Description

During the CCAM lunch seminar this week, we will participate in a group activity to meet each other, share resources, and identify folks in the CCAM community who have experience with conferences, workshops, internships, grants, or other resources that you may be interested in for the future. The seminar will take the form of an interactive bingo activity, where folks will be asked to find others in the group who have experience with a range of mathematical resources and activities (i.e., AMS Mathematics Resource Communities, different NSF research institutes and travel grants, teaching various classes, industry applications, etc). This activity has been used during icebreaker events at past SIAM conferences, including the 2024 SIAM Annual Meeting and the 2025 SIAM Conference on Applications of Dynamical Systems.  

Title: Multi-objective Bayesian inference in a stochastic agent-based model of zebrafish pattern formation via topological data analysis

Abstract

In many biological settings, agent-based models provide a natural framework for capturing stochasticity and individual-level interactions amongst large number of cells. However, inferring the parameters in such models poses significant challenges that limit the predictive power of these models. We demonstrate that combining topological data analysis with approximate-approximate Bayesian computation is a computationally feasible approach to addressing these challenges. In our study, we focus on an existing agent-based model of pattern formation in zebrafish skin, and we show how to estimate parameters and perform identifiability analysis in this complex, stochastic model. In particular, we show how to use multi-objective inference to combine multiple biologically meaningful summaries of model output to be able to accurately determine parameter values.

Title: Data-Driven Closure Models (DDCMs)

Abstract

Data-driven closure models (DDCMs) are machine learning models that are embedded with computational simulations with the overall goal of capturing "the missing physics" (closure term) of a system. Data-assimilation uses statistical techniques to create more accurate and reliable predictions in complex systems, by combining real-world observations with computational simulations. In this research, we used an SIQR exemplary model as our physical simulation with closure term to be estimated. This, because we want to capture the closure term as accurately as possible, so that the entire model is accurate as a whole. We provide a brief, informal introduction to data assimilation, and present the preliminary results of the sensitivity analysis of the estimate of an algorithmic parameter for data assimilation.

Title: Parallel Transport Convolution: A Geometric Framework for CNNs on Manifolds

Abstract

Convolution Neural Networks (CNN) rely fundamentally on translation invariance in Euclidean space, a property that does not generalize naturally to curved manifolds. In this talk, I will present the Parallel Transport Convolution (PTC), a geometrically principled definition of convolution on Riemannian manifolds that preserves the key structure of classical CNN. The central idea is to replace Euclidean translation with parallel transport along geodesics, allowing a locally defined kernel to be consistently propagated across the manifold using intrinsic geometry. I will outline the mathematical construction of PTC using the exponential map and parallel transport, show how it recovers standard convolution in the flat case, and discuss its discretization on meshes.

Title: Accurate Reconstruction of Plastic Metal Objects in X-ray CT Imaging

Abstract

X-ray CT imaging of objects that contain a combination of metal and plastic materials is challenging because the metal artifacts tend to distort the plastic reconstruction. We present an Iterative Plastic–Metal Reconstruction (IPMR) algorithm that reduces artifacts by segmenting the object, estimating the material beam hardening parameters for each material, and then reconstructing the corrected sinogram. Results on scanned data indicate the IPMR algorithm can significantly improve the quality of plastic reconstruction while maintaining the quality of the metal.

Title: A CSIDH Stroll through Isogeny-based Post-Quantum Cryptography

Abstract

In recent years, focus has been placed on the development of key exchange protocols that could serve as post-quantum successors to existing cryptographic infrastructure. Some of these potential successors are based on the action of the class group of an order of an imaginary quadratic field on the set of Fp-rational elliptic curves defined over Fp. These protocols are thought to have the potential to become a suitable alternative to lattice-based protocols currently being standardized by NIST, the National Institute of Standards and Technology, which is holding a competition calling for the submission of new post-quantum cryptosystem candidates.

In this talk, I give a brief overview of what post-quantum cryptography is and what motivates the study of it, and offer a look into the fascinating world of isogeny-based post-quantum cryptography. Specifically, I will focus on the CSIDH key exchange protocol and recent advancements related to it.