Coffee and Refreshments 8:15  8:30 in Park 339
Talk 8:30  9:45 in Park 328
Date 
Speaker  Topic  Abstract  
Tuesday September 12 
Eamonn Tweedy, Widener University 
The Heegaard Floer dinvariant and some applications  Ozsvath and Szabo defined the socalled "dinvariant" or "correction term" as a part of their Heegaard Floer homology package. For each (torsion) spinc structure t on a closed oriented connected 3manifold M, there is a rational number d(M,t). This number is an invariant of the spinc rational homology cobordism type of (M,t), which leads to applications To the study of homology cobordism and knot concordance. This invariant arises from examining maps on Heegaard Floer homologies associated to fourdimensional cobordisms. In this series I will explain the definition of the dinvariant, discuss a few applications, and describe several cases in which calculations are tractable.  
Tuesday September 19 
Eamonn Tweedy  continued  
Tuesday September 26 
Kyle Hayden, Boston College  Complex curves through a contact lens 
Every fourdimensional Stein domain has a Morse function whose regular level sets are contact threemanifolds. This allows us to study complex curves in the Stein domain via their intersection with these contact level sets, where we can comfortably apply threedimensional tools. We use this perspective to characterize the links in Steinfillable contact manifolds that bound complex curves in their Stein fillings. (Some of this is joint work with Baykur, Etnyre, Hedden, Kawamuro, and Van HornMorris.)  
Friday October 6, 2017 PATCH at Temple

Inanc Baykur, UMass Amherst
& Serge Tabachnikov, Penn State 
Symplectic and Exotic 4Manifolds via Positive Factorizations
&&&&&& Introducing symplectic billiards 
We will discuss new ideas and techniques for producing positive Dehn twist factorizations of surface mapping classes that yield novel constructions of interesting symplectic and smooth 4manifolds, such as samll symplectic CalabiYau surfaces and exotic rational surfaces, via Leftschetz fibrations and pencils. &&&&&&&&&&&&&& I shall introduce a simple dynamical system called symplectic billiards. As opposed to the usual (Birkhoff) billiards, where length is the generating function, for symplectic billiards the symplectic area is the generating function. I shall explore basic properties and exhibit several similarities, but also differences, of symplectic billiards to Birkhoff billiards. Symplectic billiards can be defined not only in the plane, but also in linear symplectic spaces. In this multidimensional setting, I shall discuss the existence of periodic trajectories and describe the integrable dynamics of symplectic billiards in ellipsoids. In the morning, I shall survey the conventional and outer billiards to provide context for my afternoon talk. 

Tuesday October 10  Samantha Pezzimenti  Fillings of Legendrian Knots: Obstructions and Constructions 
A classic question in knot theory is: Given a smooth knot in the 3sphere, what surfaces in the 4ball can it bound? A version of this question can also be asked about Legendrian knots, which are knots that satisfy an additional geometric condition imposed by a contact structure. Now the natural question is: Given a Legendrian knot, what Lagrangian surfaces can it bound? Whereas a smooth knot always can be filled by an infinite number of topologically distinct surfaces, a polynomial associated to the Legendrian knot determines the genus of any embedded Lagrangian filling (or determines that there is no Lagrangian filling!). Although embedded fillings might not exist, it is known that there will always be immersed Lagrangian fillings. I will describe how this polynomial gives information about the minimal number of double points in any immersed Lagrangian filling. I will also cover some constructive arguments about when these “minimal” immersed fillings can be realized.


Tuesday October 17

No Meeting  Fall Break  
No Oct 24 meeting due to: PATCH @ Penn Thursday October 26

5:45 Mohammed Abouzaid (Columbia) 

Tuesday October 31 
No Meeting (Construction) 

Tuesday November 7  Eamonn Tweedy  Continued  
Tuesday November 14: no meeting due to: PATCH at Haverford Friday November 17

Daniel Studenmund, Univ of Utah (3  4) & Yu Pan, MIT (4:305:30) 
Duality and semiduality in cohomology of arithmetic groups
&&&&&&&
Exact Lagrangian cobordisms the Augmentation category 
Abstract: A duality group has a pairing exhibiting isomorphisms &&&&&&&&&&&&&&
To a Legendrian knot, one can associate an $A_{\infty}$ category, the augmentation category. An exact Lagrangian cobordism between two Legendrian knots gives a functor of the augmentation categories of the two knots. We study the functor and establish a long exact sequence relating the corresponding cohomology of morphisms of the two ends. As applications, we prove that the functor between augmentation categories is injective on the level of equivalence classes of objects and find new obstructions to the existence of exact Lagrangian cobordisms in terms of linearized contact homology and ruling polynomials. 

Tuesday Nov 28 
Eamonn Tweedy  Continued 


Tuesday Dec 5 
Hannah Schwartz  My second favorite theorem 
This talk will examine smooth 4manifolds obtained by "surgery on a twin", introduced by Montesinos and Plotnick in the 80's. Special families of these manifolds are reminiscent of the 3dimensional Seifert fibered spaces they have effective circle actions which we shall describe explicitly. In addition to providing plenty of background, I hope to discuss why these manifolds are all in fact the 4sphere, as well as sketch Giffen's proof from the 60's that the generalized Smith conjecture does not hold in dimension 4. 
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.