PACT is an informal learning seminar on contact, symplectic, and low-dimensional topology, organized by Tri-Co topology faculty members Allison Miller (Swarthmore), Joshua Sabloff (Haverford), and Lisa Traynor (Bryn Mawr). We meet most Tuesdays at 8:30 am via zoom, and have participants from a range of northeastern undergraduate focused institutions.
If you're interested in joining us, please email jsabloff@haverford.edu.
PATCH seminar runs 2-3 times a semester, rotating between Bryn Mawr College, Haverford College, Swarthmore College, Temple University, and the University of Pennsylvania and organized by faculty at all of these institutions. It is usually a full day Friday event with two speakers, each of which who give a background talk in the morning, aimed at graduate students, and a research talk in the afternoon, aimed at everyone.
9:45: JSJ decompositions of knot exteriors, Laura Wakelin
11:15: Background on unmarked simple length spectral rigidity for covers, Nick Miller
12:15 Lunch (provided)
2:30: Effective bounds on characterising slopes for all knots, Laura Wakelin
4:00: Unmarked simple length spectral rigidity for covers, Nick Miller
9:30: JZ background talk: Contact structures and foliations
11:00: TM background talk: Symplectic structures and convexity
12:00 Lunch (provided)
2:30: JZ research talk: Ziggurats and taut foliations
4:00: TM research talk: Contact type hypersurfaces in small symplectic 4-manifolds
Abstract: A rational slope p/q is characterising for a knot K if the oriented homeomorphism type of the 3-manifold obtained via p/q-surgery on K uniquely determines the knot K. I will discuss joint work with Patricia Sorya in which we show that the JSJ decomposition of the exterior of K determines an explicit bound C(K) such that |q|>C(K) guarantees that the slope p/q is characterising for K.
In the introductory talk, we’ll talk about JSJ decompositions of knot exteriors and how they behave under Dehn surgery.
Abstract: A long studied problem in geometry is the extent to which a manifold is determined by its collection of lengths of closed geodesics. For instance, Otal showed that any negatively curved metric on a surface is determined up to isometry by its marked length spectrum. By classic work of Fricke, the similar result is true if one restricts this function only to simple closed curves.
By celebrated constructions of Vignéras and Sunada, we now know that the corresponding statement is false when one forgets the marking, that is, there exist non-isometric surfaces which have the same collections of lengths of closed geodesics. In this talk, we will explore the extent to which surfaces arising from Sunada's construction can have the same collection of lengths of simple closed curves. Along the way we will also discuss some new general results about how simple lifts of curves can determine equivalence of covers. This is joint work with Tarik Aougab, Max Lahn, and Marissa Loving.
In the morning background talk, we will review some of the ingredients that go into the research talk. Topics are likely to include constructions of hyperbolic surfaces and Teichmuller space, its boundary, and maps between Teichmuller spaces in the presence of finite covers, as well as some examples of constructions of isospectral manifolds via Sunada's method.
Abstract: If L is a link in a 3-manifold, which Dehn surgery multislopes give rise to 3-manifolds with taut foliations? In this talk, I will discuss the ziggurat phenomenon: if one restricts to foliations transverse to a fixed flow on the link complement, the set of multislopes typically has a fractal staircase shape with rational corners. In work in progress with Thomas Massoni, we explain the ziggurat phenomenon in some contexts using tools from contact geometry.
In the morning background talk, I'll introduce my two favorite codimension 1 structures on 3-manifolds — contact structures and foliations — and the Eliashberg—Thurston theorem which relates them.
Abstract: A codimension-1 submanifold embedded in a symplectic manifold is called “contact type” if it satisfies a certain convexity condition with respect to the symplectic structure. Given a symplectic manifold X it is natural to ask which manifolds Y can arise as contact type hypersurfaces. We consider this question in dimension 4, which appears much more constrained than higher dimensions; in particular we review evidence that no homology 3-sphere can arise as a contact type hypersurface in R^4 except the 3-sphere. We exhibit an obstruction for a contact 3-manifold to embed in certain closed symplectic 4-manifolds as the boundary of a Weinstein domain---a slightly stronger condition than contact type---and explore consequences for the symplectic topology of small rational surfaces and potential applications to smooth 4-dimensional topology.
The morning introductory lecture will review symplectic structures, symplectic convexity, and the related notion of pseudoconvexity, together with some aspects of “embedding questions” for 3-manifolds in R^4 or other 4-manifolds.
Spring 2025
Penn: Miriam Kuzbary and Ben Lowe
Bryn Mawr: Dusa McDuff and Eriko Hironaka
Fall 2024
Temple: Tye Lidman and Chris Leininger
Penn: Kristen Hendricks and Jacob Russell
Haverford: Robert Lipshitz and Luya Wang
Spring 2024
Swarthmore: Jean Pierre Mutanguha and Anubhav Mukherjee
Penn: Nir Gadish and Ao Sun
Temple: Anna Marie Bohmann and Spencer Dowdall
Fall 2023
Bryn Mawr: Michael Landry and Hiro Lee Tanaka
Temple: Tam Cheetham-West and Siddhi Krishna
Penn: Cary Malkiewich and Robert Young
Spring 2023
Temple [Bryn Mawr] :Nick Vlamis and Jo Nelson
Swarthmore: Johanna Mangahas and Lisa Traynor
Penn: Dan Ketover
Fall 2022
Temple: Samantha Allen and Bena Tshishiku
Haverford: Braeden Reinoso and Michael Dougherty
Penn: Rob Kusner and Isaac Sundberg
Spring 2022
Penn: Hannah Schwartz and Franco Vargas Pallete
Temple: Katie Mann and Inbar Klang
Fall 2021
Temple: Allison Miller and Andrew Yarmola
Penn: Yasha Eliashberg and Tarik Aougab
Bryn Mawr Emily Stark and Emmy Murphy
Spring 2020
Haverford: Diana Hubbard and Ian Biringer
Fall 2019
Bryn Mawr: Bulent Tosun and Jessica Purcell
Penn: Effie Kalfagianni and Roberta Guadagni
Temple: Dan Margalit and Kyle Hayden
Spring 2019
Penn: Alex Nabutovsky and Rina Rotman
Temple: Chris Millichap and Dan Rutherford
Haverford: Oleg Lazarev and Francesco Lin
Fall 2018
Bryn Mawr: Lisa Piccirillo and Erica Flapan
Penn: Ana Menezes and Jonathan Hanselman
Temple: Ilya Kofman and Duncan McCoy
Spring 2018
Bryn Mawr: Feng Luo and Caitlin Leverson
Penn: Natasa Sesum and Matthias Schwarz
Temple: Christine Lee and Olga Plamenevskaya
Fall 2017
Haverford: Daniel Studenmund and Yu Pan
Temple: Sergei Tabachnikov and Inanc Baykur
Penn: Casey Kelleher and Mohammed Abouzaid
Spring 2017
Haverford: David Treumann and Anastasiia Tsvietkova
Temple: Sara Maloni and Laura Starkston
Penn: Thomas Church and Denis Auroux
Fall 2016
Penn: Dave Auckly and Otis Chodosh
Temple: Moira Chas and Robert Ghrist
Bryn Mawr: Roger Casals and Jason Deblois
Spring 2016
Penn: Andrew Hicks and Nancy Hingston
Bryn Mawr: John Etnyre and Genevieve Walsh
Temple: Josh Greene and Lenny Ng
Fall 2015
Bryn Mawr: Abby Thompson and Chuck Livingston
Temple: ?????????
Penn: Renato Bettiol and Saul Schleimer
*Thanks, Josh!