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Events happening on February 19, 2019

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Feb. 19, 2019 11am (MATH 350)	Number Theory Dang-Khoa Nguyen (University of Calgary) X For every complex number , let . Let be a number field, let , and let be non-zero algebraic numbers. We solve the problem of the existence of such that there are infinitely many tuples satisfying where and having small logarithmic height compared to . In the special case when have the form for fixed , our work yields results on algebraic approximations of of the form with and . Various results on linear recurrence sequences also follow as an immediate consequence. The case and is essentially a rational integer was obtained by Corvaja and Zannier and settled a long-standing question of Mahler. The use of the Schmidt's Subspace Theorem based on work of Corvaja-Zannier together with several modifications play an important role in the proof. This is joint work with Kulkarni and Mavraki. An Extension of Results by Mahler and Corvaja-Zannier
Feb. 19, 2019 12:10pm (MATH …	Kempner Brian Rider (Temple) X Random matrix theory grew out of fundamental considerations in mathematical statistics and theoretical physics, and now has applications to such disparate areas as number theory, wireless communications and bioinformatics. A perfect example of the field's reach is offered by the Tracy-Widom laws. First discovered as the fluctuation limit of the largest eigenvalue of certain symmetric random matrices at infinite dimension, these laws are now understood to serve the role of the "bell curve” for a wide area of nonlinear phenomena. I will discuss a relatively new description of the Tracy-Widom laws (along with a natural family of generalizations) in terms of random Schroedinger type operators. Operator limits of random matrices
Feb. 19, 2019 2pm (MATH 220)	Michael Wheeler (CU Boulder) p = t via Nonstandard Models of Set Theory, Part 4
Feb. 19, 2019 2pm (MATH 350)	Lie Theory Sarah Salmon (CU) X This talk will focus on previous work done in describing the center of the nil Temperley–Lieb algebra of type affine A. We will describe a faithful representation using particle configurations and give small hints toward future work. Exploring the nil Temperley–Lieb algebra of type affine A
Feb. 19, 2019 3pm (MATH 350)	Probability Brian Rider (Temple) X In random matrix theory there are three fundamental local limit regimes of interest: the spectral bulk and the so-called “hard” and “soft” edges. At this point all three regimes, for all values of the inverse temperature parameter beta, have descriptions in terms of random differential operators. On the other hand, the mathematical physics literature abounds with more exotic limits theorems arising from degenerate situations or various double scalings. With few exceptions, the latter have been restricted to beta = 2 on account of the presence of exact formulas in that setting. I’ll describe, via random operators, the first general beta result for a crossover (double scaling) ensemble. This is joint work with Jose Ramirez (Universidad de Costa Rica). A general beta crossover ensemble
Feb. 19, 2019 4pm (MATH 350)	Topology Jonathan Quartin (CU Boulder) Symmetric monoidal categories and other categorical preliminaries

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