Coffee and Refreshments 8:15  8:30 in Park 339
Talk 8:30  9:45 in Park 328
Date 
Speaker  Topic  Abstract  
Tuesday Feb 6 
Josh Sabloff

Nonorientable Lagrangian Fillings of Legendrian Knots  Lagrangian fillings of Legendrian knots are interesting objects that are related, on one hand, to the 4genus of the underlying smooth knot and, on the other hand, to Floertype invariants of Legendrian knots. Most work on Lagrangian fillings to date has concentrated on orientable fillings. I will present some first steps in constructions of and obstructions to the existence of (decomposable exact) nonorientable Lagrangian fillings. In addition, I will discuss links between the 4dimensional crosscap number of a knot and the nonorientable Lagrangian fillings of its Legendrian representatives. This is joint work in progress with Linyi Chen, Grant CriderPhilips, Braeden Reinoso, and Natalie Yao.  
Tuesday February 13 
Paul Melvin  One is enough  Using Gabai's recent proof of the 4dimensional lightbulb theorem, we show that any two homologous surfaces of the same genus embedded with simplyconnected complements in a smooth 4manifold become smoothly isotopic after one stabilization (connected summing with a 2sphere bundle over the 2sphere). This is joint work with Auckly, Kim, Ruberman and Schwartz.  
Friday February 23 PATCH @ Temple 
Olga Plamenevskaya, SUNY Stony Brook ***** Christine Lee, University of Texas

Planar open books and singularities
***** Understanding quantum link invariants via surfaces in 3manifolds 
https://math.temple.edu/events/seminars/geometry/  
Tuesday February 27

Daniel Ruberman  Double covers of links and 4manifold invariants  The standard methods for defining invariants of a closed 4manifold X via gauge theory require that X have nontrivial second homology. In recent years, I (with Mrowka and Saveliev) defined a SeibergWitten invariant LSW(X) for the opposite situation, where X has the homology of a circle cross the 3sphere. An extension of Witten’s conjecture relating Donaldson and SeibergWitten invariants to this situation would be that this invariant can be computed in terms of a count of flat SU(2) connections. I will discuss new work with Lin and Saveliev on the computation of LSW(X) when X is a mapping torus of an involution arising from the double branched cover of a link in the 3sphere. This verifies (the extended) Witten’s conjecture for this class of manifolds.  
Tuesday March 6 
Hannah Schwartz  
Tuesday March 13 
Spring Break  
Thursday March 22  PATCH @ Penn 
Natasa Sesum (Rutgers) & Matthias Schwarz (Leipzig / IAS) 

Tuesday March 27  Eamonn Tweedy  Seifert fibered homology spheres and their fibers  The Seifert fibered spaces constitute a very concrete class of 3manifolds which serves as a nice "playground" for topologists. Although they are straightforward to describe, there is rich structure even in the Seifert fibered homology spheres (e.g. infinite families which are linearly independent in the homology cobordism group). We give an introduction to Seifert fibered homology spheres and discuss some properties of their homology cobordism classes and the homology concordance classes of their fibers. The new results are joint work w/ Tye Lidman.  

Eamonn Tweedy  (continued)  
Tuesday April 10 
Eamonn Tweedy + Paul Melvin 
(continued) 


Friday April 20 (PATCH @ Bryn Mawr) 
Caitlin Leverson + Feng Luo 
Legendrian satellite knots, DGA representations, and the colored HOMFLYPT polynomial ******** Discrete conformal geometry of polyhedral surfaces 
Legendrian knots are topological knots which satisfy extra geometric conditions. Two classes of invariants of Legendrian knots in $S^3$ are ruling polynomials and representations of the ChekanovEliashberg differential graded algebra (DGA). Given a knot $K$ and a positive permutation braid $\beta$, we give a precise formula relating a specialization of the ruling polynomial of the satellite $S(K,\beta)$ with certain counts of representations of the DGA of the original knot $K$. We also introduce an $n$colored ruling polynomial, defined analogously to the $n$colored HOMFLYPT polynomial, and show that the 2graded version of it arises as a specialization of the $n$colored HOMFLYPT polynomial. This is joint work with Dan Rutherford. We discuss some of the recent work on discrete conformal 

Tuesday April 24  Roberta Guadagni  Weinstein handle decomposition 
Abstract: Handles, as defined in Morse theory, are smooth manifolds with corners, but they can be given standard symplectic structures so that it makes sense to talk about symplectic handlebodies. Similarly to the smooth case, one can sometimes find an appropriate Morse function that gives a decomposition of a symplectic manifolds by symplectic handles. We'll see exactly when this happens (in this case, the manifold is said to be Weinstein). 

Tuesday April 29 
Roberta Guadagni

(continued) 


Monday May 14 
Noémie Legout

Product structures on Floer homology of Lagrangian cobordisms  When studying exact Lagrangian cobordisms with cylindrical Legendrian ends, the following two natural questions can be asked: given the Legendrians on the boundary, can we recover some information about the topology of the Lagrangian? And reciprocally, what information about the Legendrians gives the topology of an exact Lagrangian cobordism? A lot of people have worked on such questions and this talk will be based on a work done by Chantraine, DimitroglouRizell, Ghiggini and Golovko. A few years ago, they defined the Cthulhu complex which is a Floer complex associated to a pair of exact Lagrangian cobordisms with cylindrical Legendrian ends. I will recall briefly the definition of this complex, and then I will explain how to construct a product on a subcomplex of the Cthulhu complex. In particular, when the cobordisms are Lagrangian fillings, this product recovers the cup product, and the EkholmSeidel isomorphism (isomorphism between the singular cohomology of a filling and the corresponding linearized Legendrian contact cohomology of the Legendrian boundary) is a ring isomorphism. 
The PACT Seminar is funded by the Mellon TriCollege Faculty Forum Program and hosts research talks on a broad range of topics from contact/symplectic topology, lowdimensional topology, and algebraic topology. The seminar is jointly organized by Professor Thomas Hunter (Swarthmore), Professor Paul Melvin (Bryn Mawr), Professor Josh Sabloff (Haverford), and Professor Lisa Traynor (Bryn Mawr). We are a friendly and mathematically engaged group composed of members of mathematics departments around the Philadelphia area including Bryn Mawr, Haverford, Swarthmore, Penn, Temple, Eastern, and Widener.
Goals for the seminar are:
· To explore new developments in contact, symplectic, and lowdimensional topology;
· To encourage collaboration between participants, and to find entry points for such collaboration through the exchange of ideas and works in progress;
· To involve advanced undergraduate and graduate students in ongoing research in a seminar format; and
· To share, support, and critique work in progress.
The PACT seminar typically meets weekly (Tuesday mornings!) to enable detailed discussions of the participants’ own work or topics of particular interest to the participants. The seminar is usually conducted in a “minicourse” format, in which one member typically spends three to six sessions explaining research ideas in more depth than is feasible during a onetime seminar, and with more of an emphasis on underlying ideas than can easily be gleaned from a formal paper. Not only do the other members gain greater insight into the presenter’s ideas, but the level of detail also allows for greater opportunity to find places where collaboration might be fruitful.
The PACT seminar meets on Bryn Mawr's beautiful campus, which is easy to reach from any of Philadelphia's campuses by car or train. The talk is from 8:30  9:45 a.m. in Park 328, and is preceded by coffee and breakfast refreshments at 8:15 in the math and physics lounge, Park 339.