All talks will be in Skiles 006. 

The conference will begin with one talk at 4:00 on Friday (preceded by a tea) and end by around 1:00 on Sunday.

Lightning talks session 1:

Lightning talks session 2:

Titles and Abstracts

Autumn Kent
Title: Atoroidal Surface bundles
Abstract: I will discuss joint work with Chris Leininger in which we establish the existence of purely pseudo-Anosov surface subgroups of mapping class groups. We do this by constructing a type-preserving representation of the figure eight knot group into the mapping class group of the thrice-punctured sphere. As a corollary we obtain the first examples of closed atoroidal surface bundles over surfaces.

Dan Margalit
Title: Mapping class groups in complex dynamics
Abstract: A polynomial in one complex variable gives a branched cover of the Riemann sphere. But which branched covers of the Riemann sphere come from polynomials? In the early 1980s, William Thurston gave one answer to this question: the "obvious" obstruction is the only obstruction. Shortly thereafter, Hubbard asked his famous twisted rabbit problem: if we post-compose a particular polynomial by a homeomorphism, which polynomial is obtained, if any? A solution to this was found by Bartholdi and Nekrashevych in 2006. In this talk, I will give an introduction to this circle of ideas, highlighting recent work that draws strong parallels with the theory of mapping class groups of surfaces.

Roberta Shapiro
Title: Geometry, topology, and combinatorics of fine curve graph variants
Abstract: The fine curve graph of a surface S is a graph whose vertices are essential simple closed curves in S and whose edges connect curves that are disjoint. This contrasts past work on the curve graph, which is similar to the above but considers everything up to isotopy. In this talk, we will explore existing and new results on both classical and fine curve graphs and their variants. We will reach into the fields of geometry, topology, and combinatorics to gain new perspectives on these graphs and the surfaces used to construct them. We will further prove a sampling of results about finitary curve graphs, whose vertices are essential simple closed curves in S and edges connect curves that intersect at finitely many points.

Shunyu Wan
Title: Negative contact surgery on Legendrian non-simple knot
Abstract: Etnyre first asked the question on when contact surgery on different Legendrian knots produces different contact manifolds, and he showed that +1 contact surgeries on certain non Legendrian isotopic representatives of the twist knots always produce the same contact 3-manifold. However, later Bourgeois-Ekholm-Eliashberg showed that -1 contact surgery on those representatives produces different contact 3-manifolds. Using the Heegaard Floer theory we are able to show that any negative contact surgery on certain Legendrian twist knots always produces different contact manifolds. In this talk, I will first talk about the background, and focus on a specific example for explanation. This is joint work with Hugo Zhou.

Liam Watson
Title: Tangles, immersed curves, and mutation
Abstract: Using knot mutation as a running theme, this talk gives an overview of Khovanov homology for tangles in terms of immersed curves. In particular, I will give a new proof that Khovanov’s invariant with mod 2 coefficients is unchanged under knot mutation—this is originally due to Bloom and Wehrli. This new point of view suggests how to work with signs, towards establishing that reduced Khovanov homology, working over any field, is unchanged under mutation. This is joint work with Artem Kotelskiy and Claudius Zibrowius.

Angela Wu
Title: The contact cut graph and a Weinstein L-invariant
Abstract: The cut complex associated to a surface is a powerful tool in the study of smooth 4-manifolds. In this talk, I will introduce the cut complex and its analogue in the contact and symplectic setting. Adding a restriction to the allowable curves in a cut system, the contact cut graph is a subgraph of the cut complex. I will go through some recent results exploring the structure of the contact cut graph, and use it to define a new invariant of 4-dimensional Weinstein domains. This is based on joint work with Castro, Islambouli, Min, Sakalli, and Starkston.

Melissa Zhang
Title: Skein Lasagna Modules and Categorified Projectors
Abstract: Morrison, Walker, and Wedrich’s skein lasagna modules are 4-manifold invariants defined using Khovanov-Rozansky homology similarly to how skein modules for 3-manifolds are defined. In 2020, Manolescu and Neithalath developed a formula for computing this invariant for 2-handlebodies by defining an isomorphic object called cabled Khovanov-Rozansky homology; this is computed as a colimit of cables of the attaching link in the Kirby diagram of the 4-manifold.

