November 13, 2023 - November 17, 2023
Public Access Category: All |
|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
- Time:
- 4:00pm-5:00pm
- Description:
Analysis and PDE seminar
Monday 13th Nov, 2023, 4 pm - 5 pm
=======================
Venue: Ramanujan Hall
Host: Chandan Biswas
Speaker: Senthil Raani
Affiliation: IISER Berhampur
Title: Distance Set Problems
Abstract: The distance set ∆(E) of a set E in Euclidean space consists of all non-negative numbers that represent distances between pairs of points in E. How does the structure of E impact that of ∆(E)? Questions of this nature play a fundamental role in geometric measure theory. We will begin with a brief history of results and conjectures on ∆(E). Apart from measure theoretic techniques, the asymptotic of the Fourier transform of measures supported on E plays a vital role in this study. Our main goal in this talk is to discuss a few properties of ∆(E) when E is sparse but has a large Hausdorff dimension. This is based on recent joint work with Prof. Malabika Pramanik.
- Time:
- 4:00pm-5:00pm
- Location:
- Ramanujan Hall, Department of Mathematics
- Description:
Mathematics Colloquium
Wednesday, 15 November, 4-5 pm
=======================
Venue: Ramanujan Hall
Hosts: Sanjiv Sabnis and Radhe Srivastava
Speaker: Prof. Sujit Ghosh
Affiliation: North Carolina State University
Title: Multivariate Dependence Beyond Correlation: Nonparametric CopulasAbstract: In the field of climate, finance, insurance, system reliability, etc., it is often of interest to measure the dependence among variables by modeling a multivariate distribution using a copula. The copula models with parametric assumptions are easy to estimate but can be highly biased when such assumptions are false, while the empirical copulas are non-smooth and often not genuine copula, making the inference about dependence challenging in practice. As a compromise, the empirical Bernstein copula provides a smooth estimator, but the estimation of tuning parameters remains elusive. In this paper, by using the so-called empirical checkerboard copula, we build a hierarchical empirical Bayes model that enables the estimation of a smooth copula function for arbitrary dimensions. The proposed estimator based on the multivariate Bernstein polynomials is itself a genuine copula, and the selection of its dimension-varying degrees is data-dependent. We also show that the proposed copula estimator provides a more accurate estimate of several multivariate dependence measures, which can be obtained in closed form. We investigate the asymptotic and finite-sample performance of the proposed estimator and compare it with some nonparametric estimators through simulation studies. An application to portfolio risk management is presented, along with a quantification of estimation uncertainty.
The presentation is based on a recently published paper with Dr. Lu Lu:
https://doi.org/10.3390/math11204383
- Time:
- 3:30pm-4:30pm
- Description:
Analysis and PDE seminar
Thursday 16th Nov, 2023, 3.30-4.30 pm
==========================
Venue: Ramanujan Hall
Host: Chandan Biswas
Speaker : Chandan Biswas, IIT Bombay
Title: A basic introduction to Fourier restriction estimatesAbstract: This is the sixth talk of the series. We will finish our discussion on Fourier restriction to the moment curve.
- Time:
- 4:00pm-5:00pm
- Location:
- Room No 215, Department of Mathematics
- Description:
Commutative algebra Seminar
Thursday 16 Nov 4-5 pm
=====================
Venue: Room 215
Host: Tony Puthenpurakal
Speaker: R. V. Gurjar, IIT Bombay
Title: Brieskorn-Pham Singularities.
Abstract: Let B=k[X_1,...,X_{n+1}]/(X_1^{a_1}+...+X_{n+1}^{n+1}) where k is the field of complex numbers and X the corresponding affine variety. These have been studied from many angles: (1) Brieskorn-Pham, Milnor, (2) from the topological viewpoint, giving rise to exotic spheres. (3) Storch for calculating the divisor class group of B (4) Flenner, Keichi Watanabe for characterizing rational singularities among them. (4) Recently Michael Chitayat wrote a beautiful thesis at Univ. of Ottawa characterizing 3-dimensional B-P singularities that admit a non-trivial locally nilpotent derivation (which is equivalent to having a G_a action on X). He has solved a conjecture about this completely. (5) I asked Michael which of the 3-dimensional B-P singularities define rational varieties in the sense of function field. Using ideas in his thesis he answered this completely.