- Time:
- 3:00pm - 4:00pm
- Location:
- Room No. 216
- Description:
- Title: Estimating parameters of directional distributions

Abstract: Data related to spread of disease bacteria, wind directions, seasonal variations etc. can be represented by directional distributions. Langevin distribution is one of most commonly used directional distributions. We unify the results on admissibility, minimaxity and best equivariance of MLE of direction parameter. Various other estimators of direction parameter are compared with respect to robustness and asymptotic efficiency. Methods of improving estimators for spherical location are developed. Special applications to problems in restricted parameter spaces are given.

- Time:
- 3:30pm - 4:30pm
- Location:
- Mini conference room, Mathematics department
- Description:
- Title: Study of a nonlinear renewal equation with diffusion

Abstract: We consider a nonlinear age structured McKendrick-von Foerster

population model with diffusion term (MV-D). We prove the existence and

uniqueness of solution of the MV-D equation. We also prove the convergence

of the solution to its steady state as time tends to infinity using the generalized relative entropy inequality and Poincare Writinger type inequality.

We propose a numerical scheme for the linear MV-D equation. We discretize

the time variable to get a system of second order ordinary differential

equations. Convergence of the scheme is established using the stability

estimates by introducing Rothe’s function.

- Time:
- 4:00pm
- Location:
- Ramanujan Hall
- Description:
- Speaker: Prof. Dinakar Ramakrishnan

Title: Rational Points

Abstract: Since time immemorial, people have been trying to understand the rational number solutions of systems of homogeneous polynomial equations with integer coefficients (called a Diophantine system). It is more convenient to think of them as rational points on associated projective varieties X, which we wll take to be smooth. This talk will introduce the various questions of this topic, and briefly review the reasonably well understood one-dimensional situation. But then the focus will be on dimension 2, and some progress for those covered by the unit ball will be discussed. The talk will end with a program (joint with Mladen Dimitrov) to establish an analogue of a result of Mazur.

- Time:
- 11:00am - 12:00pm
- Location:
- Ramanujan Hall
- Description:
- Speaker: Dr. Samiran Ghosh,

Associate Professor of Biostatistics

Department of Family Medicine and Public Health Sciences,

Wayne State University School of Medicine

Title: “ON THE ESTIMATION OF THE INCIDENCE AND PREVALENCE RATE IN A TWO-PHASE LONGITUDINAL SAMPLING DESIGN”

Abstract:

Two-phase sampling design is a common practice in many medical studies with rare disorders. Generally, the first-phase classification is fallible but relatively cheap, while the accurate second-phase state of-the-art medical diagnosis is complex and rather expensive to perform. When constructed efficiently it offers great potential for higher true case detection as well as for higher precision. In this talk, we consider epidemiological studies with two-phase sampling design. However, instead of a single two-phase study we consider a scenario where a series of two-phase studies are done in longitudinal fashion. Efficient and simultaneous estimation of prevalence as well incidence rate are being considered at multiple time points from a sampling design perspective. Simulation study is presented to measure accuracy of the proposed estimation technique under many different circumstances. Finally, proposed method is applied to a population of elderly adults for the prognosis of major depressive disorder.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall
- Description:
- Title: Rost nilpotence

Abstract:The Rost nilpotence principle is an important tool in the study of motivic decompositions of smooth projective varieties over a field. We will introduce this principle and briefly survey the cases in which it is known to hold. We will then outline a new approach to the question using etale motivic cohomology, which helps us to give a simpler and more conceptual proof of Rost nilpotence for surfaces, generalize the known results over one-dimensional bases and sheds more light on the situation in higher dimensions. The talk is based on joint work with Andreas Rosenschon.

- Time:
- 11:30am
- Location:
- Ramanujan Hall
- Description:
- Title: Bayesian Variable Selection in Linear and Time-to-Event Models

Abstract: We consider the question of variable selection in complex models. This is often a difficult problem due to the inherent nonlinearity of the models and the resulting non-conjugacy in their Bayesian analysis. Bayesian variable selection in time-to-event models often utilize cross-validated predictive model selection criteria which can be relatively easy to estimate for a given model. However, the performances of these criteria are not well-studied in large-scale variable selection problems and, evaluation of these criteria for each model under consideration can be difficult to infeasible. An alternative criterion is based on the highest posterior model but its implementation is difficult in non-conjugate lifetime models. In this presentation, we compare the performances of these different criteria in complex lifetime data models including models with limited failure. We also propose an efficient variable selection method and illustrate its performance in simulation studies and real example.

- Time:
- 10:00am
- Location:
- Ramanujan Hall
- Description:
- Title: Control of compressible Navier-Stokes system

Abstract: We consider the one dimensional compressible Navier-Stokes system near a constant steady state with the periodic boundary conditions. The linearized system around the constant steady state is a hyperbolic-parabolic coupled system. We discuss some of the properties of the linearized system and its spectrum. Next we study some controllability results of the system.

