Seminar Calendar
for events the day of Tuesday, May 2, 2017.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, May 2, 2017

Topology Seminar
11:00 am   in 345 Altgeld Hall,  Tuesday, May 2, 2017
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Submitted by rezk.
 Nathan Perlmutter (Stanford)Parametrized Morse Theory, Cobordism Categories, and Positive Scalar CurvatureAbstract: In this talk I will construct a cobordism category consisting of manifolds equipped with a choice of Morse function, whose critical points occupy a prescribed range of degrees. I will identify the homotopy the of this cobordism category with the infinite loopspace of a certain Thom spectrum. Using the parametrized version of the Gromov-Lawson construction, I will then show how to use this cobordism category to probe the space of positive scalar curvature metrics on a closed, spin manifold of dimension > 4. Our main result detects many non-trivial homotopy groups in this space of positive scalar curvature metrics.

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Tuesday, May 2, 2017
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Submitted by sahlgren.
 Iván Blanco-Chacón (University College Dublin)p-adic Gross-Zagier formula for Hilbert modular forms

Geometry, Groups, and Dynamics/GEAR
12:00 pm   in 243 Altgeld Hall,  Tuesday, May 2, 2017
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Submitted by clein.
 Matthew Durham (Michigan Math)To Be Announced

Probability Seminar
2:00 pm   in 347 Altgeld Hall,  Tuesday, May 2, 2017
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Submitted by wangjing.
 Dana Mendelson (University of Chicago)To Be Announced

Diversity Training
3:00 pm   in 245 Altgeld Hall,  Tuesday, May 2, 2017
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Submitted by seminar.
 Teaching to Transform: Addressing Race & Racism in the ClassroomAbstract: Teaching to Transform: Addressing Race & Racism in the Classroom will be held from 3-5 pm. All members of the Department of Mathematics are invited to attend.

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, May 2, 2017
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Submitted by molla.
 Louis DeBiasio (Miami University)Infinite graph-Ramsey theoryAbstract: Ramsey's theorem guarantees a monochromatic copy of any countably infinite graph $G$ in any $r$-coloring of the edges of the complete graph $K_\mathbb{N}$. It is natural to wonder how "large" of a monochromatic copy of $G$ we can find with respect to some measure -- for instance, the (upper) density of the vertex set of $G$ in $\mathbb{N}$. Unlike finite graph-Ramsey theory, where this question has been studied extensively, the infinite version has been mostly overlooked. Erdős and Galvin proved that in every 2-coloring of $K_\mathbb{N}$, there exists a monochromatic path whose vertex set has upper density at least $2/3$, but it is not possible to do better than $8/9$. They also showed that there exists a monochromatic path $P$ such that for infinitely many $n$, the set $\{1,2,...,n\}$ contains the first $\frac{n}{3+\sqrt{3}}$ vertices of $P$, but it is not possible to do better than $2n/3$. We improve both results, in the former case achieving an upper density at least $3/4$ and in the latter case obtaining a tight bound of $2/3$. Inspired by this, we consider infinite analogs of well-known finite results on directed paths, trees (connected subgraphs), and graphs of bounded maximum degree/chromatic number. Joint work with Paul McKenney