room 105.

Title: Neutron Transport meets Luc Tartar.

Abstract: In this talk, we will address the homogenization of a neutron

transport model while the scattering coefficients in the equation exhibit

rapid oscillations with respect to the energy variable.

It turns out that this problem has very close links to a result of Luc

Tartar from late 1980's. Hence we will be revisiting this paper of Luc

Tartar.

Our discussions will revolve around

(i) Laplace transform and Bernstein's theorem from the theory of Regular

variation

(ii) Nevanlinna-Herglotz function from complex analysis

(iii) Two-scale convergence and Young measures from the theory of

homogenization.

This talk is based on a recent preprint:

Harsha Hutridurga, Olga Mula, Francesco Salvarani,

Homogenization in the energy variable for a neutron transport model,

arXiv:1901.10164

Weblink: https://arxiv.org/pdf/1901.10164.pdf

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

Speaker: Ronnie Sebastian.

Date and Time: Friday 15 February, 3 pm

Venue: Ramanujan Hall.

Title: Algebraic vector bundle.

- Time:
- 3:30pm - 5:00pm
- Location:
- Room No. 215 Department of Mathematics
- Description:
- PDE Seminar.

Speaker: Harsha Hutridurga.

Date and Time: Tuesday 19 February, 3.30pm - 5.00pm.

Venue: Room 215.

Title: Structure breaking by homogenization.

Abstract: In this talk, we will give an alternate (and constructive) proof

to a result of Luc Tartar which demonstrated the loss of semi-group

structure due to the presence of high frequency oscillations in

coefficients. The discussions will revolve around

(i) the notion of weak convergence in Lp spaces;

(ii) the notion of two-scale convergence in the theory of homogenization.

Furthermore, we shall discuss some interesting results in the context of

(i) structure breaking in other differential equations;

(ii) inverse homogenization.

We also intend to list some related open problems which are accessible to

available techniques.

- Time:
- 3:00pm - 3:50pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Prof. Vydas Cekanavicius.

Affiliation: Vilnius University, Lithuania.

Date and Time: Wednesday 20 February, 3.00 pm - 3.50 pm.

Venue: Ramanujan Hall.

Title: Multivariate Compound Poisson approximations for sums of weakly

dependent random vectors.

Abstract: See attached document.

- Time:
- 4:10pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Speaker: Prof. Hira Lal Koul.

Affiliation: Michigan State University, USA.

Date and Time: Wednesday 20 February, 04:10 pm - 05.00 pm.

Venue: Ramanujan Hall.

Title: Asymptotic distribution of the bias corrected LSEs in measurement

error linear regression models under long memory.

Abstract: See attached document.

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

Speaker: Sutanu Roy.

Affiliation: NISER Bhubaneswar.

Date and Time: Friday 22 February, 3:00 pm - 4:00 pm.

Venue: Ramanujan Hall.

Title: Quantum plane and duality.

Abstract: A quantum analogue of complex plane is the C*-algebra B

"generated" by an unbounded operator n satisfying the commutation relation

n^{*}n=q^{2}nn^{*} for some real number 0will be the construction of the (braided) quantum group structure on B.

The braiding is governed by the canonical action of the circle group and

the group of integers on n. Moreover, I shall briefly present (generalised

Pontrjagin) duality result for B.

- Time:
- 5:00pm - 6:30pm
- Location:
- Room No. 114 Department of Mathematics
- Description:
- CACAAG seminar.

Speaker: Prof. Balasubramanian.

Date and Time: Friday 22 February, 5.00pm - 6.30pm.

Venue: Room 114.

Title: Zeta Functions Associated to Graphs.

Abstract: This series of talks will cover various notions of zeta

functions associated to graphs.

- Time:
- 3:00pm - 4:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Combinatorics and Theoretical Computer Science seminar.

Speaker: Yuval Filmus.

Affiliation: Technion, Haifa, Israel.

Date and Time: Monday 25 February, 3.00pm - 4.00pm.

Venue: Ramanujan Hall, Mathematics Department, IIT Bombay.

Title: Twenty Questions: Distributional Search Theory.

Abstract: I’m thinking of a person in the audience. How long will it

take you to find whom, using only Yes/No questions?

We consider this puzzle, which underlies search theory, with a twist: I’m

choosing the person according to a known distribution, and your goal is to

minimize the expected number of questions. How does the performance of

your strategy depend on the type of question you’re allowed to ask? On the

type of distribution I am allowed to choose? What happens if I can lie?

Joint work with Yuval Dagan (MIT), Ariel Gabizon (Zcash), Daniel

Kane(UCSD), Shay Moran (IAS).