[English] [ίΜvO]

Tea: 16:30 -- 17:00 R[

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42ϊ -- 056Ί, 17:00 -- 18:30

Jongil Park (Seoul National University)

Abstract: One of active research areas in symplectic 4-manifolds is to classify symplectic fillings of certain 3-manifolds equipped with a contact structure. Among them, people have long studied symplectic fillings of the link of a normal surface singularity. Note that the link of a normal surface singularity carries a canonical contact structure which is also known as the Milnor fillable contact structure.

In this talk, Ifd like to investigate a topological surgery description for minimal symplectic fillings of the link of quotient surface singularities and weighted homogeneous surface singularities with a canonical contact structure.
Explicitly, Ifll show that every minimal symplectic filling of the link of quotient surface singularities
and weighted homogeneous surface singularities satisfying certain conditions
can be obtained by a sequence of rational blowdowns from the minimal resolution of the corresponding surface singularity.
This is joint work with Hakho Choi.

49ϊ -- 056Ί, 17:00 -- 18:30

[ (Kavli IPMU, εwεw@Θw€Θ)

Abstract: I will give an introduction to a mathematical definition of Coulomb branches of 3-dimensional SUSY gauge theories, given by my joint work with Braverman and Finkelberg. I will emphasize on the role of hypothetical 3d TQFT associated with gauge theories.

416ϊ -- 056Ί, 17:00 -- 18:30

ε κ (wK@εw)

Abstract: The bounded image theorem by Thurston constitutes an important step in the proof of his unifomisation theorem for Haken manifolds. Thurstonfs original argument was never published and has been unknown up to now. It has turned out a weaker form of this theorem is enough for the proof, and books by Kappovich and by Otal use this weaker version. In this talk, I will show how to prove Thurstonfs original version making use of more recent technology. This is joint work with Cyril Lecuire.

423ϊ -- 056Ί, 17:00 -- 18:30

Christine Vespa (Université de Strasbourg)

Abstract: Higher Hochschild homology generalizes classical Hochschild homology for rings. Recently, Turchin and Willwacher computed higher Hochschild homology of a finite wedge of circles with coefficients in the Loday functor associated to the ring of dual numbers over the rationals. In particular, they obtained linear representations of the groups Out(F_n) which do not factorize through GL(n,Z).

In this talk, I will begin by recalling what is Hochschild homology and higher Hochschild homology. Then I will explain how viewing higher Hochschild homology of a finite wedge of circles as a functor on the category of free groups provides a conceptual framework which allows powerful tools such as exponential functors and polynomial functors to be used. In particular, this allows the generalization of the results of Turchin and Willwacher; this gives rise to new linear representations of Out(F_n) which do not factorize through GL(n,Z).

(This is joint work with Geoffrey Powell.)

514ϊ -- 056Ί, 17:00 -- 18:30

J. Scott Carter (University of South Alabama, εγs§εw)

Abstract: Three main ideas will be explored. First, a higher dimensional category (a category that has arrows, double arrows, triple arrows, and quadruple arrows) that is based upon the axioms of a Frobenius algebra will be outlined. Then these structures will be promoted into one higher dimension so that braiding can be introduced. Second, relationships between braiding and multiplication will be studied from a homological perspective. Third, the next order relations will be used to formulate a system of abstract tensor equations that are analogous to the Yang-Baxter relation. In this way, a broad outline of the notion of diagrammatic algebra will be presented.