IITG Mathematics Seminar Series

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Lecture Number:318
Title:Semi-direct Product of Groups and Beyond
Speaker:Dr. Sutanu Roy
Affiliation:NISER, Bhubaneswar
Date: 23rd May, 2018 (Wednesday)
Time: 11:00 AM

Abstract: In group theory, the semi-direct product is a basic construction generalizing direct products. Locally compact quantum groups are natural generalizations of locally compact groups within the scope of non-commutative geometry. Many interesting examples of (non-compact) locally compact quantum groups were construct as q-deformation of locally compact groups. Therefore, it is natural to ask for a general theory of semi-direct product of locally compact quantum groups. The goal of this talk is to motivate and discuss recent developments in this area and present some examples

Lecture Number:317
Title:Robust and Efficient Computation in Dynamic Networks with Heavy Churn
Speaker:Prof. John Augustine
Affiliation:Indian Institute of Technology, Madras
Date: 6th April, 2018 (Friday)
Time: 4:00 PM

Abstract: Peer-to-Peer (P2P) networks "typically overlays on top of the Internet" pose some unique challenges to the algorithm designer. Primarily, the difficulty comes from constant churn owing to the short life span of most nodes in the network. Reminiscent of Theseus paradox, most nodes in a typical P2P network churn out within an hour only to be replenished with incoming new nodes. In order to maintain a well-connected network despite churn at this level, the overlay is constantly reworked. This results in the overlay network graph being an evolving graph that exhibits both edge dynamism and node churn. In this talk, we will discuss the somewhat surprising line of work in which we show how to design fast algorithms that are robust against heavy churn.

We will begin with a discussion on how to create an overlay network that has good expansion despite adversarial churn. Subsequently, assuming such an overlay network with good expansion, we will present a few basic techniques like fast information dissemination, random walks, and support estimation. Finally, we show how to use these techniques to design algorithms to solve fundamental problems like agreement, leader election, storing and retrieving data items.

Lecture Number:316
Title:Spectral Approximation for Self-adjoint Operators, by Truncation
Speaker:Prof. Kalyan B. Sinha
Affiliation:SERB Distinguished Associate, Theoretical Sciences Unit, JNCASR and NMI Distinguished Associate, IISc
Date: 22nd March, 2018 (Thursday)
Time: 4:15 PM

Abstract: Arveson's program of numerical spectral approximation is extended to unbounded self-adjoint operators, with a view for applications to Schrodinger Operators. Several Szego-type theorems are proven for such operators, showing that the empirical density of eigenvalues, under suitable hypothesis on the so-called degree of the operator, converges to the density of the essential spectrum.

Lecture Number:315
Title:Two Open Problems in Linear Algebra
Speaker:Prof. Michael Karow
Affiliation:Institute for Mathematics, TU Berlin, Germany
Date: 6th March, 2018 (Tuesday)
Time: 4:00 PM

Abstract: This talk is about two (unrelated) problems. The first concerns the construction of a subspace of maximal dimension on which two Hermitian forms are simultaneously positive definite. The second problem is about estimating the size of pseudospectra of block triangular matrices.

Lecture Number:314
Title:Confinement and nonlocal elasticity effects in premelting dynamics
Speaker:Dr. Satyajit Pramanik
Affiliation:Post-Doctoral Researcher, Nordic Institute for Theoretical Physics, Sweden
Date: 22nd February, 2018 (Thursday)
Time: 4:00 PM

Abstract: Abstract: We study the combined effects of non-local elasticity and confinement induced ordering on the dynamics of thermomolecular pressure gradient driven premelted films bound by an elastic membrane. The confinement induced ordering is modeled using a film thickness dependent viscosity (Pramanik & Wettlaufer 2017 *Phys. Rev. E* *96*, 052801). When there is no confinement induced ordering, we recover the similarity solution for the evolution of the elastic membrane, which exhibits an infinite sequence of oscillations (Wettlaufer *et al.* 1996 *Phys. Rev. Lett. **76*, 3602-3605). However, when the confinement-induced viscosity is comparable to the bulk viscosity, the numerical solutions of the full system reveal the conditions under which the oscillations vanish. Implications for general thermomechanical dynamics, frost heave observations, and cryogenic cell preservation are discussed.

