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for events the day of Tuesday, September 6, 2016.

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Tuesday, September 6, 2016

1:00 pm in 345 Altgeld Hall,Tuesday, September 6, 2016

Hyperfiniteness and Borel combinatorics

Andrew Marks   [email] (UCLA Math)

Abstract: A Borel graph is a graph whose vertex set is the elements of a Polish space and whose edge relation is Borel. We investigate combinatorial problems on hyperfinite Borel graphs—the simplest graphs that can display nonclassical behavior in the setting of descriptive graph combinatorics (as made precise by the Glimm–Effros dichotomy). A fundamental theorem of Kechris, Solecki, and Todorcevic states that every Borel graph of degree at most $d$ has Borel $d + 1$ coloring. Answering a question of Conley and Miller, we show that for every $d$ there is an acyclic $d$-regular hyperfinite Borel graph with no Borel $d$-coloring. This Borel result is in contrast to the measure-theoretic context, where hyperfinite graphs are known to be much simpler to measurably color than arbitrary bounded degree Borel graphs.

1:00 pm in Altgeld Hall,Tuesday, September 6, 2016

On The Essential and Absolute Spectrum of Traveling Waves

Robert Marangell (University of Sydney)

Abstract: TBA

1:00 pm in 7 Illini Hall,Tuesday, September 6, 2016

Parabolic Regularization for the KdV Equation

Erin Compaan   [email] (UIUC Math)

Abstract: In this talk, I'll present a classical result which demonstrates well-posedness of the Korteweg-de Vries (KdV) equation on R. I'll introduce the ideas of well-posedness and solutions, and then go through Bona and Smith's derivation of the existence of classical solutions for the KdV. Their proof rests on a parabolic regularization argument, in which we solve a sequence of "nicer" versions of the equation, and then take the limit. I'll close with a brief discussion of limitations of the method, and of modern techniques which improve the Bona-Smith results.

3:00 pm in 241 Altgeld Hall,Tuesday, September 6, 2016

Canvases and Coloring

Luke Postle (University of Waterloo)

Abstract: In 1994, Thomassen proved that every plane graph G is 5-choosable by proving a stronger statement, namely that if vertices in the interior have lists of size 5 and the vertices on the outer face have lists of size 3 except for two adjacent vertices on the outer face which are precolored, then G has an coloring from those lists. Let us say that, in the statement above, the lists of the outer face have been restricted. Here we outline the proof of a far reaching generalization of his result: there exists a D>0 such that if G is a plane graph and F is a set of faces, pairwise at least distance D apart, and L is a list assignment where only the faces of F are restricted, then G has an L-coloring. Joint work with Robin Thomas.

4:00 pm in 245 Altgeld Hall,Tuesday, September 6, 2016

Abstract: Information session for undergrads at UIUC who plan on applying to mathematics graduate programs in the U.S. and Canada. All welcome.