- Time:
- 3:00pm
- Location:
- Ramanujan Hall
- Description:
- Title: Fitting a Two Phase Threshold Multiplicative Error Model

Abstract. The class of multiplicative error models are particularly suited to model nonnegative time series such as financial durations, realized volatility, and squared returns. Threshold models are also known to play an important role in time series analysis. In this talk we shall present a lack-of-fit test for fitting a two-phase threshold model to the conditional mean function in a multiplicative error model. The proposed testing procedure can also be applied to a class of autoregressive conditional heteroscedastic threshold models. A simulation study shows some superiority of the proposed test over some commonly used existing tests. We shall illustrate the testing procedure by some data examples.

- Time:
- 3:30pm
- Location:
- Room No. 216
- Description:
- Title: Diophantine Arithmetic and Homogeneous Dynamics

Abstract:

In this talk I will introduce generalities of the interaction between problems in Diophantine arithmetic and dynamics of flows on homogeneous spaces, and set the tone for subsequent lectures.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall
- Description:
- Title: Some result in probability theory with application to analysis

Abstract: attached as pdf

- Time:
- 2:30pm
- Location:
- Ramanujan Hall
- Description:
- Title: Representation ring of Levi subgroups versus

cohomology ring of flag varieties

Abstract: attached as pdf

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall
- Description:
- Speaker: Manas Rachh, Yale University

Title: Integral equation formulation of the biharmonic problem with Dirichlet boundary conditions

Abstract: In this talk, we present a novel integral representation for the Dirichlet problem of the biharmonic equation. To obtain the representation, the Dirichlet problem is first converted into a related Stokes problem for which the Sherman-Lauricella integral representation can be used. However, not all potentials for the Dirichlet problem correspond to a potential for Stokes flow, and vice-versa, but we show that the integral representation can be augmented and modified accordingly, with careful attention paid to the case of multiply connected domains. The resulting integral representation has a kernel with a lower order singularity (as a function of the ambient space) than classical representations. We illustrate the accuracy, and conditioning of our method with several numerical examples.

- Time:
- 3:30pm - 5:00pm
- Location:
- Ramanujan Hall
- Description:
- Title: Koszul Algebras

Abstract: Koszul algebras are the algebras over which the resolution of

the residue class field is given entirely by linear matrices. This series

of talks will be a survey on results obtained about Koszul algebras since

they were introduced by Priddy in 1970.

In the first talk, We shall see lots of examples of Koszul algebras, and

discuss several characterizations of Koszul algebras.

- Time:
- 3:30pm - 5:00pm
- Location:
- Room 114
- Description:
- Title: Jannsen's theorem on semi-simplicity - 1

Abstract: In these lectures we shall introduce motives and present results

in Jannsen's paper, which say that the "conjectural" category of motives

is semisimple abelian iff the adequate equivalence relation taken is

numerical equivalence. We shall also explain what is still "conjectural"

about this.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall
- Description:
- Speaker: Prof. Hrushikesh N. Mhaskar, California Institute of Technology, Pasadena, and Claremont Graduate University, Claremont.

Title: Introduction to machine learning and approximation theory

Abstract: We will point out the relevance of approximation theory to

machine learning problems and review classical concepts of

approximation theory using trigonometric polynomial approximation of

periodic functions as a case study.

- Time:
- 3:30pm - 5:00pm
- Location:
- Room 216, Maths Building
- Description:
- Title: Diophantine approximation on the plane by SL(2,$\mathbb Z$) orbits.

Abstract: It is known that under the action of SL(2,$\mathbb Z$) on the plane the orbit of any vector which is not a multiple of a rational vector, is dense in the plane. Thus any vector in the plane can be approximated by points on such an orbit. This talk will discuss certain quantitative aspects of such an approximation.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall
- Description:
- Speaker: Anne-Marie Aubert, Institut de Mathematiques de Jussieu, France

Title: Preservation and non-preservation of depth under the local Langlands correspondence.

Abstract:

A central role in the representation theory of reductive p-adic groups is played by the local Langlands correspondence. It is known to exist in particular for the inner forms of general and special linear groups,

and to preserve interesting arithmetic information, like local L-functions and epsilon?-factors. Another

invariant that makes sense on both sides of the correspondence is depth. This notion will be introduced in the talk, and we will describe the known results regarding its transformation under the correspondence.

- Time:
- 10:00am - 11:00am
- Description:
- Title: A tale of two groups - mapping class group and outer automorphism group of free group

Abstract: In this talk I will define two key groups studied in geometric

group theory - the mapping class group of a surface and the outer

automorphism group of a free group. I will discuss how the theory of

mapping class groups has motivated and guided the study of Out(F_n). Both groups act on certain hyperbolic simplicial complexes. For mapping class group these actions yield useful information about the group such as homological stability, finite asymptotic dimension, quasi-isometric rigidity. I will define some of these hyperbolic complexes and classifythe group elements that act with positive translation length.

