Fall 2004

· September 14 (Tue)
Speaker: Terry Napier (Lehigh University)
Title: Relative ends and mappings to Riemann surfaces
Abstract:
Coordinates: Christmas-Saucon 336, Lehigh, 4:10—5:00

· October 19 (Tue):
Speaker: Justin Corvino (Lafayette College)
Title: The Einstein Constraint Equations
Abstract: We introduce the Einstein Constraint Equations from General Relativity.  We will survey the interplay between the geometry, topology and physics inherent in these equations, including the fundamental Positive Mass Theorem of Schoen and Yau, the Penrose Inequality, and as time permits, recent results about gluing solutions and black holes.
Coordinates: Pardee 217, Lafayette College, 4:10—5:00

· November 9 (Tue):
Speaker: Rachelle DeCoste (United States Military Academy)
Title: Closed Geodesics on Nilmanifolds constructed from 2-step Nilpotent Lie Groups
Abstract:
Coordinates: Christmas-Saucon 336, Lehigh, 4:10—5:00

· Postponded until Spring, `05 semester:
Speaker: Josh Sabloff (Haverford College)
Title: Invariants of Legendrian Knots
Abstract: I will introduce a special type of 2-plane field on R³ called the standard contact structure.  A Legendrian knot is a closed curve that is everywhere tangent to the contact structure.  Similarly to topological knot theory, a fundamental problem in Legendrian knot theory is to determine when it is possible -- or impossible -- to deform one Legendrian knot into another through Legendrian knots.  I will introduce two "classical" invariants of Legendrian knots, and then show, using some newer, "non-classical" invariants, that the classical invariants do not tell the whole story
Coordinates: Pardee 217, Lafayette College, 4:10—5:00

· November 30 (Tue):
Speaker: Alejandro Adem (University of Wisconsin, Madison & IAS)
Title: Toroidal Orbifolds and Group Cohomology
Abstract: TBA
Coordinates: Christmas-Saucon 336, Lehigh, 4:10—5:00

Spring 2005

· February 8 (Tue):
Speaker: Josh Sabloff (Haverford College)
Title: Invariants of Legendrian Knots
Abstract: I will introduce a special type of 2-plane field on R³ called the standard contact structure.  A Legendrian knot is a closed curve that is everywhere tangent to the contact structure.  Similarly to topological knot theory, a fundamental problem in Legendrian knot theory is to determine when it is possible -- or impossible -- to deform one Legendrian knot into another through Legendrian knots.  I will introduce two "classical" invariants of Legendrian knots, and then show, using some newer, "non-classical" invariants, that the classical invariants do not tell the whole story
Coordinates: Pardee 217, Lafayette College, 4:10—5:00

· February 15 (Tue):
Speaker: John Meier (Lafayette College)
Title: The Homology of the Group of Loops
Abstract: The group PS_n is something like a higher dimensional version of the pure braid group. Just as the pure braid group can be thought of as the group of motions of n points in the plane, PS_n is the group of motions of n unknotted, unlinked circles in 3-space. I will present a computation of the homology groups of PS_n. The bad news is this is a spectral sequence computation. The good news is all the hard work boils down to the combinatorics of planted forests. (Joint with Craig Jensen and Jon McCammond)
Coordinates: Pardee 217, Lafayette College, 4:10—5:00

· March 29 (Tue):
Speaker: Martin Bendersky (CUNY)
Title: A spectral sequence approach to normal forms
Abstract: The theory of normal forms has been around since Poincare's time. An incomplete list of applications are to vector fields, Hamiltonians at equilibria, differential equations and singularity theory. In general one tries to modify a given element in a Lie algebra into a particularly useful form.  The algorithm that performs the conversion (the normal form algorithm) can be a formidable computation.  I will describe the normal form algorithm (using a simple matrix example) and show how to interpret the normal form algorithm as a calculation of a particularly simple spectral sequence.
Coordinates: Christmas-Saucon 336, Lehigh, 4:10—5:00

· April 19 (Tue):
Speaker: Jean Steiner (NYU)
Title: Playing hide and go-seek on Markov Chains and surfaces (Spectral invariants on surfaces and Markov Chains)
Abstract: In this talk we will consider Green's functions on surfaces and on discrete Markov chains.  In both settings, the regularized trace of the Laplacian emerges as an interesting spectral invariant, and we will consider relevant analogies and probabilistic interpretations.
Coordinates: Christmas-Saucon 336, Lehigh, 4:10—5:00

· April 26 (Tue):
Speaker: Constance Leidy (U Penn)
Title: Algebraic Invariants of Nkots (Oops! -- Knots): Why non-commutativity is a good thing
Abstract: Almost all invariants of classical knot theory come from commutative algebra. We will discuss some relatively new invariants that involve non-commutative algebra. These include generalizations of the classical Alexander module and classical Blanchfield linking form
Coordinates: Christmas-Saucon 336, Lehigh, 4:10—5:00