Game Theory and Economics: Some Classic and Open Problems

March 24th 2014

Speaker: Marzena Rostek (Economics)

Abstract: Game theory studies behavior in strategic situations, that is when agents payoffs depend on behavior of others as well as their own. This talk will give an introduction to how economics and game theory draw on mathematics. We will discuss some classic games and new economic and game theoretic problems, where novel conceptualizations and/or tools are needed

As always, there will be free food.

When: Monday, March 24th 2014, 4:35pm

Some Surprising Issues Relating to Curvature

March 3, 2014

Speaker:  Betsy Stovall

Abstract:  In multivariable calculus, we learn about a few simple, yet fundamental curved surfaces, such as the paraboloid, the sphere, and the cone.  These simple surfaces give rise to some concrete, but very hard (and still unsolved) problems in a field called harmonic analysis.  These problems also have surprising connections to some completely geometric questions about sets in euclidean space.  In this talk, we will give a friendly introduction to some of the questions and ideas in this area.

Multistability and Hidden Attractors

February 24, 2014

Speaker: Clint Sprott, UW Department of Physics

Abstract: One characteristic of nonlinear dynamical systems is that they can have more than one stable equilibrium. Perturbations of the variables or changes in the parameters can cause the system to abruptly switch from one equilibrium to the other from which it is hard to recover (what Al Gore calls a "tipping point"). Furthermore, equilibria can become unstable and give birth to periodic oscillations and even chaos. Hence, in addition to static attractors, there can be limit cycles and strange attractors, and several such attractors can coexist in even simple systems. Sometimes these attractors are "hidden" in the sense that they cannot be found by starting from the vicinity of an unstable equilibrium. Such hidden attractors can be catastrophic if the system is a building, a bridge, or an airplane wing. Examples of such behavior will be illustrated in very simple systems of differential equations and with simple demonstrations.

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