27 May, 2022
Title: On extension of Calderon-Zygmund type singular integrals and their commutators
Speaker: Mr. Joydwip Singh, PhD Student, IISER Kolkata
Abstract: In this talk we define an extension of Calderon-Zygmund type singular integrals and their commutators. We will talk about the estimates of these singular integrals and their commutators on Lebesgue spaces, Lipschitz spaces and Hardy spaces. From our estimates one can deduce analogous estimates for the classical Calderon-Zygmund type singular integrals and their commutators.
20 May, 2022
Title: The moment method: Exact controllability of a mixed class coupled system
Speaker: Mr. Subrata Majumdar, PhD Student, IISER Kolkata
Abstract: This talk will be the continuation of the previous one presented by Jiten about the method of moments and its application. We will present how this method can be employed to study the boundary exact controllability of a hyperbolic-elliptic mixed class PDE.
13 May, 2022
Title: The Method of Moments and its Applications
Speaker: Mr. Jiten Kumbhakar, PhD Student, IISER Kolkata
Abstract: The method of moments is one of the well-known methods that can be used to construct a control and is very powerful in the analysis of the control of evolution partial differential equations. In this talk, we see some applications of this method: We first prove the null controllability of a controlled ordinary differential system in finite dimension. Finally, we prove that the heat equation in one dimension is null controllable by using a boundary control.
29 April, 2022
Title: The Laplacian spectra of Commuting Graphs
Speaker: Mr. Samiron Parui, PhD Student, IISER Kolkata
Abstract: The commuting graph associated with a group G is a graph with G as the set of vertices and there is an edge between two vertices if they commute in group G. Here we describe the spectrum of the Laplacian matrix of the commuting graph associated with a finite group, using group theoretic information.
15 April, 2022
Title: The Atiyah-Jänich Theorem
Speaker: Mr. Satwata Hans, 5th Year BS-MS, IISER Kolkata
Abstract: The space of Fredholm operators over a separable Hilbert space $\mathcal{H}$ has been an important area of study in Functional Analysis. It has gained more relevance over time due to the significant works of Sir Michael Atiyah and multiple other mathematicians, which have focused on various topological and geometric connections to the Fredholm operators. In this talk, we will see a famous theorem called the Atiyah-Jänich Theorem, which states that the space of Fredholm operators gives an alternate characterization of the K-Theory of any compact Hausdorff space.
8 April, 2022
Title : The Sensitivity Conjecture and Fourier Analysis of Boolean functions
Speaker : Mr. Debmalya Bandyopadhyay, 5th Year BS-MS, IISER Kolkata
Abstract : One of the most celebrated unsolved problems in theoretical computer science over the last three decades has been the sensitivity conjecture. After about 30 years since it was conjectured, in 2019, Hao Huang gave a 3-page proof of the conjecture using spectral techniques. The talk will introduce the conjecture and go on to explain Huang's simple proof. It will then touch upon some basics of Fourier Analysis of Boolean functions to introduce a corollary of another unsolved problem: The Fourier Entropy Influence (FEI) conjecture. Towards the end, I would be talking about the classification of flat, homogeneous, and Boolean polynomials, that I have been working on for the last few months, in connection to the FEI conjecture.
1 April, 2022
Title : Dimensionality Reduction for Multivariate and Functional Data
Speaker : Mr. Avishek Chatterjee, PhD Student, IISER Kolkata
Abstract : Dimensionality reduction as a preprocessing step to machine learning is effective in removing irrelevant and redundant information, increasing learning accuracy, and improving result comprehensibility. The complexity of any classifier depends on the number of inputs. This determines both time and space complexity and the necessary number of training instances to train such a classifier. In this talk, we discuss Principal Component Analysis (PCA) and Functional Principal Component Analysis (FPCA), the most popular and widely used dimensionality reduction techniques for multivariate and functional data respectively. Further, we talk about a local FPCA based classifier, which is especially suited for hard classification framework.