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.
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 K0 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.