The SGGT seminar meets on Fridays in Math 417, at 10:45 AM unless noted otherwise.

Previous semesters: Fall 2009, spring 2009, fall 2008, spring 2008, fall 2007, spring 2007, fall 2006.

Other area seminars. Our e-mail list.

 Date Speaker Title Jan 29 Feb 5 Feb 12 Feb 19 Christopher Woodward (Rutgers) Non-displaceability of toric moment fibers via gauged Floer theory Feb 26 Ben Webster (MIT) TBA March 5Meets at 1pm Christian Kassel (CNRS) Grid diagrams and Schubert varieties March 12 Nathan Sunukjian (Michigan State) Exotic group actions on 4-manifolds March 19 No seminar this week March 26 No seminar this week April 2 April 9 Yanki Lekili (MSRI) Lagrangian correspondences and 3-manifold invariants April 12, 11am, in Math 622. Note special date/time/place Josh Sabloff (Haverford College) Lagrangian Caps for Legendrian Knots via Generating Families April 16(Time TBA) Max Maydanskiy (MSRI) Legendrian surgery formula for symplectic cohomology and Seidel's conjecture April 23 Alex Subotic (Harvard) A Monoidal Structure for the Fukaya Category April 30 9:30 a.m.: Timothy Perutz (UT Austin) Heegaard Floer theory and Fukaya categories 10:45 a.m.: Katrin Wehrheim (MIT) Calculations of Floer homology by reduction May 7 May 14 10:45 a.m.: Adam Knapp Cobordism maps and exact sequences

# Abstracts.

#### February 19, 2010.

Christopher Woodward, " Non-displaceability of toric moment fibers via gauged Floer theory"

Abstract: I will look at some recent results of Fukaya-Oh-Ohta-Ono about non-displaceability of moment fibers in toric varieties from the point of view of gauge theory/holomorphic curve correspondence, along the lines of the gauged Lagrangian Floer theory introduced by Frauenfelder. I will describe a proof of many of FOOO's results using these ideas which does not use any Kuranishi structures or de Rham models for Floer homology, and some heuristic arguments which relate the naive and actual superpotentials via a " boundary/bulk mirror map" which arises natrually in this context.

#### March 12, 2010.

Nathan Sunukjian, " Exotic group actions on 4-manifolds"

Four-Manifolds exhibit a beguiling array of exotic behaviors ??? cases where things are smoothly distinct, but continuously the same. Examples of this phenomenon include exotic smooth structures on 4-manifolds, and exotic embeddings of surfaces in 4-manifolds. In my talk, I will review some of the techniques used to construct exotic 4-manifolds (in particular, the ???knot surgery??? construction of Fintushel and Stern) and show how such techniques can be applied to produce exotic group actions on a given smooth 4-manifold ??? that is, actions which are equivariantly homeomorphic but not equivariantly diffeomorphic. Examples will include exotic finite cyclic group actions on a class of irreducible 4-manifolds. This is joint work with R. Fintushel and R. Stern.

#### April 12, 2010.

Josh Sabloff, " Lagrangian Caps for Legendrian Knots via Generating Families"

Legendrian knots lie at the intersection of knot theory and contact topology, so one might hope to gain insight into the geometry and geography of Legendrian knots by adapting questions and techniquest from the smooth to the contact setting. In smooth knot theory, for example, one might study the 4-ball genus of a knot. For a Legendrian knot in a contact manifold X, this translates into finding Lagrangian null-cobordisms in the symplectization R x X. The question I will investigate is how to relate the Legendrian invariants of K to topological invariants of L. I will discuss an answer to this question using the technique of generating families, and will also describe how to combinatorially construct Lagrangian caps of Legendrian knots in R^3. This is joint work with Lsa Traynor (Bryn Mawr).

#### April 30, 2009.

Tim Perutz, " Heegaard Floer theory and Fukaya categories"

Abstract: I'll explain aspects of a joint project with Yanki Lekili in which we construct invariants for 3-manifolds with boundary. These invariants take the shape of functors between extended Fukaya categories of $g$-fold symmetric products of the boundary surfaces. These invariants satisfy a TQFT-style gluing law, and the closed 3-manifold invariants are Heegaard Floer cohomology groups. Recent work of Auroux explains the connection to bordered Heegaard Floer theory of Lipshitz-Ozsvath-Thurson. In this talk I'll focus especially on the Fukaya-categorical aspects, hoping to complement the content of Lekili's recent talk on this work.

#### April 30, 2010.

Katrin Wehrheim, " Calculations of Floer homology by reduction"

I will give some examples of calculating monotone Floer homology from a general strip shrinking isomorphism in quilted Floer homology (for sequences of Lagrangian correspondences). Examples include the Clifford torus in CP^n (previously known by Cho) and nondisplaceable T^{n-k}\times S^{2k-1} in CP^n\times CP^{k-1}. Moreover, the bijection of trajectory moduli spaces can be somewhat generalized to multiply covered compositions of correspondences, yieding e.g. calculations of the Floer homology between Clifford tori and RP^n in CP^n (confirming work by Allston). Finally, "figure eight" bubbling obstructions can be understood explicitly. Work is in progress on overcoming these for the Chekanov/Polterovich torus in S^2\times S^2, using symmetries and twisted coefficients.

#### May 14, 2010.

Adam Knapp, "Cobordism maps and exact sequences"

Abstract: Given a cobordism W from Y to Y_0 and a surgery exact triangle with 3 manifolds terms Y_0,Y_1,Y_2, I will give a method of computing the monopole Floer maps for W in terms of two cobordism maps from Y into Y_1 and Y_2.

# Other relevant information.

## Our e-mail list.

Announcements for this seminar, as well as for related seminars and events, are sent to the "Floer Homology" e-mail list maintained via Google Groups. You can subscribe directly via Google Groups or by contacting R. Lipshitz.