UIUC Dept. of Mathematics Seminar Calendar

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Friday, October 29, 2010

Graduate Analysis Seminar
1:00 pm in 241 Altgeld Hall, Friday, October 29, 2010

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Submitted by savsec2.

Andrew Vlasic (UIUC Math)
To Be Announced
Abstract: Let $S_1,\dots S_n$ be pure strategies and $a_{ij}}$ be the payoff of $S_i$ playing against $S_j$. Given all of these strategies in a population, how would the frequencies of people playing a particular strategy evolve over time. The Replicator equation is a great model for this type of population dynamics. The problem with this dynamic is that it does not adjust for random fluctuations of the payoffs. Fudenberg and Harris worked with this concept and added a Brownian motion into the model. Since Brownian motion is a.s. continuous it fails to capture random one time impacts. We will build off of this model by further adding a compensated Poisson integral to adjust for these anomalies.

Model Theory and Descriptive Set Theory Seminar
4:00 pm in 345 Altgeld Hall, Friday, October 29, 2010

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Submitted by phierony.

Mojtaba Moniri (Western Illinois University)
Some Gap Realization in Discrete Structures, and Gap Definability in Ordered Fields
Abstract: We discuss two separate issues. First, let R be a real closed field and D a maximal discrete subring of R. We show that the ordered additive reduct of D need not be maximal (as a discrete additive subgroup of R). The field R may realize some gaps in D, and this is preventive (J. Schmerl, 1985). This is the tip of the iceberg related to some recent results of D'Aquino-Knight-Lange. Next, we present an ordered field which is not real closed (so it has p-definable gaps), but none of its gaps are 0-definable. This is based on a construction due to van den Dries (of a non real-closed field of power series where the set of infinitesimals is not 0-definable), and our earlier inconclusive arguments with Eivazloo. We raise some related questions on traversing gaps, definably.

Women in Mathematics Seminar
4:00 pm in 241 Altgeld Hall, Friday, October 29, 2010

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Submitted by asecele2.

Jane Butterfield (UIUC)
Games played on graphs
Abstract: We will present one of two games that can be played on graphs: "Grab the Gold!" or "Revolutionaries versus Spies". Both were studied last summer in the Combinatorics REGS group, and researchers will be presenting some of the results they came up with then. The talk will be accessible to any graduate (or undergraduate for that matter), and won't assume prior knowledge about graphs or graph theory. In "Grab the Gold!", the vertices of a tree have piles of gold on them. Each player takes turns deleting a leaf and taking its gold--the winner is the one with the most gold when the tree has been entirely deleted. In "Revolutionaries versus Spies", there are r revolutionaries and s spies sitting on vertices of a graph. The revolutionaries want to form a meeting (get m revolutionaries onto the same vertex) and the spies want to spy on each meeting. The game ends if the revolutionaries can form a spy-free meeting.