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for events the day of Tuesday, February 28, 2017.

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Tuesday, February 28, 2017

1:00 pm in 345 Altgeld Hall,Tuesday, February 28, 2017

Complexity in Dual Banach Spaces

Robert Kaufman (UIUC)

Abstract: X is a Banach space, X* is its dual space, composed of bounded linear functionals on X. The norm of a functional in X* is its supremum over the closed unit ball in X. NA is the set of functionals whose norm is attained there. S (for "sharp") is the set of functionals whose norm is attained at precisely one point in the closed ball. To obtain interesting conclusions about the complexity of these sets, the space X is re-normed. (This is not as scary as it sounds.)

1:00 pm in Altgeld Hall,Tuesday, February 28, 2017

To Be Announced

2:00 pm in 241 Altgeld Hall,Tuesday, February 28, 2017

Weighted Partition Identities

Hannah Burson (UIUC)

Abstract: Ali Uncu and Alexander Berkovich recently completed some work proving several new weighted partition identities. We will discuss some of their theorems, which focus on the smallest part of partitions. Additionally, we will talk about some of the motivating work done by Krishna Alladi.

3:00 pm in 243 Altgeld Hall,Tuesday, February 28, 2017

BPS Counts on K3 surfaces and their products with elliptic curves

Sheldon Katz (UIUC)

Abstract: In this survey talk, I begin by reviewing the string theory-based BPS spectrum computations I wrote about with Klemm and Vafa in the late 1990s. These were presented to the algebraic geometry community as a prediction for Gromov-Witten invariants. But our calculations of the BPS spectrum contained much more information than could be interpreted via algebraic geometry at that time. During the intervening years, Donaldson-Thomas invariants were introduced, used by Pandharipande and Thomas in their 2014 proof of the original KKV conjecture. It has since become apparent that the full meaning of the KKV calculations, and more recent extensions, can be mathematically interpreted via motivic Donaldson-Thomas invariants. With this understanding, we arrive at precise and deep conjectures. I conclude by surveying the more recent work of myself and others in testing and extending these physics-inspired conjectures on motivic BPS invariants.

3:00 pm in 241 Altgeld Hall,Tuesday, February 28, 2017

Distance-uniform graphs with large diameter

Misha Lavrov (Carnegie Mellon University)

Abstract: We say that a graph is epsilon-distance-uniform if there is a value d (called the critical distance) such that, for every vertex v, all but an epsilon fraction of the other vertices are at distance exactly d from v. Random graphs are distance-uniform with logarithmic critical distance, and it was conjectured by Alon, Demaine, Hajiaghayi, and Leighton that the critical distance (equivalently, the diameter) of a distance-uniform graph must always be logarithmic. In this talk, we use a generalization of the Towers of Hanoi puzzle to construct distance-uniform graphs with a much larger diameter: for constant epsilon, as large as n^O(1/log log n). We show that this construction is more or less worst possible for sufficiently small epsilon, leaving open the possibility that for large epsilon, much worse cases exist. This is joint work with Po-Shen Loh.

4:00 pm in 131 English,Tuesday, February 28, 2017

John's ellipsoid theorem and applications

Matthew Romney   [email] (UIUC Math)

Abstract: We will discuss and prove a beautiful piece of classical mathematics, a theorem of Fritz John (1948) which characterizes the ellipsoid of maximal volume contained in a convex body in Euclidean space. Among many other applications, it has proven useful in my area of research, quasiconformal mappings.