Lightning talk

Neda Bagherifard
Title: An excision formula in Heegaard Floer theory
Abstract: In my talk, I will discuss the excision construction for 3-manifolds, which relates two closed, oriented 3-manifolds, Y and Y′, through a process of cutting and regluing along surfaces. I will explain how this construction leads to the isomorphism of twisted Heegaard Floer homology groups of Y and Y'. Additionally, I will present applications of our excision formula, including examples that demonstrate certain manifolds cannot be related by this construction. Furthermore, I will show how twisted Heegaard Floer homology groups for specific families of 3-manifolds can be computed using our excision formula.

Arka Banerjee
Title: Urysohn 1-width and covers
Abstract: A metric space has small Urysohn 1-width if it admits a continuous map to a 1-dimensional complex where the preimage of each point has small diameter. An open problem is, if a space's universal cover has small Urysohn 1-width, must the original space also have small Urysohn 1-width? While one might intuitively expect this to be true, there are strange examples that suggest otherwise. In this talk, I will share some partial progress we have made in understanding it. This is a joint work with H. Alpert and P. Papasoglu.

Nilangshu Bhattacharyya Bhattacharyya
Title: Transverse invariant as Khovanov skein spectrum at its Extreme Alexander grading
Abstract: Olga Plamenevskaya described a transverse link invariant as an element of Khovanov homology. Lawrence Roberts gave a link surgery spectral sequence whose $E^2$ page is the reduced Khovanov skein homology (with $\mathbb{Z}_{2}$ coefficient) of a closed braid $L$ with odd number of strands and $E^{\infty}$ page is the knot Floer homology of the lift of the braid axis in the double branch cover, and the spectral sequence splits with respect to the Alexander grading. The transverse invariant does not vanish in the Khovanov skein homology, and under the above spectral sequence and upon mapping the knot Floer homology to the Heegard Floer homology, the transverse invariant corresponds to the contact invariant. Lipshitz-Sarkar gave a stable homotopy type invariant of links in $S^{3}$. Subsequently, Lipshitz-Ng-Sarkar found a cohomotopy element in the Khovanov spectrum associated to the Plamenevskaya invariant. We can think of this element as a map from Khovanov spectra at its extreme quantum grading to the sphere spectrum. We constructed a stable homotopy type for Khovanov skein homology and showed that we can think of the cohomotopy transverse element as a map from the Khovanov spectra at its extreme quantum grading to the Khovanov skein spectra at its extreme Alexander grading. This is a joint work with Adithyan Pandikkadan, which will be presented in this talk.

Katherine Booth
Title: Automorphisms of the smooth fine curve graph
Abstract: The smooth fine curve graph of a surface is an analogue of the fine curve graph that only contains smooth curves. It is natural to guess that the automorphism group of the smooth fine curve graph is isomorphic to the diffeomorphism group of the surface. But it has recently been shown that this is not the case. In this talk, I will give more examples with increasingly wild behavior and give a characterization of this automorphism group for the particular case of continuously differentiable curves.

Xinle Dai
Title: Sectorial Decompositions of Symmetric Products and Homological Mirror Symmetry
Abstract: Symmetric products of Riemann surfaces play a crucial role in symplectic geometry and low-dimensional topology. They are essential ingredients for defining Heegaard Floer homology and serve as important examples of Liouville manifolds when the surfaces are open. In this talk, I will discuss ongoing work on the symplectic topology of these spaces through Liouville sectorial methods, along with examples as applications of this decomposition construction to homological mirror symmetry.

Nursultan Kuanyshov
Title: Numerical invariants of group homomorphisms
Abstract: Numerical invariants we consider are Lusternik-Schnirelmann category, cohomological dimensions, and topological complexity. In this talk, we extend the classical results from numerical invariants of groups to group homomorphisms. In addition, we provide a characterization of the cohomological dimension of group homomorphisms. Time permitting, we will conclude the talk with a discussion of several open problems.

Shiyu Liang
Title: Spherical simple knots in lens spaces
Abstract: A knot in a lens space is said to be spherical if it admits Dehn surgery yielding $S^1\times S^2$. We classify spherical simple knots and thereby confirm the conjecture of Baker, Buck, and Lecuona using rational Seifert surfaces and Morse functions. Additionally, we show that the homology classes of spherical knots are determined by simple knots, analogous to Greene's work in the context of the Berge Conjecture (i.e., surgeries yielding $S^3$).

Trent Lucas
Title: Homeomorphisms, Isotopy, and Group Actions
Abstract: Given a finite group action on a manifold, we study the relationship between isotopy and equivariant isotopy.  This relationship is well-understood for surfaces; we show it behaves quite differently for 3-manifolds.

