Seminar Calendar
for events the day of Tuesday, September 4, 2012.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, September 4, 2012

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, September 4, 2012
 Del Edit Copy
Submitted by franklan.
 Jim McClure (Purdue University)Verdier duality and Poincare dualityAbstract: There is a well-known argument that deduces Poincare duality from Verdier duality. In the lecture I will review the relevant sheaf-theoretic background and show that the isomorphism obtained in this way is the same as the classical isomorphism obtained from the cap product. As a byproduct I will observe that Verdier duality is not actually needed for the well-known argument mentioned above. Everything I will say has an analogue for intersection homology (in particular, Verdier duality is not needed for the proof of Poincare duality in that situation either); I'll say something about this at the end if time allows.

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, September 4, 2012
 Del Edit Copy
Submitted by phierony.
 Andrew Arana (UIUC Philosophy & Math)Transfer in algebraic geometryAbstract: The focal question of this talk is to investigate the value of transfer between algebra and geometry, of the sort exemplified by the Nullstellensatz. Algebraic geometers frequently talk of such transfer principles as a "dictionary" between algebra and geometry, & claim that these dictionaries are fundamental to their practice. We'll first need to get clear on what such transfer consists in. We'll then investigate what how such transfer might improve how knowledge is gathered in algebraic geometric practice.

Probability Seminar
2:00 pm   in Altgeld Hall 347,  Tuesday, September 4, 2012
 Del Edit Copy
Submitted by kkirkpat.
 Michael Damron (Princeton U)Invasion percolation, the incipient infinite cluster and random walks in 2DAbstract: In this talk I will define two percolation models: the invasion percolation cluster (IPC) and the incipient infinite cluster (IIC). Both of these are closely related to critical independent percolation, and have similar critical exponents and fractal structure. I will explain recent results with Phil Sosoe and Jack Hanson (Ph. D. students at Princeton) about quenched subdiffusivity of random walks on both graphs. This extends work of H. Kesten, who showed in the 80's that a random walk on the IIC is subdiffusive in an averaged sense.

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, September 4, 2012
 Del Edit Copy
Submitted by lidicky.
 Derrick Stolee   [email] (UIUC)Uniquely $K_r$-Saturated Cayley GraphsAbstract: A graph is uniquely $H$-saturated if it contains no copy of $H$ but adding any missing edge creates exactly one copy of $H$. In the case of $H$ being a complete graph, very little is known about which graphs are uniquely $K_r$-saturated. The only two infinite families previously known are books and the complements of odd cycles. In this talk, we will discuss two new infinite families of uniquely $K_r$-saturated graphs which are complements of Cayley graphs with small generator sets. One of these proofs is the first example of using discharging to bound the clique number of a graph. This is joint work with Stephen G. Hartke.