#### Tuesday, September 23, 2014

2:00 pm

Yajing Liu (UCLA) - L-space surgeries on links

An L-space link is a link on which all large surgeries are L-spaces. These links turn out to be rich in geometry and simple in algebra. I will present some properties and examples of L-space links in contrast to L-space knots, give bounds on the ranks of their Floer homology and on the coefficients in the multi-variable Alexander polynomials, and show that how to use Manolescu-Ozsvath link surgery formula to give a free resolution of the Floer homology of surgeries on any L-space links. As an application, we compute the whole package of Heegaard Floer homology of surgeries on 2-component L-space links only in terms of Alexander polynomial and the surgery framing.

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3:15 pm

Tea Time

#### Wednesday, September 24, 2014

3:30 pm

Leo Petrov* (joint with Algebra, meets at 3:30p) - Random tilings, representation theory and Macdonald processes I

http://www.northeastern.edu/petrov/

I will discuss random lozenge tilings of polygons, their representation-theoretic interpretation (including connections to the character theory of the infinite-dimensional unitary group), and how this circle of ideas leads to Macdonald processes. The latter give rise to other probabilistic models such as random polymers and similar interacting stochastic particle systems

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3:30 pm

Leonid Petrov (UVA) - Random tilings, representation theory and Macdonald processes. Lecture 1.

http://www.northeastern.edu/petrov/

I will discuss random lozenge tilings of polygons, their representation-theoretic interpretation (including connections to the character theory of the infinite-dimensional unitary group), and how this circle of ideas leads to Macdonald processes. The latter give rise to other probabilistic models such as random polymers and similar interacting stochastic particle systems.

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#### Thursday, September 25, 2014

2:00 pm

Greg Arone (UVA) - Meditations on the Whitehead conjecture and its bu analogue

3:30 pm

Tea Time

4:00 pm

Dietmar Bisch (Vanderbilt) - Subfactors with infinite representation theory

http://www.math.vanderbilt.edu/~bisch/

Since the discovery of the Jones polynomial in the 1980's, it is well-known that subfactors of von Neumann factors are intimately related to quantum topology. A subfactor has infinite representation theory, or infinite depth, if its standard representation generates infinitely many non-equivalent irreducibles. Such subfactors are hard to construct, and very few methods are known to produce interesting examples. I will highlight one such procedure, due to Jones and myself, and discuss analytical properties of these subfactors. The talk will be accessible to non-experts.

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#### Friday, September 26, 2014

3:30 pm

David Zureick-Brown (Emory) - The canonical ring of a stacky curve

http://www.mathcs.emory.edu/~dzb/

We give a generalization to stacks of the classical theorem of Petri -- i.e., we give a presentation for the canonical ring of a stacky curve. This is motivated by the following application: we give an explicit presentation for the ring of modular forms for a Fuchsian group with cofinite area, which depends on the signature of the group. (The talk will be mostly geometric and will require little understanding of modular forms.) This is joint work with John Voight.

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