Boston Graduate Topology Seminar

Boston College Meeting

Saturday, December 3, 9:30AM-12:15PM

Math Department, Maloney Hall, Room 560

Speakers:

9:30-10:15: Andras Stipsicz (Princeton/Renyi Institute)

Title: Homomorphisms on the concordance group

Abstract: We will review the definition of the concordance group of knots in the three-space (and by analogy the homology cobordism group of integral homology 3-spheres), I will recall some classical invariants which provide homomorphisms on these groups and we will discuss a modification of knot Floer homology which provides an infinite collection of homomorphisms on the concordance group.

10:30-11:15: Kevin Sackel (MIT)

Title: Graph Theoretic Legendrian Surfaces and Augmentations

Abstract: Treumann and Zaslow defined and studied a class of Legendrian surfaces arising from cubic planar graphs on the 2-sphere. In work in preparation, Casals and Murphy define a purely graph theoretic differential graded algebra (DGA) from the underlying cubic planar graph which is conjecturally equivalent to the usual Legendrian Contact DGA for this surface. We prove that over any field, the space of augmentations of this graph theoretic DGA is isomorphic to the expected space of microlocal rank 1 constructible sheaves as per the usual "augmentations are sheaves" philosophy.

11:30-12:15: Kyle Hayden (BC)

Title: Complex curves through a contact lens

Abstract: We study complex curves in complex 2-space​by considering their interaction with the natural contact structure on each level 3-sphere of constant radius. This approach is inspired by Boileau and Orevkov's proof that the generic intersection of a complex curve in complex 2-space with the unit 3-sphere is a quasipositive link. We show that complex curves can be represented using "movies" of links in the 3-sphere that are positively transverse to the standard contact structure. As an application, we sketch an adapted proof of Boileau and Orevkov's theorem

Location & Parking:

The Math Department is located on the fifth floor of Maloney Hall (shown on some campus maps as 21 Campanella Way), near the center of the main campus (shown in red on the map below). It is adjacent to the Commonwealth Garage. See this for more directions (including Public Transportation information) for getting to campus.

Visitor parking is available in the Commonwealth Garage or the Beacon Street Garage.