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Junior Colloquium – 2019-2020

Thursday, February 6th
Title: The Traveling Salesman Problem
Speaker: Vyron Vellis
TIME: 3:40
ROOM: Ayres 405
Abstract: One of the most famous problems in computer science is the Traveling Salesman Problem (TSP) which asks the following question: “Given a finite list of cities, what is the shortest possible route a traveling salesman has to take to visit each city?”. The problem was first formulated in 1930 and is one of the most intensively studied problems in optimization. In analysis, we asked ourselves a more general question: “Given again a list of cities (possibly infinite, even uncountable, or better, a continuum!), when can our traveling salesman travel them all in finite (optimal, in some sense) time?”. This question (known as the Analyst’s TSP) has been one of the core questions of geometric measure theory and its applications span almost all fields of modern analysis. In this talk, we will discuss this problem, its solution and related results.

Thursday, November 14th
TITLE: Bose-Einstein condensation of an Ideal Gas
SPEAKER: Maximilian Pechmann
TIME: 3:40 PM
ROOM: Ayres 405
Abstract: A Bose-Einstein condensate is a state of matter of a Bose gas and an exotic quantum phenomenon. It was theoretically predicted by Bose and Einstein in 1924, but was long considered a mathematical curiosity without practical use. However, since the experimental observation of such a condensate in 1995, Bose-Einstein condensation is a field of research of great interest. Although this phenomenon is well understood from a physical point of view, its mathematically rigorous description is still incomplete. We present a mathematical precise treatment of the Bose-Einstein condensation in the simple case of an ideal Bose gas in a box.

Thursday, October 10th
Title: Hydrocode Modeling of Impact Craters
Speaker: Wendy CaldwellArizona State University
Room: Ayres 405
Time: 3:35pm
Abstract: Asteroid 16 Psyche is the largest M-type (metallic) Main Belt Asteroid (MBA). Radar albedo data indicate Psyche’s surface is rich in metallic content, but estimates for Psyche’s bulk structure vary widely. Psyche has two large impact structures in its Southern hemisphere. In this work, we present results from 2D and 3D simulations of the formation of these craters using the FLAG hydrocode, developed and maintained by Los Alamos National Laboratory. FLAG has been verified and validated for impact cratering simulations, with good agreement to theoretical and experimental results. Through quantitative comparison of the simulated crater dimensions with measured values, our models suggest that Psyche is largely composed of porous, metallic material. In addition, our work indicates that the impacts were likely oblique, with angles at least 45 degrees from vertical.