Spring Semester 2006

 

 

Spring’s talks are organized into a mini-conference which will meet on Saturday, March 25, 2006

 

All talks will be on the second floor of Pardee Hall at Lafayette College.  Directions to Lafayette College can be found here, and a campus map can be found here.  Visitors can either park in front of Pardee Hall and enter through the door facing the quad or can park at the Markle Deck.  From Markle Deck, cross High street and head towards the quad (the library, the building with a lot of glass, should be on your right).  Cross the quad; Pardee will be in front of you and slightly to the left.  Enter through the door facing the quad.

 

 

 

Schedule of Events

 

 

9:45 – 10:00

 

Coffee and snacks

 

 

10:00 – 10:55

Zoran Sunik

(Texas A & M)

Title: Hanoi Towers, Schreier Graphs, Iterated Monodromy Groups and Julia sets

 

Abstract: We model the well known Hanoi Towers Problem on k pegs by a self-similar group H(k) acting on a k-regular rooted tree. The Schreier graph of the action of the group H(k) on level n in the tree models the n-disk version of the problem. As n goes to infinity the obtained limiting graph is the Schreier graph of the action of H(k) on the boundary of the  k-ary tree.

 

For the original version of Hanoi Towers on 3 pegs the obtained group H(3) is an automaton group branching regularly over its commutator. The corresponding finite Schreier graphs are 3-regular graphs that approximate the Sierpinski gasket. The group H(3) can be described as the iterated monodromy group of a post-critically finite map f on the Riemann sphere. The Julia set of the map f is homeomorphic to the limiting infinite Schreier graph.

 

The action of H(3) on the levels of the tree provides permutational representations that can be used to determine the spectrum of the Markov operator on the associated Schreier graphs. The spectrum can be described as the closure of the backward orbit of a quadratic polynomial p. It consists of a countable set of isolated points that accumulate to a Cantor set, which is the Julia set of the polynomial p.

11:05 – 12:00

Bi-Zhong Hu, (Binghamton University)

Title: Complexity of parallelizable aspherical manifolds

 

Abstract: There are as many closed aspherical manifolds as there are parallelizable ones and the parallelizable ones

can be as complicated as the unparallelizable ones.  We will discuss: constructing parallelizable closed aspherical / nonpositively curved manifolds using relative hyperbolization; implications on the issue of homotopy invariance of Pontrjagin classes; the classical source of parallelizable aspherical mainfolds from Lie groups.

12:00 – 1:30

Lunch

 

1:30 – 2:30

Pedro Ontaneda, (Binghamton University)

Title: Is the space of negatively curved metrics connected?

 

Abstract: We will discuss this question in the high dimensional case.

 

 

 

Fall Semester 2005

 

  • Date:  October 18 (Tuesday)
    Speaker:     Chris Dwyer (Binghamton University)
    Title:      Twisted Equivariant K-theory for proper actions of discrete groups
    Abstract: TBA
    Coordinates:     Pardee Hall, 4:10—5:00

 

  • Date:  October 25 (Tuesday)
    Speaker:     Gabriele La Nave (Lehigh)
    Title:     Macroscopic dimension and Fundamental group of manifolds with positive isotropic curvature
    Abstract:     TBA
    Coordinates:     Christmas-Saucon 336, Lehigh, 4:10—5:00

 

  • Date:  November 15 (Tuesday)
    Speaker:     Xiaofeng Sun (Lehigh)
    Title:     Good Metrics on the Moduli Space of Riemann Surfaces
    Abstract:     We defined new complete Kähler metrics on the moduli space of hyperbolic Riemann surfaces. These new metrics have good curvature properties and were used to anchor the Kähler-Einstein metric. As corollaries, we showed that all the complete canonical metrics on the Teichmüller space and moduli space are equivalent. Furthermore, the Kähler-Einstein metric has bounded geometry. Also, the logarithmic cotangent bundle of the Deligne-Mumford moduli is strictly stable. We also proved the goodness of the Weil-Petersson metric and the new metrics
    Coordinates:     Christmas-Saucon 336, Lehigh, 4:10—5:00

 

  • Date:  November 29 (Tuesday)
    Speaker:     Susan Hermiller (University of Nebraska, Lincoln)
    Title:     Variations on almost convexity and tame combings
    Abstract:     In this talk I will describe a spectrum of definitions of almost convexity for groups, a measure of the tame combability of groups, and the relationships between these properties.  This is joint work with Sean Cleary.
    Coordinates:     Pardee Hall, Lafayette, 4:10—5:00