Upcoming Postdoc Seminars

All seminars will be held in the MBI Lecture Hall - Jennings Hall, Room 355 - unless otherwise noted.

TBD
October 02, 2014 10:20 - 11:15AM

Abstract Not Submitted

TBD
October 23, 2014 10:20 - 11:15AM

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TBD
October 30, 2014 10:20 - 11:15AM

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TBD
November 13, 2014 10:20 - 11:15AM

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TBD
November 13, 2014 10:20 - 11:15AM

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TBD
December 04, 2014 10:20 - 11:15AM

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TBD
December 11, 2014 10:20 - 11:15AM

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TBD
January 15, 2015 10:20 - 11:15AM

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TBD
January 22, 2015 10:20 - 11:15AM

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TBD
January 29, 2015 10:20 - 11:15AM

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TBD
February 12, 2015 10:20 - 11:15AM

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TBD
February 26, 2015 10:20 - 11:15AM

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TBD
March 05, 2015 10:20 - 11:15AM

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TBD
March 12, 2015 10:20 - 11:15AM

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TBD
March 19, 2015 10:20 - 11:15AM

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TBD
April 02, 2015 10:20 - 11:15AM

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TBD
April 09, 2015 10:20 - 11:15AM

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TBD
April 23, 2015 10:20 - 11:15AM

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TBD
May 07, 2015 10:20 - 11:15AM

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TBD
May 14, 2015 10:20 - 11:15AM

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Upcoming Visitor Seminars

September 24, 2014 10:20 - 11:15AM

Evolutionary games first arose in the work of Maynard Smith and Price in the 70s, who introduced the concept into ecology in order to explain why conflicts over territory between male animals of the same species are usually of the "limited war" type and do not cause serious damage. A second important application, which involves the famous Prisoner's dilemma game, is to understand the persistence of altruistic behavior. There are many other applications, including recent work seeking to understand the competition (and cooperation) of different types of cells in cancer.

Most of the analyses of evolutioanry game dynamics assume a homogeneously mixing population. However twenty years ago, Nowak and May, and Durrett and Levin showed that space could drastically change the outcome of evolutionary games, for instance allowing cooperators to persist in Prisoner's dilemma. There is now an extensive literature on spatial games, but much of it is based on heuristic principles or approximate analyses. In this talk we will explain how recent work of Cox, Durrett, and Perkins for voter model perturbations can be applied to study spatial evolutionary games in which all relative fitness are close to 1, a situation which covers many applications to cancer.

The main result is that the effect of space is equivalent to (i) changing the entries of the game matrix and (ii) replacing the replicator ODE by a related PDE. The first idea is due to Ohtsuki and Nowak (for the pair approximation) while the second is well known in the theory of stochastic spatial processes. A remarkable aspect of our result is that the limiting PDE depends on the kernel which dictates the interaction between players only through the values of two simple probabilities associated with it (an idea initially proposed by Corina Tarnita et al. Due to results of Aronson and Weinberger, and Fife and McLeod, we can analyze any 2x2 game. However, when there are three strategies the limiting object is a system of reaction diffusion equations. Many results can be derived using techniques from my AMS Memoir "Mutual Invadability implies Coexistence" but it is important open problem to understand what happens in the spatial game when the replicator dynamics show bistability.

TBA
October 07, 2014 10:20 - 11:15AM

Abstract not submitted.

TBA
October 21, 2014 10:20 - 11:15AM

Abstract not submitted.

upcoming special seminars