Feb 3 (Tues, 10am): John Etnyre (Penn) Contact Geometry, Topology and Dynamics
Contact geometry is a venerable subject that arose out of the study of Geometric Optics in the 1800's. Though the years it has repeatedly cropped up in many areas of mathematics, but only in the past 30 years or so has it received serious attention. Recently there has been great progress in understanding contact structures. Depending on ones perspective contact structures sometimes seem like topological objects, sometimes geometric objects and sometimes dynamical objects. In this talk I will begin by discussing how contact structures arise out of natural problems and how they have deep connections with topology and dynamics. Then after surveying a few topics about contact structures in low dimensions I will define contact homology in certain situations. Contact homology is a new invariant of contact structures (and/or certain submanifolds of them) that is similar, in spirit, to Gromov-Witten invariants of symplectic manifolds or Floer homology of Lagrangian submanifolds in symplectic manifolds. I then will proceed to discuss applications of contact homology, in particular, I will describe how it yields potentially new invariants of submanifolds of Euclidean space.
Feb 6: Bjorn Dundas (Norwegian University of Science and Technology) Elliptic cohomology via 2-bundles?
Feb. 12 (Thurs, 4pm 6438 - Department Colloquium): Nitya Kitchloo (Johns Hopkins University) Topology of Infinite dimensional Groups
I will give a general framework to study the topology of infinite dimensional groups via their actions on contractible spaces known as Buildings. The groups of interest to us will be loop groups, Kac-Moody groups, symplectomorphism groups and similar transformation groups. I will give examples of natural buildings associated to such groups and use them to derive some consequences.
Feb. 13: Nitya Kitchloo (Johns Hopkins University) Topology of Symplectomorphism Groups.
I describe the topology of (the classifying space of) the symplectomorphism groups of a family of symplectic 4-manifolds. In particular, we calculate the integral cohomology of these classifying spaces. We also study the space of compatible complex structures on these symplectic manifolds and outline a proof showing that this space is contractible.
Feb 19 (Thurs, 4pm 6438 - colloquium): Gunnar Carlsson (Stanford) Algebraic topology as a tool in data analysis.
I will discuss some attempts to recover topological information about geometric objects from "point cloud data" sampled from the object. Examples will include data sets obtained from image data, and the problem of recognizing shapes, i.e. subcomplexes of Euclidean 3-space.
Feb 20: Gunnar Carlsson (Stanford) Representations of Galois groups and algebraic K-theory of fields.
This talk will discuss some conjectures about the relationship between the algebraic K-theory of a field on the one hand and the so-called derived completed complex representation theory of the absolute Galois group of the field. I will also discuss the connection of this derived completion with the study of the space of deformations of a given representation.
March 5: Alissa Crans (UC Riverside) Lie 2-algebras and the Zamolodchikov Tetrahedron Equation
March 11 (Thursday, Colloquium 4pm 6438): Frank Quinn (Virginia Tech) History of manifolds
Tracing the use of the term over 150 years gives insight into the way mathematicians name things, and the things mathematicians name.
March 12: Stefan Friedl (Munich, Germany) Examples of topologically slice knots
justin@math.ucsd.edu
Image of (-2,3,-5) pretzel knot from Rob Scharein's KnotPlot Site.
