Abstract:

In this talk, we deal with the problem of efficient sampling from a stochastic differential equation, given the drift function and the diffusion matrix. The proposed approach leverages a recent model for probabilities (the positive semi-definite -- PSD model) from which it is possible to obtain independent and identically distributed (i.i.d.) samples at precision with a cost that is where is the dimension of the model, the dimension of the space. The proposed approach consists of: first, computing the PSD model that satisfies the Fokker-Planck equation (or its fractional variant) associated with the SDE, up to error, and then sampling from the resulting PSD model. Assuming some regularity of the Fokker-Planck solution (i.e. -times differentiability plus some geometric condition onits zeros) We obtain an algorithm that: (a) in the preparatory phase obtains a PSD model with L2 distance from the solution of the equation, with a model of dimension where is the fractional power to the Laplacian, and total computational complexity of and then (b) for Fokker-Planck equation, it can produce i.i.d. samples with error in Wasserstein-1 distance, with a cost that is per sample. Our results suggest that as the true solution gets smoother, we can circumvent the curse of dimensionality without requiring any sort of convexity.

Abstract:

The study of the Selmer group for an Artin representation was initiated by Greenberg. In this talk, we will discuss the algebraic functional equation of the dual Selmer group coming from Artin's representation of the cyclotomic Zp-extension of Q. One usually studies the algebraic functional equation of the dual Selmer group because of their connection with the Iwasawa Main Conjecture.  

Abstract:

The dimer model, also referred to as dominotilings or perfect matching, are tilings of the Z^d lattice by boxes exactly one of whose sides has length 2 and the rest have length 1. This is a very well-studied statistical physics model in two dimensions with many tools like height functions and Kasteleyn determinant representation coming to its aid. The higher dimensional picture isa little daunting because most of these tools are limited to two dimensions. In this talk I will describe what techniques can be extended to higher dimensions and give a brief account of a large deviations principle for dimer tilings in three dimensions that we prove analogous to the results by Cohn, Kenyon and Propp (2000).

Abstract:

In this talk, we present a well posed ness result of fluid-structure interaction model regarding the motion of a rigid body in a bounded domain which is filled with a compressible isentropic fluid. We prove the existence of a weak solution of the fluid-structure system up to collision. We will also discuss the case of several rigid bodies.

Abstract:

We shall state and prove the Rank-Nullity theorem and give some of its applications.

Abstract:

One of the most dynamically evolving research areas, with both practical and theoretical interests, is that of sampling and reconstruction. In 1949, the celebrated Shannon sampling theorem was proved which turned out to be a milestone in this field of study and set the foundation for information theory. Over these years, the theory of sampling has been intensively studied.

In this talk, we discuss the problem of regular and irregular average sampling over certain classes of shift-invariant space of functions. We also consider the random average sampling problems for certain suitable subsets of shift-invariant subspaces of mixed Lebesgue spaces. Finally, based on this work, we will see some future directions.

Short Biography:

Dr. Ankush Kumar Garg is a visiting scientist at the Indian Statistical Institute Bangalore, specializing in the field of Harmonic Analysis. He earned his doctorate from the Indian Institute of Science Education and Research Thiruvananthapuram, where he was mentored by Dr. P. Devaraj. His dissertation, entitled ”A Study on Reconstruction from Local Average and Random Average Samples over Shift-Invariant Spaces,” was successfully defended in November2022. Dr. Garg’s research interests primarily revolve around frame theory, sampling and reconstruction theory, as well as invariant subspace characterization. His contributions to the field have been published in numerous peer-reviewed journals. In addition to his research accomplishments, Dr. Garg is also a passionate educator who enjoys sharing his knowledge with others. He has a strong commitment to teaching

Abstract:

Initiated by Elias Stein in late1960's the Fourier restriction conjecture has played a central part in the development of modern harmonic analysis. Despite continuous progress over the last five decades, currently this remains out of reach in dimensions bigger than two. To get a better sense of restriction inequalities, we consider Fourier restriction estimates onto curves $\gamma : \R \to \Rd$. Even in this well-explored setting, there are many basic questions that remain open such as the question of existence of maximizers for such inequalities. This talk will be a gentle introduction to such questions and some recent progress on these. This is based on our recent works with Betsy Stovall (at University of Wisconsin Madison).

