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

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Tuesday, February 28, 2017

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, February 28, 2017
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Submitted by erikw.
Robert Kaufman (UIUC)
Complexity in Dual Banach Spaces
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
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Submitted by seminar.
To Be Announced

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, February 28, 2017
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Submitted by rtramel.
Sheldon Katz (UIUC)
BPS Counts on K3 surfaces and their products with elliptic curves
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.

Graph Theory and Combinatorics Seminar
3:00 pm   in 241 Altgeld Hall,  Tuesday, February 28, 2017
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Submitted by molla.
Misha Lavrov (Carnegie Mellon University)
Distance-uniform graphs with large diameter
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.

Graduate Student Analysis Seminar
4:00 pm   in 131 English,  Tuesday, February 28, 2017
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Submitted by compaan2.
Matthew Romney   [email] (UIUC Math)
John's ellipsoid theorem and applications
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.