September 8-9, 2018
University of Kentucky
Chem-Phys Building: CP 139505 Rose St
Lexington, KY 40508
The funding deadline has passed. If you are a graduate student or early career researcher and would like to be considered for funding, please apply promptly. We may still be able to provide some funding.
Saturday, September 89:00 – 10:00 Coffee, bagels, fruit
10:00 – 11:00 Arnav Tripathy (Harvard)
A geometric model for complex analytic equivariant elliptic cohomology
Abstract: Elliptic cohomology has always been a natural big brother to ordinary cohomology and K-theory. However, in contrast to the plethora of geometric objects that provide representatives for cohomology and K-theory classes, we do not know any geometric objects that provide representatives for elliptic cohomology. I will explain in this talk a step forward for the case of equivariant elliptic cohomology over the complex numbers by using constructions from supersymmetric field theory as geometric models in joint work with D. Berwick-Evans. This talk will need no prior knowledge of either elliptic cohomology or physics of field theories
11:30 – 12:30 Andrew Blumberg (Texas-Austin)
Towards infinite-dimensional norms
Abstract: The description of multiplicative structures on the equivariant stable category for finite groups G in terms of HHR norms has been very successful, and resulted in an essentially algebraic perspective. We know much less in the context of infinite compact Lie groups G. This talk will describe some progress in understanding and speculation about the general setting, inspired by work on a relative version of THH that takes Cn ring spectra as input. This is joint work with Vigleik Angeltveit, Teena Gerhardt, Mike Hill, Mike Mandell, and Tyler Lawson, in various combinations.
12:30 – 2:30 Lunch
2:30 – 3:30 Martina Rovelli (Johns Hopkins)
Characteristic classes as complete obstructions
Abstract: We propose a uniform interpretation of characteristic classes as complete obstructions to the reduction of the structure group of a principal bundle, and to the existence of an equivariant extension of a certain homomorphism defined a priori only on a single fiber. By plugging in the correct parameters, we recover several classical theorems. This leads to the definition of a family of invariants for principal bundles that detect the number of group reductions associated to characteristic classes that a principal bundle admits.
3:30 – 4:00 Coffee, fruit
4:00 – 5:00 Ciprian Manolescu (UCLA)
Homology cobordism and triangulations
Abstract: The study of triangulations on manifolds is closely related to understanding the three-dimensional homology cobordism group. We will survey what is known about this group, with an emphasis on the local equivalence methods coming from Pin(2)-equivariant Seiberg-Witten Floer spectra and involutive Heegaard Floer homology.
5:30 – 7:00 Refreshments at the Math House
Sunday, September 99:00 – 10:00 Coffee, bagels, fruit
10:00 – 11:00 Kristen Hendricks (Michigan State)
A simplicial construction of G-equivariant Lagrangian Floer homology
Abstract: Lagrangian Floer homology is an invariant introduced (along with other related invariants) by A. Floer in the 1980's which associates to a pair of Lagrangian submanifolds in a symplectic manifold M the homology of a graded chain complex with a differential arising from considering solutions to a system of partial differential equations. This construction has been an extremely fruitful source of new invariants in symplectic geometry and low-dimensional topology. In this talk we discuss some of the history of equivariant versions of Lagrangian Floer homology. For a Lie group G acting on a symplectic manifold M and preserving a pair of Lagrangians, under certain hypotheses not including equivariant transversality we then construct a G-equivariant Lagrangian Floer homology. This is joint work with R. Lipshitz and S. Sarkar.
11:30 – 12:30 Ben Antieau (UIC)
Cartier modules and cyclotomic spectra
Abstract: I will describe new joint work with Thomas Nikolaus, which describes a t-structure on cyclotomic spectra. Using this t-structure, I will explain how to recover some results of Bhatt--Morrow--Scholze on the relationship between topological periodic cyclic homology of smooth schemes in characteristic p and crystalline cohomology.
Mike Hill (UCLA) will also give the Hayden-Howard lecture on Monday, Sept 10 at 4pm in Room 110 of the Whitehall Classroom Building.
AccomodationsWe have reserved a block of rooms at the
Holiday Inn Express and Suites Hotel
Downtown at the University
1000 Export Street, Lexington, KY 40504
Please make your reservation before August 17 in order to
qualify for the group rate (group name Midwest Topology).