Abstract:

This talk will be an introduction to the notion of derivative in several variables Calculus. We will introduce the notion of derivatives and will observe that many of the fundamental properties such as the chain rule from one variable theory continue to hold inseveral variables.

Abstract:

The main purpose of this talk is to describe the invariant subspaces of a class of operators on Hilbert space.

This presentation is devoted to generalizing the famous Beurling’s Invariant sub space Theorem for the shift operator to the case of the tuple of operators, where the operators assumed are weaker than isometries, we will be referring to this weaker condition of operators as near-isometries. To begin with, we first derive a generalization of Slocinski’s well-known Wold type decomposition of a pair of doubly commuting isometries to the case of an n-tuple of doubly commuting operators near-isometries. Then, with the help of Wold decomposition for the n-tuple of doubly commuting near-isometries, we will represent in concrete fashion those Hilbert spaces that are vector subspaces of the Hardy spaces Hp(Dn) (1 ≤ p ≤ ∞) that remain invariant under the action of coordinate wise multiplication by an n-tuple(TB1,...,TBn ) of operators where for each 1 ≤ i ≤n, Bi is a finite Blaschke factor on the open unit disc. The critical point to be noted is that these TBi are assumed to be near-isometries.

Abstract:

In this talk, we discuss non-trivial bounds for the Rankin Selberg L- function associated with a GL(3) form of levelP_1 and a

GL(2) form of level P_2 when P_1 and P_2 are large. This family of L-functions is of particular interest because of its connection with the quantum unique Ergodicity conjecture formulated by Rudnik and Sarnak. This is joint work with Saurabh Singh and Ritabrata Munshi.

Abstract:

We will start by recalling the definition of a topological space and will see some examples. We will move on to discuss connected topological spaces and see various examples and properties of such spaces.

Abstract:

Short biography:

Manisha Aggarwal completed her Ph.D. in Mathematics at Indian Institute of Technology Delhi in 2016 under the supervision of Prof. Subiman Kundu. Since then, she has been teaching at St. Stephen's College, University of Delhi. Her research interest is analysis on metric spaces. The passion for teaching and research has motivated her to write textbooks for undergraduates and postgraduates in collaboration with Prof. Kundu. The research monograph, titled Cofinally Complete Metric Spaces and related functions, written in collaboration with Prof. Kundu and Dr. Gupta is to be published by World Scientific in 2023.

Abstract:

We are already familiar with the signicance of the study of convergence of sequences in real analysis. In the talk, we will discuss regarding pointwise and uniform convergence of a sequence of real-valued functions. The main focus will be Dini's theorem, Stone-Weierstrass theorem and their generalizations.

Short biography:

Manisha Aggarwal completed her Ph.D. in Mathematics at Indian Institute of Technology Delhi in 2016 under the supervision of Prof. Subiman Kundu. Since then, she has been teaching at St. Stephen's College, University of Delhi. Her research interest is analysis on metric spaces. The passion for teaching and research has motivated her to write textbooks for undergraduates and postgraduates in collaboration with Prof. Kundu. The research monograph, titled Cofinally Complete Metric Spaces and related functions, written in collaboration with Prof. Kundu and Dr. Gupta is to be published by World Scientific in 2023.

Abstract:

In order to prevent the in-service failure of an item or a system, it is a common practice to employ an age replacement policy, in which a working item is replaced by a new one on its failure or at a prespecified time t, whichever occurs earlier. In this context, the mean time to failure (MTTF) function plays a prominent role in the study of reliability characteristics of systems under age replacement policy. Hence it is of profound importance to have statistical test procedures for comparing MTTF functions of two life distribution functions. On the other hand, it is of practical interest to detect whether lifetime data exhibits a possible departure from exponentiality toward notions of ageing where the MTTF function is monotonic. In the first part of the talk, a flexible two-sample nonparametric test, based on two independent samples, will be discussed for comparing mean time to failure (MTTF) functions of two life distributions. Finally, a consistent test of exponentiality against alternatives belonging to the decreasing mean time to failure class of life distributions will be presented.