**Boston College Meeting**

Saturday,
April 27, 9:00AM-12:15PM

Math
Department, Maloney Hall, Room 560

**Speakers:**

**9:30-10:15:** Jen Hom (Georgia
Tech)

**Title:** Concordance homomorphisms from knot
Floer homology

**Abstract: **The knot concordance group consists
of knots in the 3-sphere modulo an equivalence
relation called concordance, with the operation
induced by connected sum. We will define some new
concordance homomorphisms coming from knot Floer
homology, relate them to previously defined
homomorphisms, and discuss some applications. This is
joint work with I. Dai, M. Stoffregen, and L. Truong.

**10:30-11:15:**
Chris Gerig (Harvard)

**Title:** Near-symplectic forms and
the smooth Poincaré conjecture

**Abstract:** Most closed 4-manifolds
do not admit symplectic forms. But most
admit "near-symplectic forms", certain
closed 2-forms which are symplectic
outside of a collection of circles. This
provides a gateway from the symplectic
world to the non-symplectic world. I will
first sketch an application, a geometric
interpretation of the Seiberg-Witten
invariants in terms of J-holomorphic
curves that are compatible with the
near-symplectic form. Although the SW
invariants don't apply to (potentially
exotic) 4-spheres, nor do these spheres
admit near-symplectic forms (because the
4-sphere has trivial 2nd de Rham
cohomology), there is still a way to bring
in near-symplectic techniques. I will
describe my failed attempt at building
invariants of such spheres.

**11:30-12:15:** Zhenkun Li
(MIT)

**Title:** Gradings on the sutured monopole Floer
homology

**Abstract: **Give a balanced sutured manifold M
and a properly embedded surface S in M, we can
construct a grading associated to S on the sutured
monopole Floer homology of M. This grading, however,
does not only depends on the isotopy class of S, but
also depends on the intersection of S with the suture.
Under some circumstances, we could prove a formula
relating different gradings associated to surfaces
which are isotopic but have different intersections
with the suture. We will discuss two applications of
this formula. The first is to compute the sutured
monopole Floer homology of a solid torus with any
sutures. The second is to construct a minus version of
monopole knot Floer homology, with an
Alexander-grading and a U of degree -1.

**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.