All events (except the conference dinner) will be held in Maseeh Hall 462 in the campus of Portland State University. There is no registration fees to attend CTS. But we request all attendees to register by filling out this form. Thanks to NSF, we may have limited funding for early career researchers. You can request for funding  while registering.  Funding requests must be received by Thursday, May 14.

Speakers (with talk titles)

• Richard Canary, Univ. Michigan

An invitation to Anosov representations 

• Orsola Capovilla-Searle, Oregon State U.

Which polynomials can be ruling polynomials of Legendrian links?

• Chad Giusti, Oregon State U.

• Ryan Grady, Montana State U.

Concordance Bicategories

Titles & Abstracts of Talks

Lia Buchbinder: Minimal Homotopies in Three Dimensions: A Cable System Approach 

Abstract:  We study null homotopies of immersed spheres in \R^3 and the volume they sweep during contraction. For a smooth immersion with finitely many transverse self-intersections, we introduce a cable system that connects each bounded region of the complement to the exterior. From this construction we define the cable index and prove that it agrees with the Brouwer degree on each complementary region. Using this identification, we derive a degree-weighted lower bound for the swept volume of any Lipschitz null homotopy. We show that the bound is attained whenever the homotopy is sense-preserving, meaning the surface moves in a consistent direction, and the index evolves monotonically along the homotopy. In addition, in the case where the immersion arises as the boundary of an immersed ball, we construct an explicit homotopy that realizes this lower bound via a deformation of the ball. Finally, we present a linear-time algorithm that computes all cable indices from a finite cable system, providing a concrete and computable method for evaluating the lower bound.  arXiv: 2605.06565.

Richard Canary: An invitation to Anosov representations

Abstract: Fuchsian groups arise naturally as groups of covering transformations of hyperbolic surfaces. One may view them as images of discrete faithful representation of free groups and surface groups into PSL(2,R). The study of hyperbolic surfaces and deformation spaces of Fuchsian groups is a rich and classical subject. One may naturally generalize this to the study of groups of covering transformations of hyperbolic manifolds and this also has a beautiful, well-developed theory especially in dimension three.

Introduced in 2006, the theory of Anosov representations into semi-simple Lie groups (e.g. PSL(d,R)) has emerged as a higher rank analogue of the theory of Fuchsian groups. Our talk will begin by recalling some of the classical facts about Fuchsian groups. We will then gently introduce the subject of Anosov representations and their emerging theory. 

Orsola Capovilla-Searle: Which polynomials can be ruling polynomials of Legendrian links?

Abstract:  An important problem in symplectic and contact topology is to classify exact Lagrangian surfaces in the symplectic 4-ball that intersect the boundary contact 3-sphere as Legendrian links up to exact Lagrangian isotopy fixing the boundary. Such surfaces are called fillings of the Legendrian link. In the last decade, our understanding of the moduli space of fillings for various families of Legendrians has greatly improved thanks to tools from sheaf theory, Floer theory and cluster algebras. The ruling polynomial is a Legendrian invariant in a many to one correspondence with immersed fillings. In joint work with Yu Pan we show that any even degree polynomial can be realized as the ruling polynomial of a Legendrian. The Legendrian links we construct have augmentation varieties with trivial cluster algebras and fillings that are not smoothly isotopic. Our family of Legendrians exhibits distinct behavior to that of the better studied Legendrian (-1) closures of positive braids containing a full twist.

Ryan Grady: Concordance Bicategories

Abstract:  In this talk I'll talk about a sequence of bicategories that encode embeddings of manifolds and concordances (as opposed to isotopies) of such embeddings.  I'll focus on low dimensions, so we will see generalizations of the tangle category and relationship to low dimensional bordism categories.  I'll show how these structures encode natural objects, e.g., the (smooth) concordance group of knots and the action of satellite patterns on it.

Jonathon McCollum: Methods for Cycle Comparison Between Data Samples with a Cross-dissimilarity Measure

Abstract: This talk covers methods that have been created to measure similarity between first homology cycle representatives in separate finite metric spaces with a cross-dissimilarity measure. The methods leverage the witness complex, the Grassmannian distance, and the analogous bars method. Two variations on the comparison will be presented. The first is computationally efficient and suited high similarity, high density data. The second leverages filtration over dissimilarity scores between elementary 1-chains to ensure find cycle representatives in the appropriate complex when possible. 

Jackson Morris: Higher Witt K-theory

Abstract:  A useful tool for detecting periodicity in stable homotopy theory are the higher real K-theory spectra, which arise as fixed points of the Lubin-Tate spectra. In motivic homotopy theory, periodicity is more complicated, and it has been less obvious how to systematically study this exotic structure. In joint work with Ormsby, we show that the Tate fixed points of the motivic Lubin-Tate spectra, which we call Higher Witt K-theories, are viable candidates for studying exotic periodicity. Curiously, these spectra demonstrate a diachromatic blueshift phenomenon: if the motivic Lubin Tate theory is of height n, then the associated Higher Witt K-theory detects height n-1 exotic phenomena. This is work in progress.

Connor Progin: From Directed Graphs to Maximum Flows via Cellular Sheaves

Abstract: Cellular sheaves provide a powerful tool for modeling problems in network theory. A notable example is the flow sheaf, which encodes a feasible s-t flow on a directed graph as a cellular sheaf of vector spaces, realizing the flow value as the dimension of the space of global sections. Generalizing this construction to compute the maximum s-t flow value is a natural goal. We discuss an approach using cellular sheaves of polynomial rings, where variables allow us to parameterize all possible routing options. Optimization determines specific relations between these variables, and evaluating at an optimal solution recovers a cellular sheaf of vector spaces. We then use cohomology to compute the space of global sections as before. This is work in progress. 

Elizabeth Thompson: A Stable Measure of Chaos in Dynamical Systems using Persistent Homology

Abstract:  Dynamical systems model real-world motion in a variety of interdisciplinary fields. One commonly used measure of chaos the maximal Lyapunov exponent, which is less robust to small trajectory perturbations in practice. We leverage the theoretical stability of persistent homology to construct a stable measure of chaos using 0-dimensional persistence, termed the 0-persistence exponent. We prove the stability of the 0-persistence exponent, the existence of an upper bound, and that positive Lyapunov estimates guarantee positive 0-persistence estimates for sufficient trajectory conditions. We show greater experimental stability of our 0-persistence exponent on the Lorenz and Rössler systems, and on real time-series data of an autocatalytic chemical reaction. We experimentally show high correlation between both measures on the Lorenz and Rössler  systems. arXiv: 2601.10900.

Alex Waugh: An equivariant transgression theorem 

Abstract: Kudo's description of how differentials in the Serre spectral sequence interact with power operations vastly increased the effectiveness of the Serre spectral sequence as a computational tool. For example, this was a key input to Serre's computation of the cohomology of Eilenberg–MacLane spaces and Cohen–May's calculation of the homology of iterated loop spaces. My thesis and recent joint work with Bhattacharya, Zeng, and Zou constructs G-equivariant power operations and Steenrod operations for any finite group G, providing the exact analogues to those used in these classical computations. In this talk, I will outline an equivariant transgression theorem showing how these operations interact with the differentials of Hill–Hopkins–Ravenel's slice spectral sequence.