CAS - Department of Mathematics - Colloquium
http://www.uab.edu/cas/mathematics/2016-2017
Thu, 29 Sep 2016 17:22:55 -0500Joomla! - Open Source Content Managementen-gbcasweb@uab.edu (casmath)October 14, Jason Teutsch, UAB
http://www.uab.edu/cas/mathematics/2016-2017/418-october-14-jason-teutsch-uab
http://www.uab.edu/cas/mathematics/2016-2017/418-october-14-jason-teutsch-uabTitle: A brief on short descriptions

Abstract: Given a binary string, can one find a short description for it? The well-known answer is "no, Kolmogorov complexity is not computable.'' Faced with this barrier, one might instead seek a short list of candidates which includes a laconic description. In fact, efficiently computable short lists do exist, and I will discuss the extent to which one can obtain them. This talk will include a gentle introduction to Kolmogorov complexity followed by a discussion connecting list approximations to classical combinatorics and randomness extraction. The program will roughly follow a recent SIGACT News survey coauthored with Marius Zimand.]]>selinger@uab.edu (Nikita Selinger)2016-2017Thu, 29 Sep 2016 18:36:10 -0500October 7, Hyun-Kyoung Kwon, University of Alabama
http://www.uab.edu/cas/mathematics/2016-2017/417-october-7-hyun-kyoung-kwon-university-of-alabama
http://www.uab.edu/cas/mathematics/2016-2017/417-october-7-hyun-kyoung-kwon-university-of-alabama Abstract: The original proof of the Corona Theorem is due to L. Carleson and many different versions and generalizations of the Corona Theorem have been investigated. I will discuss one such generalization recently obtained with my graduate student. I will also explain how the technique widely used to solve the Corona problems can be applied to get results about operator equivalence (unitary equivalence and similarity) and about the degree bound in Hilbert's Nullstellensatz. ]]>selinger@uab.edu (Nikita Selinger)2016-2017Mon, 26 Sep 2016 15:14:02 -0500September 30, Kabe Moen, University of Alabama
http://www.uab.edu/cas/mathematics/2016-2017/416-september-30-kabe-moen-university-of-alabama
http://www.uab.edu/cas/mathematics/2016-2017/416-september-30-kabe-moen-university-of-alabamaTitle: When does a function belong to the union of Lebesgue spaces?

Abstract: We survey some basic facts about Lebesgue spaces. We show that the union of Lebesgue spaces is intimately related to the Hardy-Littlewood maximal function and the theory of weighted Lebesgue spaces -- Lebesgue spaces with a change of measure. We give several simple characterizations of when a function belongs the union Lebesgue spaces. This presentation will be based on a joint work with Greg Knese and John McCarthy. ]]>selinger@uab.edu (Nikita Selinger)2016-2017Mon, 26 Sep 2016 15:09:33 -0500September 23, Jesse Prince-Lubawy, University of North Alabama
http://www.uab.edu/cas/mathematics/2016-2017/413-test
http://www.uab.edu/cas/mathematics/2016-2017/413-test Abstract: A handlebody orbifold consists of finitely many quotients of the 3-ball by spherical groups (Z_{n}, D_{n}, A_{4}, S_{4}, and A_{5}) connected by 1-handle orbifolds respecting singular axes and their orders, and such that topologically the outcome is an orientable handlebody. We will first examine the handlebody of genus two, V_{2}, and the handlebody orbifolds V_{2}/G, where G is a finite group. We will then discuss equivalence of group actions and see that, up to equivalence, there are 13 actions on V_{2}. This will lead into my work, where we consider cyclic p-squared actions, where p is prime, on a handlebody of genus g.]]>selinger@uab.edu (Nikita Selinger)2016-2017Thu, 08 Sep 2016 20:11:46 -0500September 16, Ted Mahavier, Lamar University
http://www.uab.edu/cas/mathematics/2016-2017/412-september-16-ted-mahavier-lamar-university
http://www.uab.edu/cas/mathematics/2016-2017/412-september-16-ted-mahavier-lamar-universityTitle: Sobolev Steepest Descent for Differential Equations

Abstract: Solving differential equations using steepest descent methods based on the Euclidean norm has long been established as ineffective, although pre-conditioning techniques may alleviate this problem to some extent. However, steepest descent in spaces with a better choice of norm can be quite efficient. Beginning with an example accessible to undergraduates, we will outline Sobolev descent on a few elementary examples and demonstrate at least one interesting open problem in the area. This talk should be accessible to undergraduates, graduate students and faculty not necessarily experts in numerical differential equations.]]>selinger@uab.edu (Nikita Selinger)2016-2017Thu, 08 Sep 2016 16:38:32 -0500