Fall 2026

Sep 14, 2026 : Zach Martin

Title: A Characterization of Size 2 Orbits of Plane Partitions Under Rowmotion

Abstract:  We study the action of rowmotion on plane partitions in the [a]×[b]×[c] poset, focusing on orbits of size 2. We identify orbits of size 2 with a coloring approach that helps identify the hidden structures of orbits of size 2. These colorings are shown to have restrictive properties that force conditions on the dimensions of our poset a, b, and c. We then show that these conditions entirely describe all posets [a] × [b] × [c] that will contain orbits of size 2. Finally, we show that these colorings are in bijection with lozenge tilings of zonogons with dimensions corresponding a, b, and c allowing us to count all orbits of size 2 in a given poset by using Macmahon’s box formula and generate all orbits of size 2 by following our bijection. 

Sep 21, 2026 : Alexandra Squires

Title: The Bounded Geodesic Image Theorem for the Nonperipheral Arc and Curve Graph

Abstract: The Bounded Geodesic Image Theorem is a powerful tool originally proven by Masur and Minsky and used in many landmark results in geometric group theory. Operating in the nonperipheral curve graph introduced by Qing and Rafi and using proof techniques introduced by Webb, we prove that under mild assumptions on a surface of finite or infinite type, the Bounded Geodesic Image Theorem holds for the graph of nonperipheral curves on the surface, under projection to the nonperipheral arc and curve graph. Specifically, suppose that an infinite type surface $\Sigma$ is stable and of sufficiently high end-complexity. Let $Y\subset \Sigma$, possibly noncompact but with finitely many boundary components, be a nonperipheral subsurface that is disjoint from at least one noneripheral curve. Then there exists a uniform constant $M>0$ such that any geodesic segment in the graph of nonperipheral curves on $\Sigma$ that cut $Y$ projects to a set bounded above in diameter by $M$ in the graph of nonperipheral arcs and curves on $Y$.

Sep 28, 2026 : Milap Rajgor

Title: Zigzag Persistent Homology for Protein Molecular Dynamics

Abstract: Proteins are dynamic molecular systems, and molecular-dynamics trajectories can reveal structural changes that are not captured by individual static conformations. Zigzag persistent homology provides a natural framework for tracking topological features across time-varying protein structures. We applied this approach to mdCATH domain trajectories, following loop-like features across temperatures. From the resulting (H_1) zigzag barcodes, we defined tau_top, a descriptor of temporal topological organization. Across the studied domains, tau_top decreased with increasing temperature, consistent with thermal structural reorganization. By mapping representative topological features back onto protein structures, we further found that residue participation was associated with burial and lower root-mean-square fluctuation (RMSF), suggesting a connection to local structural rigidity. We also developed TopoMol, an interactive tool for locating and visualizing representative topological loops and cavities within proteins. Together, zigzag barcodes and TopoMol provide a framework for studying how protein topology evolves throughout molecular-dynamics trajectories.

*Oct 12, 2026 : Corey Nelson

Title:  Permutation Sorting and the Basis of Foot-sortable Sock Orderings

Abstract: In this talk, I'll discuss the toy problem of permutation sorting with a stack data structure, as well as how this problem generalizes to sorting permutations of multisets. The more basic problem was introduced in the 1970s in Donald Knuth's "Art of Computer Programming," while the latter emerged only a few years ago from Defant and Kravitz. The latter portion of the talk will be based on prior work with Theodore Molla (University of South Florida) and our paper "The Basis of Foot-sortable Sock Orderings"