Tue, October 16, 2018
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October 2018
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4:00pm [4:00pm] Prof. Ravi Prakash, University of Concepcion, Chile.
PDE & Numerical Analysis Seminar Date and Time: 16th October 2018, at 4PM Venue: Ramanujan Hall, Mathematics Department. Speaker: Prof. Ravi Prakash, University of Concepcion, Chile. Title: "Homogenization: Oscillating Boundary Domains" Abstract of the seminar: Homogenization is a branch of science where we try to understand microscopic structures via a macroscopic medium. Hence, it has applications in various branches of science and engineering. This study is basically developed from material science in the creation of composite materials though the contemporary applications are much far and wide. It is a process of understanding the microscopic behavior of an in-homogeneous medium via a homogenized medium. Mathematically, it is a kind of asymptotic analysis. We are interested in the asymptotic behavior of elliptic boundary value problems posed in domains with highly oscillating boundary. In fact, we will consider different types of unfolding operators to study many types of oscillating boundary domains with various model problems posed in them. We will also see some interesting optimal boundary control problem posed in such domains. In total, the presentation will start from the asymptotic behavior of Laplacian in a simple rectangular oscillating boundary domains to the future possibilities of the shapes of oscillations in the boundary keeping in mind the mathematical issues arise in topology optimization.

5:00pm [5:00pm] Neeraj Kumar
CACAAG Seminar Speaker: Neeraj Kumar. Time: 5pm, Tuesday, 16 October 2018. Venue: Ramanujan Hall. Title: Wilf's conjecture on numerical semigroups Abstract: The aim of the talk is to give a brief survey on the Wilf's conjecture, and to present a commutative algebra formulation of it. We will verify Wilf's conjecture in some cases. A numerical semigroup $S$ is a subset of the nonnegative integers $N$ that is closed under addition, contains 0, and has finite complement in $N$. The Frobenius number $F$ of numerical semigroup $S$ is the largest integer not in $S$. Let $d$ be the minimal number of generators of $S$ and $n$ be the number of representable integers in the interval $[0, F]$. Wilf's conjecture states that $F +1 \leq n d$.