Rob McConkey
Title: Whitehead Doubles of Dual Knots are Deeply Slice
Abstract: In Collaboration with St. Clair, Wells-Filbert, and Zhang. We will briefly cover the tools we are using to show the dual knot to the 1/n surgery on 6_1 in the three sphere is deeply slice in a contractible 4-manifold. One of the main tools used in our work is the immersed curve perspective of bordered Floer Homology and knot Floer Homology.

Everett Meike
Title: Cataloguing 2-adjacent knots
Abstract: Generalizing unknotting number, n-adjacent knots have n crossings such that changing any non-empty subset of them results in the unknot. We determine the 2-adjacent knots through 12 crossings, with one exception. Using Heegaard Floer d-invariants and the Alexander polynomial, we develop a new technique to obstruct 2-adjacency, and we prove conjectures of Ito and Kato regarding 2-adjacent knots. (Joint with John Carney)

Carlos Pérez Estrada
Title: Non-extremely amenable subgroups of big mapping class groups
Abstract: A topological group is extremely amenable if it admits a common fixed point for all its elements in every compact space on which it acts with a jointly continuous action. In this talk we discuss a geometric criterion, based on Ramsey-theoretic ideas, that allow us to discard extreme amenability of several subgroups of big mapping class groups.

Evan Scott
Title: Equivariant Trisections and Hyperelliptic 4-Manifolds
Abstract: A smooth 4--Manifold $X$ with an orientation-preserving involution $\iota$ is called \emph{hyperelliptic} if the quotient $X/\iota$ is $S^4$. When some extra homological conditions are satisfied, such $X$ are classified up to homeomorphism by Hambleton and Hausmann. We survey applications to these spaces of upcoming joint work with Jeffrey Meier on Equivariant Trisections; namely that $(X, \iota)$ is hyperelliptic if and only if it admits an equivariant trisection so that $\iota$ restricts to the central surface as a hyperelliptic involution of that surface, and that for such an equivariant trisection the fixed-point set (a surface) is 'automatically' in bridge position.

Ivan So
Title: Slice-Bennequin Inequality for the RP3 s-invariantA
Abstract: We present our ongoing work on a slice-Bennequin inequality for the $ \RP^3 $ $ s $-invariant defined in Manolescu-Willis. Subsequently, we will discuss some of the applications, including an obstruction result on whether certain fibered transverse knot support the standard tight contact structure on $ \RP^3 $ and minimal genus results regarding surfaces with such boundary,

Alex Tepper
Title: Constructing Immersions with Specified Self-Intersections
Abstract: The space of immersions Imm(M,N) can be studied through Hirsch-Smale theory, which reveals information about the algebraic topology of Imm(M,N). However, it is not always clear how to produce a representative of a given regular homotopy class.  I will present a construction which produces immersions through the introduction and resolution of simply arranged singularities. This work generalizes a construction in the dim(M) = 1 and 2, dim(N) = dim(M) + 1 cases which is known to produce all regular homotopy classes of Imm(M,N). The corresponding statement for dim(M) = 3 is work in progress.

Konstantinos Varvarezos
Title: On Contact Invariants in Bordered Floer Homology
Abstract: In this paper, we define contact invariants in bordered sutured Floer homology. Given a contact 3-manifold with convex boundary, we apply a result of Zarev to derive contact invariants in the bordered sutured modules BSA and BSD, as well as in bimodules BSAA, BSDD, BSDA in the case of two boundary components. In the connected boundary case, our invariants appear to agree with bordered contact invariants defined by Alishahi-Földvári-Hendricks-Licata-Petkova-Vértesi whenever the latter are defined, although ours can be defined in broader contexts. We prove that these invariants satisfy a pairing theorem, which is a bordered extension of the Honda-Kazez-Matić gluing map for sutured Floer homology. We also show that there is a correspondence between certain A-infinity operations in bordered type-A modules and bypass attachment maps in sutured Floer homology. As an application, we characterize the Stipsicz-Vértesi map from SFH to HFK as an A-infinity action on CFA. We also apply the immersed curve interpretation of Hanselman-Rasmussen-Watson to prove results involving contact surgery.

Ethan (Yang) Zhou
Title: Symplectic fillings of the link of a triangle singularity
Abstract: Triangle singularities are a special class of algebraic surface singularities. They naturally come from the hyperbolic triangles inside the Poincare disk. The link of a triangle singularity is a 3 dimensional contact manifold. In this lightning talk, I will explain my project on investigating the Stein fillings of the link of a triangle singularity.