Department of

Mathematics


Seminar Calendar
for events the day of Friday, March 19, 2021.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, March 19, 2021

2:00 pm in Contact for zoom link,Friday, March 19, 2021

The descriptive complexity of classes of Banach lattices

Mary Angelica Gramcko-Tursi (UIUC Math)

Abstract: The descriptive complexity of a class of spaces gives us an initial sense of how "nice" the class is. When a set is not "nice," this fact can also be used to derive results related to the existence of universal spaces. In this talk, we present some examples of Borel and non-Borel classes of Banach lattices and some related results derived from their descriptive complexity. We also show areas where the descriptive complexity results on Banach lattices compare and contrast with previously done analogous work on Banach spaces.

4:00 pm in Zoom,Friday, March 19, 2021

Free products of Abelian groups in Mod(S)

Chris Loa (UIUC)

Abstract: In 2002, Farb and Mosher introduced a notion of convex cocompactness for mapping class groups. The original notion of convex cocompactness comes from Kleinian groups, where it is a special case of geometric finiteness. In recent work Dowdall, Durham, Leininger, and Sisto have introduced a notion of “parabolic” geometric finiteness for mapping class groups. Examples include convex cocompact groups (as one would hope) and finitely generated Veech groups by work of Tang. In this talk we’ll construct a new family of examples of parabolically geometrically finite groups and show why they are undistorted in Mod(S). Please email basilio3 (at) illinois (dot) edu for Zoom information.

4:00 pm in Zoom,Friday, March 19, 2021

Benford's Law: Adventures in Undergraduate Research

AJ Hildebrand   [email] (UIUC Math)

Abstract: If one makes a list of the areas of all 200 countries in the world, one finds that around 30 percent of those numbers begin with the digit 1, around 17 percent begin with the digit 2, while only around 5 percent begin with the digit 9. Similar frequencies of first digits have been observed in all sorts of real world data—from populations of cities to heights of tallest buildings to numbers in tax returns and numbers of Twitter followers. This near-universal phenomenon is called Benford's Law. In the first part of this talk I will give an overview of Benford's Law and its applications and explain the math behind it. In the second part I will focus on Benford's Law for mathematical sequences such as the powers of 2. I will describe an undergraduate research project that started out back in 2015 as an IGL project, then turned into a multi-year research adventure full of surprises and unexpected twists, and ended up being the most fun, rewarding, and interesting undergraduate research project I have ever supervised.

For zoom info, email drthoma2@illinois.edu