**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 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.

**Lunch Break**

**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.

**Coffee Break**

**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.

**Bill Menasco**

**Claudia Miller**

**Adam Sikora**

**Stephan Wehrli**

**Inna Zakharevich**