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Title: Fractional Borg-Levinson problem.
Speaker: Saumyajit Das
Abstract: In this talk, we analyze how the spectral inequality and boundary scattering determine the noise from the sub-Brownian sound vibration.
Title: Skew Braces and Set-Theoretic Solutions of the Yang–Baxter Equation
Speaker: Susanta Mondal
Abstract: In this talk, we introduce the notion of skew braces and discuss their basic properties and examples. We also present set-theoretic solutions of the Yang–Baxter equation and describe the strong connection between skew braces and such solutions. This relationship provides an important algebraic frame-work for studying the Yang–Baxter equation and its applications.
Title: Multivariate Period Rings
Speaker: Rohit Pokhrel
Abstract: p-adic Hodge theory aims to classify p-adic representations of a p-adic field. This is achieved by constructing various period rings, which provide different Tannakian subcategories for classification. In this talk, I will discuss the analogous story in multivariate p-adic Hodge theory. This is a work in progress.
Title: The main conjecture for CM elliptic curves at supersingular primes
Speaker: Selvam V
Abstract: At a prime of ordinary reduction, the Iwasawa “main conjecture” for elliptic curves relates a Selmer group to a p-adic L-function. In the supersingular case, neither the Selmer group nor the p-adic L-function is well-behaved. Kobayashi has discovered an equivalent formulation relating modified Selmer groups de-
fined by him with the modified p-adic L-function defined by Pollack. We discuss the proof of Kobayashi’s Conjecture for CM elliptic curves.
Title: Norm Convergence of Ergodic Averages
Speaker: Rithwik M R
Abstract: In this talk, I shall define the preliminaries to study ergodic averages, and briefly, using a few examples, show why studying the norm convergence of ergodic averages are useful. I shall also give a review of the existing research in this field, from von-Neumann’s mean ergodic theorem to the celebrated result of M. Walsh on norm convergence of nilpotent averages. In the latter half of the talk, I shall outline the proof of a portion of Walsh’s result, which utilizes the Geometric Hahn-Banach theorem.
Title: Heegner Points and p-adic L-Functions
Speaker: Muskan Bansal
Abstract: Let p be an odd prime. Let F a totally real field in which p is inert. Suppose E is a modular elliptic curve defined over F with analytic rank 1. Denote by f the Hilbert modular form attached to E/F . One can define a two-variable p-adic L-function attached to the Hida family passing through f . If E has split multiplicative reduction at the unique prime lying above p, then this p-adic L-function vanishes to order at least 2 on the central critical line. So the natural question to ask is what is the second-order derivative? In this talk, we describe the second derivative of the p-adic L-function in terms of Heegner points.
Title: Steenrod algebra and Moore spectra
Speaker: Bikramjit Kundu
Abstract: We will start with a brief discussion about Steenrod algebra. Using Mod 2-Steenrod operations we will see that that degree 2 map of Mod 2-Moore space is stably essential. This will lead to an important result in stable homotopy theory that the Spanier-Whitehead category is not algebraic.
Title: Transversality in Smooth Manifolds
Speaker: Arkadeepta Roy
Abstract: We know that the solutions of an equation f(x) = y form a smooth manifold, provided that y is a regular value of the map f: X -> Y. What happens when the set of points in X whose functional values are constrained, not necessarily to be a constant y, but to satisfy an arbitrary smooth condition? This question leads us to a new differential property, an extension of the notion of regularity, known as transversality. In this talk, we introduce the notion of transversality for smooth maps and submanifolds, begining with its geometric interpretation in terms of tangent spaces and intersections. We discuss fundamental examples illustrating transverse and non-transverse intersections.
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