Seminars and Colloquia

Tuesday, November 15, 2011

12:00 pm - 01:00 pm

DnA Seminar: The Mathematics of Iterated Paperfolding

Speaker: Michel Dekking, Delft, Wesleyan <br />Abstract: I will present some old and some new results in a project which has been going on for 35 years. There are bits of algebra (representation theory), bits of topology (The Jordan curve theorem, Hausdorff metric), bits of graph theory (Euler's 1736 theorem), bits of number theory (Gaussian primes, Lvschian numbers), bits of theoretical computer science (automatic sequences) and bits of measure theory (Hausdorff dimension).NOTE: This talk will be appropriate for undergraduates.

ESC 638

Tuesday, November 08, 2011

12:00 pm - 01:00 pm

DnA Seminar: Sequences of Intergers Associated wtih Infinte Measure Preserving Transformations

Speaker: Yuji ItoAbstract: Infinite measure preserving ergodic transformations cannot, because of ergodicity, admit a finite, equivalent, invariant measure. Because of this fact, there exist various kinds of infinite sequences of integers that one can associate with such transformations, which are isomorphism invariants. I will discuss some of these sequences, such as weakly wandering sequences, dissipative sequences, recurrent sequences and so on and describe some of their properties.

ESC 638

Tuesday, November 01, 2011

12:00 pm - 01:00 pm

DnA Seminar: Sequences of Integers Associated With Infinite Measure Preserving Transformations

Speaker: Yuji ItoAbstract: Infinnite measure preserving ergodic transformations cannot, because of ergodicity, admit a finite, equivalent, invariant measure. Because of this fact, there exist various kinds of infinite sequences of integers that one can associate with such transformations, which are isomorphism invariants. I will discuss some of these sequences, such as weakly wandering sequences, dissipative sequences, recurrent sequences and so on and describe some of their properties.

ESC 638

Tuesday, October 18, 2011

12:00 pm - 01:00 pm

DnA Seminar: How fractal is the sum of two random fractals?

Speaker: Michel Dekking, Delft/WesleyanAbstract: The Palis conjecture states that if one takes two Cantor sets, such that the sum of their Hausdorff dimensions is greater than 1, then generically it should be true that their algebraic sum should contain an interval. I shall discuss this conjecture in a probabilistic setting.

ESC 638

Tuesday, October 11, 2011

12:00 pm - 01:00 pm

Dynamics 'n Analysis Seminar: Weakly Wandering, Exhaustive Weakly Wandering and Strongly Weakly Wandering Sequences for Measure Preserving Transformations

Speaker: Vidhu Prasad (UML)Abstract: We consider sequences of distinct integers associated to T, an ergodic invertible measure preserving transformation of an infinite measure space. It is well known that such a transformation always has associated to it weakly wandering (WW) sequences, and exhaustive weaklywandering sequences (EWW). Despite this there are many well-known Tfor which not a single EWW is known.In this talk, we consider a class of sequences for T called strongly weakly wandering (SWW). All SWW sequences are also EWW. Their advantage is that the conditions implying SWW are easier to verify than the conditions implying EWW.We will examine SWW sequences for type zero ergodic transformations. An example of a type zero transformation is simple random walk on the integers. All concepts will be defined in the talk. If time permits we connect these sequences to tiling the integers with a single infinite tile. This represents joint work with Eigen, Hajian and Ito.

ESC 638

Tuesday, October 04, 2011

12:00 pm - 01:00 pm

The dynamics of the Nash map for 2 by 2 Games

Speaker: Bruce Kitchens, IUPUI, BUAbstract: J. Nash defined a continuous map from a product of simplices, corresponding to the strategies for a finite game, to itself and used it to show that every finite game has a Nash equilibrium. The map is known as the Nash better response map and a point is a fixed point for the map if and only it is a Nash equilibrium for the game. In the case of a 2 by 2 game the map reduces to a continuous, piecewise rational map of the unit square to itself. I will discuss the dynamics of the map for several 2 by 2 games - prisoner's dilemma, matching pennies and chicken. The dynamics of the map divide the games into three classes, those having a dominant strategy, those having elliptic dynamics and those having hyperbolic dynamics. The dynamics of the map for the game of matching pennies will be discussed in detail.

ESC 638

Monday, April 18, 2011

04:10 pm - 06:00 pm

Exceptional Points For Cocompact Fuchsian Groups

Speaker: Joseph Fera, Wesleyan UniversityAbstract: Let G be a cocompact Fuchsian group acting on the hyperbolic plane H. If G covers a compact hyperbolic surface of genus g (at least 2), then almost every Dirichlet region for G has 12g-6 sides. In this talk, we discuss the exceptional points for G, i.e., the points in H associated to Dirichlet regions for G with strictly less than 12g-6 sides. More specifically, we show that uncountably many exceptional points exist for any cocompact group. We also define and prove the existence of higher order exceptional points for any such group.

ESC 638