Iterates, invariance, and chaos
Thursday, January 25, 12:00 p.m. Room 268 in the Olin Science Building.
Abstract: We will consider what happens when we repeatedly compose a given function with itself, focusing particularly on where this repeated composition (known as iteration) sends individual inputs. Various phenomena will be discussed, including the notions of invariance and what some might call chaos.
Evolutionary game theory: the mathematics of cooperation
Thursday, February 8, 12:00 p.m. Room 268 in the Olin Science Building.
Why do we (or any living organisms) cooperate? Cooperation, the act of expending one’s own energy or resources for the good of the group, is a necessary part of life, but is also exploitable by so-called “defectors” who choose not to help out yet still reap the benefits that cooperation yields. In fact, under fairly general assumptions, every rational individual will (theoretically) choose to defect, thereby extinguishing cooperation and dooming society. Of course, cooperation has not been extinguished and is in fact quite common in the natural world. This observation brings us back to the question posed at the beginning of this abstract. In this talk, I will discuss a mathematical framework through which cooperation is often studied called evolutionary game theory, and present several classic and recent results from the field.