November 2017
Public Access Category: All |

- Time:
- 11:00am - 12:30pm
- Location:
- Ramanujan Hall
- Description:
- Title: Eigenvalues and eigenvectors of the perfect matching association

scheme.

Abstract:

We revisit the Bose-Mesner algebra of the perfect matching association

scheme (aka the Hecke algebra of the Gelfand pair (S_2n, H_n), where

H_n is the hyperoctahedral group).

Our main results are:

(1) An algorithm to compute the eigenvalues from symmetric group

characters by solving linear equations.

(2) Universal formulas, as content evaluations of symmetric functions,

for the eigenvalues of fixed orbitals (generalizing a result of

Diaconis and Holmes).

(3) An inductive construction of the eigenvectors (generalizing a

result of Godsil and Meagher).

- Time:
- 11:00am
- Location:
- Room 215
- Description:
- Speaker: Reebhu Bhattacharya

Topic: Universal Bundles and Classifying Spaces

Abstract: We will talk about the classifying theorem of principal

G-bundles for a topological group G. For every group G, there is a

classifying space BG so that the homotopy classes of maps from a space X

to BG are in bijective correspondence with the set of isomorphism classes

of principal G-bundles over X. We will be outlining the construction, due

to Milnor, of a classifying space for any group G.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall
- Description:
- Speaker: Jerome Droniou, Monash university, Melbourne.

Title: ELLAM schemes for a model of miscible flow in porous medium: design

and analysis.

Abstract: Tertiary oil recovery is the process which consists in injecting

a solvent through a well in an underground oil reservoir, that will mix

with the oil and reduce its viscosity, thus enabling it to flow towards a

second reservoir. Mathematically, this process is represented by a coupled

system of an elliptic equation (for the pressure) and a parabolic equation

(for the concentration).

The parabolic equation is strongly convection-dominated, and discretising

the convection term properly is therefore essential to obtain accurate

numerical representations of the solution. One of the possible

discretisation techniques for this term involves using characteristic

methods, applied on the test functions. This is called the

Eulerian-Lagrangian Localised Adjoint Method (ELLAM).

In practice, due to the ground heterogeneities, the available grids can be

non-conforming and have cells of various geometries, including generic

polytopal cells. Along with the non-linear and heterogeneous/anisotropic

diffusion tensors present in the model, this creates issues in the

discretisation of the diffusion terms.

In this talk, we will present a generic framework, agnostic to the

specific discretisation of the diffusion terms, to design and analyse

ELLAM schemes. Our convergence result applies to a range of possible

schemes for the diffusion terms, such as finite elements, finite volumes,

discontinuous Galerkin, etc. Numerical results will be presented on

various grid geometries.

- Time:
- 3:30pm
- Location:
- Room 215, Department of Mathematics
- Description:
- Title: Higgs bundles

Abstract: We will describe the general fiber of the Hitchin fibration

for the classical groups.

- Time:
- 10:00am - 11:25am
- Location:
- Ramanujan Hall
- Description:
- Title: Gotzmann's regularity and persistence theorem - III

Abstract: Gotzmann's regularity theorem establishes a bound on

Castelnuovo-Mumford regularity using a binomial representation (the

Macaulay representation) of the Hilbert polynomial of a standard graded

algebra. Gotzmann's persistence theorem shows that once the Hilbert

function of a homogeneous ideal achieves minimal growth then it grows

minimally for ever. We start with a proof of Eisenbud-Goto's theorem to

establish regularity in terms of graded Betti numbers. Then we discuss

Gotzmann's theorems in the language of commutative algebra.

- Time:
- 10:00am - 11:00am
- Location:
- Room 215
- Description:
- Speaker: Udit Mavinkurve

Title: An Introduction to K-theory

Abstract: Topological K-theory was one of the first instances of a

generalized cohomology theory being used to successfully resolve classical

problems involving very concrete objects like vector fields and division

algebras. In this talk, we will briefly review some properties of vector

bundles, introduce the complex K groups, and discuss some of their

properties - including the all-important Bott periodicity theorem.

