Abstract: This workshop aims to explore connections between p-adic Arthur and ABV packets and geometric representation theory/the geometric Langlands program.
Abstract: This talk presents a hybrid mathematical modeling and bioinformatics strategy to uncover interactions between neoplastic cells and the microenvironment during carcinogenesis and therapeutic response. As pancreatic cancer develops, it forms a complex microenvironment of multiple interacting cells. The microenvironment of advanced cancer includes a dense composition of cells, such as macrophages and fibroblasts, that are associated with immunosuppression. New single-cell and spatial molecular profiling technologies enable unprecedented characterization of the cellular and molecular composition of the microenvironment. These technologies provide the potential to identify candidate therapeutics to intercept immunosuppression. Inventing new mathematical approaches in computational biology are essential to uncover mechanistic insights from high-throughput data for these precision interception strategies. Here, we demonstrate how converging technology development, machine learning, and mathematical modeling can relate the tumor microenvironment to carcinogenesis and therapeutic response. Combining genomics with mathematical modeling provides a forecast system that can yield computational predictions to anticipate when and how the cancer is progressing for therapeutic selection. This mathematical forecast system will empower a new predictive oncology paradigm, which selects therapeutics to intercept the pathways that would otherwise cause future cancer progression.
Abstract: Cellular migration is impacted by the environment in which cells move. Seductive chemical signals, anchors for climbing, repulsion from neighbors are critical for progression toward an ultimate physiological goal. The space between cells provides the domain for chemoattractant to diffuse, and the geometry of that space can have a significant effect on timing of the trajectory of a cluster of migrating cells. For data of the border cells from the Drosophila melanogaster egg chamber exhibiting this behavior, we present a simplified one-dimensional hybrid agent-based migration model coupled to a reaction-diffusion model of chemoattractant in a canonical geometry. Our results suggest that geometry-induced chemoattractant distribution is sufficient to capture the observed variation in migration trajectories. Predicted counterintuitive slowing of the border cells during overexpression of chemoattractant while maintaining trajectory variation was confirmed. This slowing in overexpression was rescued by mutation.
This work is in collaboration with Naghmeh Akhavan and experimentalists Alex George and Michelle Starz-Gaiano
Abstract: In recent joint work with Pablo Cubides Kovacsics and Jinhe Ye on beautiful pairs in the unstable context, the amalgamation property (AP) for the class of global definable types plays a key role. In the talk, we will first indicate some important cases in which AP holds, and we will then present the construction of examples of theories - some even NIP - obtained in joint work with Rosario Mennuni, where AP fails.
Abstract: Origami folds have found a large range of applications in Engineering as solar panels for satellites or to produce inexpensive mechanical metamaterials. This talk will first focus on the direct problem of computing the deformation of periodic origami surfaces. A homogenization process for origami folds proposed in [Nassar et al, 2017] and then extended in [Xu, Tobasco and Plucinsky, 2023], is first discussed.The talk will then focus on the PDEs describing the Miura fold, which is a classical origami fold. We study existence and uniqueness of solutions and then propose a finite element method to approximate them.In a second time, we will focus on the inverse problem of computing an optimal fold set approximating a given target surface. The folding of a thin elastic sheet is modeled as a two-dimensional nonlinear Kirchhoff plate with an isometry constraint.We formulate the problem as a minimization in the set of special functions of bounded variation and prove the existence of minimizers. Then, we use a phase-field damage model and a discontinuous finite element method to approximate the minimizers. We subsequently prove that this approximation $\Gamma$-converges to the sharp interface model. Finally, some numerical examples are presented.
Abstract: The goal of this session is to find interesting mathematical content in the papers that were featured in the QIP 2025 conference (https://rsvp.duke.edu/event/qip2025/home) last month. The session will open with a report from Carl Miller about talks that he attended at QIP 2025. Links to some online papers from the conference will be provided, and then attendees will be invited to work together to summarize the math from these papers. We will try to identify avenues for future research.
Abstract: Many low-temperature dynamics in high-dimensional landscapes are expected to exhibit a sharp form of metastability (akin to that of fixed-dimensional small-noise diffusions), where the state space can be partitioned into wells, such that the equilibration time within each well is much faster than the transit time between wells, and the process tracking which well the Markov chain belongs to, itself is asymptotically Markovian. We overview this predicted picture for spin system dynamics, and then describe recent results with Curtis Grant proving this for Glauber dynamics for mean-field heavy-tailed spin glasses.
Abstract: Symplectic capacities are, roughly speaking, a means of measuring the "size" of symplectic manifolds, arising from various themes in Hamiltonian dynamics and symplectic topology. Viterbo's conjecture, an isoperimetric-type question introduced in 2000, asserted that the ball has the largest capacity among all convex domains with the same volume. Despite its simple formulation, this conjecture remained unresolved for many years, sparking extensive research, partly due to its encapsulation of the nontrivial interplay between convex and symplectic geometries. In this talk, I will present a counterexample to Viterbo's conjecture, based on joint work with Yaron Ostrover, and discuss its implications for further research.
Abstract: What would happen if we were to reintroduce wolves to the DMV area? How would it affect the local deer population? The Lotka-Volterra model of population dynamics provides a framework for answering such questions. A system of seemingly simple differential equations leads to complex behaviors, featuring bifurcations, numerical instabilities, and counterintuitive results. Let us explore these fascinating properties by considering a variety of modeling scenarios and the model predictions - and how aligned they are with observations in the real world.