Michigan Topology Intercity Symposium (MITIS)


The Michigan Topology Intercity Symposium (MITIS) is an annual meeting of topologists in Michigan.  

The 2023 symposium will be held on Saturday, November 11, 2023 at University of Michigan in Ann Arbor, MI.  


Speakers:

Sally Collins (Michigan State University)

Nathan Dunfield (University of Illinois at Urbana-Champaign)

Peter Johnson (Michigan State University)

Beibei Liu (Ohio State University)


Organizers: Matt Hedden, Matt Stoffregen, and Linh Truong


Registration:  If you would like to attend, please register here, where you can also indicate whether you are requesting travel funding or will attend the conference dinner. The registration deadline is October 20 for those who would like to attend the conference dinner. 


Schedule:  Talks will be held in East Hall room 1360 on the first floor of East Hall. Refreshments will be available in the upper atrium on the 2nd floor. 

9:30-10am Refreshments

10:00-10:50am Nathan Dunfield

11:10-12:00pm Sally Collins

12:00-2:00pm Lunch Break

2:00-2:50pm Peter Johnson

3:00-3:30pm Refreshments 

3:30-4:20pm Beibei Liu

6:00pm-    Dinner 


Contact:  For questions, email tlinh@umich.edu

Titles and Abstracts


Title: TBA

Abstract: TBA


Title: Counting essential surfaces in 3-manifolds

Abstract: Counting embedded curves on a surface as a function of their length has been much studied by Mirzakhani and others. I will discuss analogous questions about counting surfaces in a 3-manifold, with the key difference that now the surfaces themselves have more intrinsic topology. As there are only finitely many essential surfaces of bounded Euler characteristic up to isotopy in an atoroidal 3-manifold, it makes sense to ask how the number of isotopy classes grows as a function of the Euler characteristic. Using Haken’s normal surface theory, we can characterize not just the rate of growth but show the exact count is a quasi-polynomial.  Moreover, our method allows for explicit computations in reasonably complicated examples. This is joint work with Stavros Garoufalidis and Hyam Rubinstein and the reference is our paper with the same title in Inventiones (2022).

The only background I will assume is the notion of a manifold, the genus of a surface, and a little about the fundamental group.


Title: Lattice homology and q-series invariants of plumbed 3-manifolds and knots.

Abstract: I will discuss a relationship between two invariants of negative definite plumbed 3-manifolds, lattice homology and Z-hat. Lattice homology is a graded Z[U]-module due to Némethi, building on earlier work of Ozsváth-Szabó. Z-hat, on the other hand, is a one variable power series due to Gukov-Pei-Putrov-Vafa coming from physics. The relationship I will describe between these two theories comes in the form of an object that we call a weighted graded root, which generalizes/unifies Z-hat and the homological degree 0 part of lattice homology. I will additionally discuss a version of this for plumbed knot complements, namely a relationship between the Gukov-Manolescu two variable series and knot lattice homology. The work on closed plumbed 3-manifolds is joint with Ross Akhmechet and Slava Krushkal. The work on plumbed knot complements is joint with Ross Akhmechet and Sunghyuk Park.


Title: Torus links and colored Heegaard Floer homology

Abstract: Link Floer homology is a filtered version of the Heegaard Floer homology defined for links in 3-manifolds. In this talk, we will introduce an algorithm to compute the link Floer homology of algebraic links from its Alexander polynomials. In particular, we give explicit descriptions of link Floer homology of torus link T(n, mn). As an application, we compute the limit of the link Floer homology when m goes to infinity, using some cobordism maps, which can be used to define colored link Floer homology.  This talk includes joint work with Borodzik, Zemke, and with  Alishahi, Gorksy.