Brandeis Topology Seminar, Spring 2026

Organizers: Carolyn Abbott (carolynabbott@brandeis.edu), Dani Álvarez-Gavela (dgavela@brandeis.edu) Kiyoshi Igusa (igusa@brandeis.edu), Thomas Ng (thomasng@brandeis.edu), Surena Hozoori (hozoori@brandeis.edu)

January 15: Seraphina Lee 

Title: Infinitely many Lefschetz pencils on ruled surfaces

Abstract: Works of Donaldson and Gompf show that a closed, oriented 4-manifold admits a symplectic structure if and only if it admits the structure of a Lefschetz pencil. However, the question of how many Lefschetz pencils (or fibrations) a given symplectic 4-manifold admits remains open. Works of Park--Yun and Baykur construct 4-manifolds admitting arbitrarily large (but finite) numbers of Lefschetz pencils or fibrations of the same genus. In this talk, we will construct infinitely many non-isomorphic Lefschetz pencils of the same genus on ruled surfaces of negative Euler characteristic. In fact, our construction gives the first example of infinitely many non-isomorphic but diffeomorphic Lefschetz pencils and fibrations of the same genus. This is joint work in progress with Carlos A. Serván.

January 22: No seminar 

January 29: Isabella Khan (MIT) 

Title: A Heegaard Floer perspective on the Z-hat invariant

Abstract:  Heegaard Floer homology is a powerful and computable 3-manifold invariant which is known to be isomorphic to Némethi’s lattice homology construction for all plumbed 3-manifolds. In this talk, I will discuss progress towards using this isomorphism to express the Z-hat invariant from quantum topology in terms of Heegaard Floer generators, and the possible applications of such a result.

February 05: Arya Vadnere (Buffalo) 

Title: Gromov Boundary of the Grand Arc Graph

Abstract: In 1999, E. Klarreich found a very intriguing correspondence between the Gromov boundary of the curve graph for closed surfaces (a very GGT object) with the space of ending laminations on the surface (a very geometric object). Since then, Hamendstädt, Schleimer and Pho-On have thought about various proofs for this result, and generalizations to the arc graph / the arc-and-curve graph for finite-type surfaces. The grand arc graph is a type of arc graph associated with certain infinite-type surfaces, which is also an infinite-diameter hyperbolic graph. In this talk, we shall talk about a couple of ways to define  “laminations that should correspond to points on the Gromov boundary of the grand arc graph”. This work is joint with Carolyn Abbott and Assaf Bar-Natan.

February 12: Edu Fernandez (Georgia Tech)

Title: The h-principle fails for prelegendrians in corank 2 fat distributions

Abstract:  It is a classical problem to study whether the h-principle holds for certain classes of maximally non-integrable distributions. The most studied case is that of contact structures, where there is a rich interplay between flexibility and rigidity, exemplified by the overtwisted vs tight dichotomy. For other types of maximally non-integrable distributions, no examples of rigidity are currently known.

In this talk I will discuss rigidity phenomena for fat distributions, which can be viewed as higher corank generalizations of contact structures. These admit natural symplectizations and contactizations. I will introduce a natural class of submanifolds in fat manifolds, called prelegendrians, which admit canonical Legendrian lifts to the contactization. The main result of the talk is that these submanifolds exhibit rigidity: in the “standard corank-2 fat manifold” there exists an infinite family of prelegendrian tori, all of them formally equivalent but pairwise not prelegendrian isotopic. In other words, the h-principle fails for prelegendrians. The talk is based on joint work with Álvaro del Pino and Wei Zhou.

February 26: Joe Boninger (Boston College)

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March 12: Daniel Levitin

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March 19: Xiaoying He (Brandeis) 

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March 26: Shaked Bader (Oxford University) 

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April 16: Hyeran Cho (Tufts)

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April 23: Antonio Alfieri (UGA)

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April 28 (Brandeis Thursday): Mike Sullivan (UMass Amherst)

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