Join us for Topology Day 2017. The event is held in Room 250
of Mathematics Building, UB North Campus. The event is free and
open to the public, with registration required.
11:00-11:50 Mikhail Khovanov (Columbia U): How to categorify
the ring of integers with two inverted.
Abstract: The talk will go over a joint work with Yin Tian where we describe a triangulated monoidal Karoubi complete category with the Grothendieck ring isomorphic to the ring of integers localized at two.
12:10-1:00 Akhil Mathew (U of Chicago): Algebraic K-theory, polynomial functors, and lambda-rings
Abstract: The Grothendieck group K of a commutative ring is well-known to be a lambda-ring, via taking exterior powers of modules. In joint work in progress with Barwick, Glasman, and Nikolaus, we study space-level refinements of this structure. Namely, we show that the K-theory space of a category is naturally functorial for polynomial functors, and describe a universal property of the extended K-theory functor. This leads to a natural spectral refinement of the notion of a lambda-ring.
2:30-3:20 Robert Lipshitz (U of Oregon): Bordered Heegaard Floer homology and incompressible surfaces
Abstract: Heegaard Floer homology is an invariant of closed 3-manifolds and 4-manifolds with boundary; bordered Heegaard Floer homology is an extension of one variant of Heegaard Floer homology to 3-manifolds with boundary. After sketching some of the formal structure of these theories and some of their basic definitions, we will deduce from a theorem of Ni's that bordered Heegaard Floer homology detects homologically essential compressing disks. Time permitting, we will also give a version of this statement for tangles, and talk about what a computer implementation of this algorithm looks like. This is joint work with Akram Alishahi, and builds on earlier joint work with Peter Ozsváth and Dylan Thurston.
3:50-4:40 Christopher J. Leininger (UIUC): Surface bundles over Teichmuller curves.
Abstract: I will discuss joint work-in-progress with Dowdall, Durham, and Sisto on the coarse geometry of the canonical surface bundle over a Teichmuller curve with the goal of developing a notion of geometric finiteness in the mapping class group.