Boston Graduate Topology Seminar

Boston College Meeting

Saturday, April 14, 9:00AM-12:15PM

Math Department, Maloney Hall, Room 560


9:30-10:15: Katie Mann (Brown)

Title: Groups acting on the circle

Abstract: This talk will introduce you to the study of groups acting on the circle, and the moduli spaces of such actions. I’ll discuss the role of these "moduli spaces" in my research and in other areas of geometric topology, and survey some techniques, results, and open problems.

10:30-11:15: Zhouli Xu (MIT)

Title: Smooth structures, stable homotopy groups of spheres and motivic homotopy theory

Abstract: Following Kervaire-Milnor, Browder and Hill-Hopkins-Ravenel, Guozhen Wang and I showed that the 61-sphere has a unique smooth structure and is the last odd dimensional case: S^1, S^3, S^5 and S^61 are the only odd dimensional spheres with a unique smooth structure. The proof is a computation of stable homotopy groups of spheres. We introduce a method that computes differentials in the Adams spectral sequence by comparing with differentials in the Atiyah-Hirzebruch spectral sequence for real projective spectra through Kahn-Priddy theorem. I will also discuss recent progress of computing stable stems using motivic homotopy theory with Dan Isaksen and Guozhen Wang.

11:30-12:15: Siddhi Krishna (BC)

Title: Taut Foliations, Positive 3-Braids, and the L-Space Conjecture

Abstract: The L-Space Conjecture is taking the low-dimensional topology community by storm. It aims to relate seemingly distinct Floer homological, algebraic, and geometric properties of a closed 3-manifold M. In particular, it predicts a 3-manifold Y isn't "simple" from the perspective of Heegaard-Floer homology if and only if Y admits a taut foliation. The reverse implication was proved by Ozsvath and Szabo. In this talk, we'll present a new theorem supporting the forward implication. Namely, we'll discuss how to build taut foliations for manifolds obtained by surgery on positive 3-braid closures. No background in Heegaard-Floer or foliation theories will be assumed.

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.