Georgia Institute of Technology College of Sciences

Recent advances in fluid dynamics reveal that the recurrent flows observed in moderate Reynolds number turbulence result from close passes to unstable invariant solutions of Navier-Stokes equations. By now hundreds of such solutions been computed for a variety of flow geometries, but always confined to small computational domains (minimal cells).Pipe, channel and plane flows, however, are flows on infinite spatial domains. We propose to recast the Navier-Stokes equations as a space-time theory, with the unstable invariant solutions now being the space-time tori (and not the 1-dimensional periodic orbits of the classical periodic orbit theory). The symbolic dynamics is likewise higher-dimensional (rather than a single temporal string of symbols). In this theory there is no time, there is only a repertoire of admissible spatiotemporal patterns.We illustrate the strategy by solving a very simple classical field theory on a lattice modelling many-particle quantum chaos, adiscretized screened Poisson equation, or the ``spatiotemporal cat.'' No actual cats, graduate or undergraduate, have showninterest in, or were harmed during this research.

In this series of talks, we will study the relationship between the Alexander module and the bordered Floer homology of the Seifert surface complement. In particular, we will show that bordered Floer categorifies Donaldson's TQFT description of the Alexander module. No prior knowledge of the Alexander module or Heegaard Floer homology will be assumed.

In this talk we will discuss the paper of Adiprasito, Huh, and Katz titled "Hodge Theory for Combinatorial Geometries," which establishes the log-concavity of the characteristic polynomial of a matroid.

This is Lecture 2 of a series of 3 lectures by the speaker. See the abstract on Tuesday's ACO colloquium of this week. (Please note that this lecture will be 80 minutes' long.)