November 2017
Public Access Category: All |
11am» Murali Srinivasan- 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.