Wednesday December 12, 2018 4:00 PM Math Tower 5127
 Analysis Student Seminar Jae Ho Cho, Stony Brook University
SLE: Transition from simple curves to nonsimple curvesTo finish up the semester, we discuss the proof that SLE$(\kappa)$ transitions from being a simple curve to a nonsimple curve when $\kappa = 4$.

Wednesday December 12, 2018 4:00 PM  5:30 PM Math Tower P131
 Algebraic geometry seminar Bhargav Bhatt, University of Michigan
Etale cohomology of affinoid spacesThis talk has two distinct but related parts. First, I will discuss a new Grothendieck topology (the arc topology) on the category of schemes and its usefulness in addressing some foundational questions in etale cohomology (including excision as well as new proofs of the FujiwaraGabber theorem and some results of Huber). Secondly, I will explain how to prove the analog of the Artin vanishing theorem in rigid analytic geometry. (Joint work with Akhil Mathew.)

Wednesday December 12, 2018 2:30 PM  3:30 PM Math Tower P131
 Colloquium Manuel Rivera, University of Miami
A new point in topologyOne knows in algebraic topology the homotopical properties of geometric spaces can be recast into the language of infinite dimensional topological groups determined by function spaces of closed loops in the geometric spaces. For example the zeroth homology of the function space of based loops can be naturally identified with the group algebra of the fundamental group of the geometric space. This group algebra has a compatible coproduct determined by saying the group elements are grouplike for the coproduct. Conversely the group like elements in this coalgebra form a group equivalent to the given one.
The new point in topology says this bialgebra determining the fundamental group and higher dimensional aspects can, in complete generality, be determined directly from algebraic structure on geometric chains in the geometric space itself. The algebraic construction that does this produces a free differential algebra from a differential coalgebra and was introduced sixty years ago for simply connected spaces. Remarkably it is understood only now to work fine for all geometric spaces if one adds something to it.
The new idea beyond technique is to combine the algebraic construction from the past with the infinite homotopical symmetry of chain approximations to the diagonal mapping of the geometric space which is itself perfectly symmetrical. This makes the chain coalgebra on the geometric space cocommutative in a derived sense so that the construction from the past becomes enriched to a bialgebra in a derived sense. One now sees the fundamental group in the zeroth homology of the enhanced algebraic construction and furthermore one sees higher dimensional homotopical information about the geometric space in the homotopy type of the enhanced algebraic construction.

Thursday December 13, 2018 2:15 PM  3:15 PM MATH 5127
 Symplectic Geometry Seminar Chris Woodward, Rutgers
Invariance of immersed Floer cohomology under Lagrangian surgeryThis is a joint work with Joseph Palmer, and uses heavily earlier
the chapter of FukayaOhOhtaOno on the behavior of holomorphic disks under surgery. The motivation is a larger project, partly joint with Sushmita Venogopalan, to prove a HarderNarasimhan filtration for the Fukaya category under KahlerRicci flow (KRF): For any KRF surgery, some copies of the Fukaya category of the center of the surgery embed in the presurgery Fukaya category and the quotient is the postsurgery Fukaya category. In order to carry this out, one has to understand how immersed Floer cohomology behaves under combined KRF/mean curvature flow. One of the bad things that can happen is that the bounding cochain can hit a "wall" where the qvaluation of one of the coefficients becomes zero. We show that one can continue past the wall by using a Polterovich surgery, so that the Floer cohomology is isomorphic. Some previous cases of this were known by work of PascaleffTonkonog, DimitroglouRizellEkholmTonkonog, and HongKimLau.

Thursday December 13, 2018 4:00 PM  5:00 PM Math Tower P131
 Colloquium Bhargav Bhatt, University of Michigan
Interpolating padic cohomology theoriesIntegration of differential forms against cycles on a complex manifold helps relate de Rham cohomology to singular cohomology, which forms the beginning of Hodge theory. The analogous story for padic manifolds, which is the subject of padic Hodge theory, is richer due to a wider variety of available cohomology theories (de Rham, etale, crystalline, and more) and torsion phenomena. In this talk, I will give a bird's eye view of this picture, guided by the recently discovered notion of prismatic cohomology that provides some cohesion to the story. (Based on joint work with Morrow and Scholze as well as work in progress with Scholze.)

Thursday December 13, 2018 1:00 PM  2:15 PM Math Tower 5127
 Seminar in Topology and Symplectic Geometry Lev TovstopyatNelip, Boston College
The transverse invariant and braid dynamicsLet K be a link braided about an open book (B,p) supporting a contact manifold (Y,x). K and B are naturally transverse links. We prove that the hat version of the transverse
link invariant defined by Baldwin, VelaVick and Vertesi is nonzero for the union of K with B. As an application, we prove that the invariant of a transverse braid having
fractional Dehn twist coefficient greater than one is nonzero. We discuss geometric consequences and future directions.