- Time:
- 3:30pm
- Location:
- Ramanujan Hall
- Description:
- Title: Koszul Algebras 2

- Time:
- 11:00am - 1:00pm
- Location:
- Room No. 215
- Description:
- Title: Jannsen's theorem on semisimplicity - 2

Abstract: In these lectures we shall introduce motives and present

results in Jannsen's paper, which say that the "conjectural" category of

motives is semisimple abelian iff the adequate equivalence relation taken

is

numerical equivalence.

- Time:
- 4:00pm - 5:00pm
- Location:
- Ramanujan Hall
- Description:
- Speaker: Prof Kishore Marathe

Professor of mathematics and physics,

Brooklyn College and the graduate center,

City University of New York

Title: What is Physical Mathematics?

Abstract: Physical mathematics is a new and very active area of research

at the interface of physics and mathematics. However, its roots go

back to antiquity. We will discuss the ancient

origins of this subject and highlight some important achievements

in this area leading up to current developments. They have given us

surprising new results and new perspectives on old results in mathematics

starting with results from experimental and theoretical physics.

- Time:
- 3:30pm - 5:00pm
- Location:
- Room No. 216
- Description:
- Title: Values of quadratic forms at integer points

Abstract: This will be an overview of the results on values of quadratic forms at integer points.

- Time:
- 11:30am - 1:00pm
- Location:
- Ramanujan Hall
- Description:
- Title. Rational Surface Singularities.

Title. We will prove a purely numerical criterion due to M. Artin to test

the rationality of a surface singularity. In practice this is the

criterion which is used when a rational surface singularity is being

considered.

- Time:
- 3:00pm - 5:00pm
- Location:
- Room No. 215
- Description:
- Title: Leray-Serre Spectral Sequence

Abstract:

In the first half of the lecture, we will talk about spectral sequences and discuss how they arise. We will discuss both the filtration and exact couple approaches.

In the second half I will give the construction of the Leray-Serre spectral sequence connected to a fibration and discuss some examples.

This talk is the first of a two- lecture series. In the second talk, Rekha will prove that the i-th homotopy groups of a sphere S^n are finite when i is greater than n, except in one particular case, using the Serre spectral sequence.

- Time:
- 3:30pm
- Location:
- Ramanujan Hall
- Description:
- Title; Koszul Algebra's

- Time:
- 11:00am - 1:00pm
- Location:
- Room No. 215
- Description:
- Title: Jannsen's theorem on semisimplicity - 3

Abstract: In these lectures we shall introduce motives and present

results in Jannsen's paper, which say that the "conjectural" category of

motives is semisimple abelian iff the adequate equivalence relation taken

is

- Time:
- 11:00am
- Location:
- Ramanujan Hall
- Description:
- TITLE: Progress in Error-Correction: A Survey

Speaker: Venkatesan Guruswami, Carnegie Mellon Univ.

ABSTRACT:

Error-correcting codes play a crucial role in safeguarding data against the

adverse effects of noise during communication and storage. They are also

powerful tools underlying several recent advances in theoretical computer

science and combinatorics. The central challenge in coding theory is to

construct codes with minimum possible redundancy for different error models

and requirements on the decoder, along with efficient algorithms for

error-correction using those codes. Much progress has been made toward this

quest in the nearly seven decades since the birth of coding theory. Several

fundamental problems, however, continue to challenge us, and exciting new

directions routinely emerge to address current technological demands as well

as applications in computational complexity and cryptography. This talk will

survey some of our recent works on error-correction in various models, such

as:

- worst-case errors, where we construct list decodable codes with redundancy

as small as the target error fraction;

- i.i.d. errors, where we show polar codes enable efficient error-correction

even as the redundancy approaches Shannon capacity;

- bit deletions, where we give codes that can correct the largest known

fraction of deletions;

- single symbol erasure, a model of substantial current interest for

tackling node failures in distributed storage, where we give novel repair

algorithms for Reed-Solomon codes as well as simple new codes with

low-bandwidth repair mechanisms.

- Time:
- 3:30pm - 5:00pm
- Location:
- Room No. 216
- Description:
- Title: Values of quadratic forms at integer points II

Abstract: This will be a continuation of the overview from the last week. Some details will be briefly recalled from the last time, for continuity and the benefit of new audience if any.

- Time:
- 5:00pm - 7:00pm
- Location:
- Room No. 215
- Description:
- Title: Some consequences of the Riemann hypothesis for varieties over

finite field

Abstract: We will talk about a result of M. Katz and W. Messing, which

says the following. From the Riemann hypothesis and the hard Lefschetz

theorem in l-adic cohomology, the corresponding facts for any Weil

cohomology follow.