All Events

from Tuesday
December 11, 2018 to Monday
December 31, 2018
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Instructions for subscribing to Stony Brook Math Department Calendars

 Month     Agenda 

Wednesday
December 12, 2018

4:00 PM
Math Tower 5-127
Analysis Student Seminar
Jae Ho Cho, Stony Brook University
SLE: Transition from simple curves to non-simple curves

To 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 P-131
Algebraic geometry seminar
Bhargav Bhatt, University of Michigan
Etale cohomology of affinoid spaces

This 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 Fujiwara-Gabber 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 P-131
Colloquium
Manuel Rivera, University of Miami
A new point in topology

One 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 group-like 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 co-algebra on the geometric space cocommutative in a derived sense so that the construction from the past becomes enriched to a bi-algebra 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 5-127
Symplectic Geometry Seminar
Chris Woodward, Rutgers
Invariance of immersed Floer cohomology under Lagrangian surgery

This is a joint work with Joseph Palmer, and uses heavily earlier
the chapter of Fukaya-Oh-Ohta-Ono on the behavior of holomorphic disks under surgery. The motivation is a larger project, partly joint with Sushmita Venogopalan, to prove a Harder-Narasimhan filtration for the Fukaya category under Kahler-Ricci flow (KRF): For any KRF surgery, some copies of the Fukaya category of the center of the surgery embed in the pre-surgery Fukaya category and the quotient is the post-surgery 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 q-valuation 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 Pascaleff--Tonkonog, Dimitroglou-Rizell--Ekholm--Tonkonog, and Hong-Kim-Lau.


Thursday
December 13, 2018

4:00 PM - 5:00 PM
Math Tower P-131
Colloquium
Bhargav Bhatt, University of Michigan
Interpolating p-adic cohomology theories

Integration 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 p-adic manifolds, which is the subject of p-adic 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 5-127
Seminar in Topology and Symplectic Geometry
Lev Tovstopyat-Nelip, Boston College
The transverse invariant and braid dynamics

Let 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, Vela-Vick and Vertesi is non-zero 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 non-zero. We discuss geometric consequences and future directions.


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Instructions for subscribing to Stony Brook Math Department Calendars