The SGGTC seminar meets on Fridays in Math 520 from 10:30-11:30am and in Math 407 from 1-2pm, unless noted otherwise (in red).

Our e-mail list.

 Date Speaker Title Feb. 1, 1pm Florent Schaffhauser (Universidad de Los Andes and Université de Strasbourg) Higher Teichmüller spaces for orbifolds Feb. 8, 1pm Siddhi Krishna (Boston College) Taut Foliations, Positive 3-Braids, and the L-Space Conjecture Feb. 15, 10:30am Marco Castronovo (Rutgers) Counting branes on the Gelfand-Cetlin Lagrangian Feb. 22, 10:30am Barney Bramham (IAS and Bochum) Orbit travel and symbolic dynamics for 3D Reeb flows using finite energy foliations Feb. 22, 1pm Nate Bottman (IAS) Family polyfolds and an A-infinity structure on the bar construction Mar. 1, 10:30am Du Pei (QGM and Caltech) TBA Mar. 1, 1pm Yaron Ostrover (IAS and Tel Aviv University) TBA Mar. 8, 10:30am Biji Wong (CIRGET, UQaM) TBA Mar. 8, 1pm Matt Hedden (Michigan State) Satellites of Infinite Rank in the Smooth Concordance Group Mar. 15, 10:30am Ran Tessler (Weizmann Institute) TBA Mar. 15, 1pm Nick Saveliev (Miami) TBA Mar. 22 Spring break! Mar. 29, 10:30am Beibei Liu (UC Davis) TBA Mar. 29, 1pm Zhengyi Zhou (IAS) TBA Apr. 5, 10:30am Aleksander Doan (Stony Brook) TBA Apr. 5, 1pm Alex Takeda (UC Berkeley) TBA Apr. 12, 10:30am Jingyu Zhao (Harvard) TBA Apr. 12, 1pm Masaki Taniguchi (Tokyo university) TBA Apr. 19, 10:30am James Pascaleff (UIUC) TBA Apr. 19, 1pm Peter Feller (ETH Zurich) TBA Apr. 26, 10:30am Baptiste Chantraine (Université of Nantes) TBA Apr. 26, 1pm Jonathan Simone (UMass Amherst) TBA May 3, 10:30am Daniel Pomerleano TBA May 3, 1pm C.-M. Michael Wong (LSU) TBA

# Abstracts

#### February 1st, 2019: Florent Schaffhauser (Universidad de Los Andes and Université de Strasbourg) " Higher Teichmüller spaces for orbifolds "

Abstract: The Teichmüller space of a compact 2-orbifold X can be defined as the space of faithful and discrete representations of the fundamental group of X into PGL(2,R). It is a contractible space. For closed orientable surfaces, "Higher analogues" of the Teichmüller space are, by definition, (unions of) connected components of representation varieties of $\pi_1(X)$ that consist entirely of discrete and faithful representations. There are two known families of such spaces, namely Hitchin representations and maximal representations, and conjectures on how to find others. In joint work with Daniele Alessandrini and Gye-Seon Lee, we show that the natural generalisation of Hitchin components to the orbifold case yield new examples of Higher Teichmüller spaces: Hitchin representations of orbifold fundamental groups are discrete and faithful, and share many other properties of Hitchin representations of surface groups. However, we also uncover new phenomena, which are specific to the orbifold case.

#### February 8th, 2019: Siddhi Krishna (Boston College) " Taut Foliations, Positive 3-Braids, and the L-Space Conjecture "

Abstract: The L-Space Conjecture is taking the low-dimensional topology community by storm. It aims to relate seemingly distinct Floer homological, algebraic, and geometric properties of a closed 3-manifold Y. In particular, it predicts a 3-manifold Y isn't "simple" from the perspective of Heegaard-Floer homology if and only if Y admits a taut foliation. The reverse implication was proved by Ozsvath and Szabo. In this talk, we'll present a new theorem supporting the forward implication. Namely, we'll build taut foliations for manifolds obtained by surgery on positive 3-braid closures. As an example, we'll construct taut foliations in *every* non-L-space obtained by surgery along the P(-2,3,7) pretzel knot. No background in Heegaard-Floer or foliation theories will be assumed.

#### February 15th, 2019: Marco Castronovo (Rutgers) " Counting branes on the Gelfand-Cetlin Lagrangian "

Abstract: Starting from Kontsevich's homological mirror symmetry conjecture, derived equivalences between symplectic and algebraic geometry have been intensely investigated, even beyond the Calabi-Yau setting. In the Fano case, Marsh-Rietsch proposed Landau-Ginzburg mirrors for the complex Grassmannians Gr(k,n) that fit in a general picture relating mirror symmetry and Langlands duality. We show that a Lagrangian torus fiber of the Gelfand-Cetlin integrable system on Gr(k,n) always supports nonzero objects of the Fukaya category, and for n prime these suffice to generate and establish an equivalence with the category of singularities of the mirror. The arithmetic restriction is curiously related to the values of Schur polynomials at roots of unity.

#### Februrary 22nd, 2019: Nate Bottman (IAS) " Family polyfolds and an $\mathcal{A}_\infty$ structure on the bar construction "

Abstract: I will describe two areas of recent progress in the construction and study of Symp, the symplectic $(\mathcal{A}_\infty,2)$-category. First, I will explain how associating operations to fiber products of 2-associahedra gives rise to a coherent algebraic structure, which in particular endows the bar construction $TA[1]$ with an $\mathcal{A}_{\infty}$ structure. This is one way to circumvent the fact that strata of 2-associahedra involve fiber products of lower-dimensional 2-associahedra. I will also mention a related construction, which exhibits $QC^*$ as a module over a decategorification of Symp. Second, I will present work-in-progress with Katrin Wehrheim in which we aim to construct a notion of "family polyfolds". This will be a framework for setting up Fredholm problems that involve adiabatic limits. Our motivating example is the strip-shrinking degeneration, which is a key feature of the moduli spaces of pseudoholomorphic quilts involved in the definition of Symp.

#### February 22th, 2019: Barney Bramham (IAS and Bochum) " Orbit travel and symbolic dynamics for 3D Reeb flows using finite energy foliations "

Abstract: Suppose a non-degenerate Reeb flow of a closed contact 3-manifold admits a finite energy foliation F. The rigid leaves in F divide the space into various regions A, B, C etc. A typical Reeb trajectory then spits out an infinite sequence of letters which record which regions it visits and in which order. It is natural to investigate the converse. Indeed, it turns out one needs surprisingly little information to determine, for a given sequence of letters, whether there exists a Reeb trajectory realising this sequence as its itineraries. I will explain this mechanism with pictures and discuss some applications. This is joint work with Umberto Hryniewicz and Gerhard Knieper.

#### March 8th, 2019: Matt Hedden (Michigan State) " Satellites of Infinite Rank in the Smooth Concordance Group "

Abstract: I'll discuss the way satellite operations act on the concordance group, and raise some questions and conjectures. In particular, I'll conjecture that satellite operations are either constant or have infinite rank, and reduce this to the difficult case of winding number zero satellites. I'll then talk about how to use SO(3) gauge theory to provide a general criterion sufficient for the image of a satellite operation to generate an infinite rank subgroup of smooth concordance, and use this to address the winding zero case. This is joint work with Juanita Pinzon-Caicedo.

## 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.