- Time:
- 3:30pm
- Location:
- Room 215, Department of Mathematics
- Description:
- Homotopy theory Seminar (Lecture 5)

Speaker: Rekha Santhanam

Time & Date: 3:30 PM 7th November

We will give proofs of Cellular approximation and then discuss fibrations

and Blaker-Massey Homotopy Excision thorem.

- Time:
- 11:00am
- Location:
- Ramanujan Hall
- Description:
- Combinatorics Seminar

Title: Eigenvalues and eigenvectors of the perfect matching

association scheme. (Part II)

Abstract:

We revisit the Bose-Mesner algebra of the perfect matching association

scheme (aka the Hecke algebra of the Gelfand pair (S_2n, H_n), where

H_n is the hyperoctahedral group).

Our main results are:

(1) An algorithm to compute the eigenvalues from symmetric group

characters by solving linear equations.

(2) Universal formulas, as content evaluations of symmetric functions,

for the eigenvalues of fixed orbitals (generalizing a result of

Diaconis and Holmes).

(3) An inductive construction of the eigenvectors (generalizing a

result of Godsil and Meagher).

- Time:
- 11:30am
- Description:
- Speaker: Prof.Cherif Amrouche, Mathematics, Universite de Pau,France.

Title: L^p -Theory for the Stokes and Navier-Stokes Equations with Different

Boundary Conditions.

Abstract: attached.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- Title: Betti Numbers of Gaussian Excursions in the Sparse Regime

Speaker: Gugan Thoppe

Date and Time: 16th November, 4.00 – 5.00 pm

Venue: Ramanujan Hall

Affiliation: Technion - Israel Institute of Technology, Haifa, Israel

(From Dec. 4th 2017, Duke University, North Carolina, USA).

Abstract is attached.

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

Speaker:Professor Bani K. Mallick, Department of Statistics, Texas A&M

University

Title:Bayesian Gaussian Graphical Models and their extensions

Abstract:

Gaussian graphical models (GGMs) are well-established tools for

probabilistic exploration of dependence structures using precision

(inverse covariance) matrices. We propose a Bayesian method for estimating

the precision matrix in GGMs. The method leads

to a sparse and adaptively shrunk estimator of the precision matrix, and

thus conduct model selection and estimation simultaneously. We extend this

method in a regression setup with the presence of covariates. We consider

both the linear as well as the nonlinear

regressions in this GGM framework. Furthermore, to relax the assumption of

the Gaussian distribution, we develop a quantile based approach for sparse

estimation of graphs. We demonstrate that the resulting graph estimator is

robust to outliers and applicable

under general distributional assumptions. We discuss a few applications of

the proposed models.

- Time:
- 2:30pm
- Location:
- Room 216
- Description:
- Classifying Spaces(Lecture II)

Abstract. We will continue our discussion of classifying spaces and talk about Milnor's construction of classifying spaces for any topological group. We will try to link this to the construction of classifying spaces given by G.Segal in his paper "Classifying Spaces and Spectral Sequences".

- Time:
- 11:00am - 12:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
- One-Sided Multicolor Discrepancy of Hyperplanes over Finite Fields

Anand Srivastav

Kiel University

Germany

Abstract:

We investigate the multicolor discrepancy and the one-sided

multicolor discrepancy of linear hyperplanes in the

finite vector space $F_{q}^{r}$.

We show that the one-sided discrepancy

is bounded from below

by $\Omega_{q}\left(\sqrt{n/c}\right)$, $c$ the number of colors, using

Fourier analysis on $\mathbb{F}_{q}^{r}$.

We also show an upper bound of

of $O_{q}(\sqrt{n\log c})$. The upper bound is derived by

the $c$--color extension of Spencer's six standard deviation theorem

and is also valid for the one-sided discrepancy.

Thus, the gap between the upper and lower bound for the one-sided

discrepancy

is a factor of $\sqrt{c\log c}$ and the bounds are tight for any

constant $c$ and $q$. For large $c$, more

precisely for $c\geq qn^{1/3}$, we reduce this gap to a factor

of $\sqrt{\log c}$. All together this exhibits a new example of

a hypergraph with (almost) sharp discrepancy bounds.