Departmental Colloquium: RAP Colloquium, by Anudeep Kumar, Aditya Potukuchi, Geoffrey Smith
September 18, 2020
3:00 PM - 3:50 PM
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Anudeep Kumar, Aditya Potukuchi, Geoffrey Smith (UIC): RAP Colloquium
This colloquium will highlight our new Research Assistant Professors. Titles/Abstracts are as follows:
Geoffrey Smith -- Title: Algebraic geometry in positive characteristic
Abstract: Algebraic geometers tend to like working in characteristic 0, and with good reason; a lot of the most basic tools we work with fall apart in positive characteristic. I'll give a couple examples of this happening and of how the extra challenges of positive characteristic have impacted my work.
Anudeep Kumar -- Title: Singularities and global solutions in the Schrödinger-Hartree equation
Abstract: In 1922, Louis de Broglie proposed wave-particle duality and introduced the idea of matter waves. In 1925, Erwin Schrödinger, proposed a wave equation for de Broglies matter waves. The Schrödinger equation is described using de Broglies matter wave, which takes the wave function, and describes its quantum state over time.
We consider a nonlinear Schrödinger type equation with nonlocal nonlinearity, of a convolution type, called the generalized Hartree (gHartree) equation. In the gHartree equation, the influence on the behavior of the solutions is global as opposed to the case of local (power type) nonlinearities. In the inter-critical regime, we first obtain a dichotomy for global (scattering) vs finite time (blow-up) existing solutions exhibiting two methods of obtaining scattering: one via Kenig-Merle concentration - compactness and another one is using Dodson-Murphy approach via Morawetz estimate and Tao's scattering criteria. Next, we investigate stable singularity formations in the mass-critical gHartree equation, and rigorously prove a stable blow-up formation in dimension 3.
Aditya Potukuchi -- Title: On the list recoverability of randomly punctured codes
Abstract: An error-correcting code of block length n is said to be (l,L) list recoverable if for any sets A_1, A_2,...,A_n of the alphabet, each for size at most l, the number of codewords in A_1 x A_2 x ... x A_n is at most L. This simple combinatorial property turns out to be useful in many contexts in Algorithms and Complexity Theory. I will talk about the list recovery properties of randomly punctured codes. In particular, we will see that these codes typically have list recoverability better than what is guaranteed by the Johnson bound. Joint work with Ben Lund (IBS).
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Sep 23, 2020
Sep 23, 2020