Lecture Number:313
Title:Finite Element Model Updating : A Wonderful Inverse Eigenvalue Problem
Speaker:Prof. Biswa Nath Datta
Affiliation:Distinguished Research Professor, Northern Illinois University, USA
Date: 20th February, 2018 (Tusday)
Time: 4:00 PM

Abstract: The Finite Element Model Updating concerns updating a finite element generated second-order model of some specified structures in such way that a set of prescribed eigenvalues and eigenvectors are reproduced, the other eigenvalues and eigenvectors remain unchanged and the updated model maintains the same structures as the original model. The problem routinely arises in vibration industries, such as automobile, aerospace, and spacecraft. A properly updated model can be used by the engineers with confidence for future designs and manufacturing.

Mathematically, it is a partially prescribed structured quadratic inverse eigenvalue problem. Since, the problem was formulated in quadratic inverse eigenvalue setting by the speaker in 2001, much research has been done by both mathematicians and engineers, but, unfortunately, the problem still has not satisfactorily been solved. The structure preservation is the most difficult aspect of the problem. Some notable progress has been made in the last few years by the speaker and his collaborators.

This talk will discuss (i) how the problem arises in industries, (iii) mathematical formulation of the problem in the quadratic inverse eigenvalue setting, (iii) mathematical, computational and engineering challenges, (iv) the progress made so far, and (v) the future research

The talk is interdisciplinary blending mathematics, scientific computing, optimization with vibration engineering and structural dynamics , and will be of interests to students, researches and practicing engineers in these disciplines.

Lecture Number:312
Title:The Journey of Lagrange and Applications of Euler-Lagrange Equations in Fluid Mechanics.
Speaker:Prof. G. P. Raja Sekhar
Affiliation:Professor, Indian Institute of Technology, Kharagpur
Date: 25th January, 2018 (Thursday)
Time: 5:00 PM

Abstract: This talk introduces in brief the popular contributions of Joseph-Louis Lagrange and his journey. A brief outline on Lagrange's interaction with Euler will be discussed before introducing the Lagrange equations of second kind or Euler-Lagrange equations. A fluid mechanical problem of lifting a large object that is sunken in a fluid and lying in a neutrally buoyant condition on top of a fluid filled anisotropic porous bed will be discussed in detail. The talk introduces the corresponding Euler-Lagrange equations and then mechanics of break -out phenomenon while lifting such an object will be discussed. This problem has direct application in salvaging sunken ships, moving object at offshore, submersible - engineering etc. .

Lecture Number:311
Title:Maximum Principle and Harnack's Inequality
Speaker:Prof. Mrinal Kanti Ghosh
Affiliation:Indian Institute of Science, Bangalore
Date: 17th January, 2018 (Wednesday)
Time: 4:00 PM

Abstract: We begin with classical harmonic functions. Using mean value theorem we show how to establish maximum principle and Harnack's inequality for classical harmonic functions. Then we provide a probabilistic approach to these problems. Next we discuss more general uniformly elliptic equations and establish similar results using probabilistic methods. Finally we treat uniformly elliptic systems with weak coupling and establish maximum principle and Harnack's inequality for such systems.

Lecture Number:310
Title:In the neighbourhood of Sato-Tate conjecture
Speaker:Dr. Sudhir Pujahari
Affiliation:Post-Doctoral Fellow, Harish-Chandra Research Institute, Allahabad
Date: 4th January, 2018 (Thursday)
Time: 3:30 PM

Abstract: In this talk, we will discuss the distribution of gaps between eigenangles of Hecke operators acting on the space of cusp forms of weight $k$ and level $N$, spaces of Hilbert modular forms of weight $\underline k=(k_1,k_2,\dots,k_r)$ and space of primitive Maass forms of weight $0$. Moreover, we will see a stronger version of multiplicity one theorem for the space of cusp forms of weight $k$ and level $N.$ The last part is a joint work with M. Ram Murty.

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