Time/Location: 2:30 - 3:30 pm, September 11th, LeConte 440

Speaker: Aaron Barrett, College of Charleston

Title: Viscoelastic Fluids and Chemical Transport in the Immersed Boundary Method

Abstract: Biological systems often involve non-Newtonian fluids that contain complex chains of elastic polymers. Mucosal membranes that line many organs exude films of mucus containing glycoproteins that serve as a first defense against infection. Blood clots are composed of interconnected platelets and fibrin, creating an elastic network structure. These networks give the fluid elastic responses to deformations, in addition to the solvent's viscous response. Further, fluid-structure interaction (FSI) plays a pivotal role in normal biological functions, from ciliary transport in the lungs to the dynamics of heart valves. In this talk, I will introduce the immersed boundary (IB) method that we use to simulate FSI and demonstrate how it can be used to study the coupling between FSI and chemical transport in viscoelastic fluids. I will demonstrate the difficulties that arise when simulating such models and discuss new techniques to address these problems. Finally, as time permits, I will show applications of the IB method to modeling thrombosis on the aortic valve and microorganism motility.

Time/Location: 2:30 - 3:30 pm, August 28th, LeConte 440

Title: The Mathematics of Spatial Ecology and Epidemiology

Speaker: Zhisheng Shuai (University of Central Florida, Orlando, USA)

Abstract:

Understanding how spatial and temporal heterogeneity influences population and disease dynamics is a central challenge in ecology and epidemiology. In this talk, we explore mathematical approaches that connect matrix theory, graph theory, and differential equations to model and analyze these complex systems. In particular, we demonstrate how generalized inverses and related linear algebra and graph theory tools can quantify variability in population persistence, growth rates, and disease invasibility across heterogeneous habitats. By integrating these techniques with differential equation models, we examine the effects of habitat structure, resource distribution, and migration on population stability and disease spread. The talk highlights how mathematical frameworks provide novel insights into ecological resilience, conservation strategies, and infectious disease management, illustrating to a general audience the interplay between mathematical theory and real-world biological systems.

Speaker: Chris Miles, University of Utah
Time/Location: 2:30 pm - 3:30 pm, April 24, 2026 / LeConte 440

Title: Learning stochastic gene expression dynamics from single-molecule imaging
Abstract: Robust cellular function emerges from inherently stochastic components. Understanding this apparent paradox requires innovations in connecting mechanistic models of molecular-scale randomness with statistical approaches capable of extracting structure from large-scale, heterogeneous datasets. This talk presents a framework for inferring subcellular gene expression dynamics from static spatial snapshots of mRNA molecules obtained from single-molecule imaging. By linking spatial point processes with tractable solutions to stochastic PDEs, we recover dynamic parameters efficiently and without large-scale simulation. I’ll highlight recent theoretical results, including how cell-to-cell heterogeneity improves inference, and discuss extensions to transcriptional bursting, feedback, and cell-cycle effects. The work illustrates how combining mechanistic modeling with modern machine learning can propel new insights into complex biological systems.

Time/Location: 2:30-3:30 pm, April 17th, LeConte 440

Speaker: Xi Huo, University of Miami

Title: Mosquito Population Dynamics in Miami - Modeling, Analysis, and Data

Abstract: This talk outlines a mathematical framework for analyzing mosquito population dynamics using a five-year surveillance dataset from Miami-Dade County. We integrate three distinct modeling approaches to address different aspects of vector control and surveillance: (1) Utilizing modern statistical methods to bridge mechanistic ODE models with longitudinal field data; (2) Implementing PDE models to evaluate the impact of various vector control strategies on vector-borne disease outbreak potentials; and (3) Integrating mechanistic-based model with machine learning techniques to refine population predictions under environmental uncertainty. We discuss how these combined approaches provide a quantitative basis for decision-making in the prevention and control of vector-borne diseases.

Time/Location: 2:30-3:30 pm, Friday, LeConte 440,

Speaker: Yuanzhe Xi, Emory University

Title: Preconditioning Stochastic Algorithms for Scientific Machine Learning

Abstract: Scientific machine learning increasingly depends on stochastic algorithms, both for training nonlinear models and for evaluating expensive linear-algebra quantities that arise in probabilistic and kernel-based methods. In practice, these algorithms are often bottlenecked by ill-conditioning, anisotropic geometry, and stochastic noise. This talk explores how preconditioning can address these bottlenecks in a unified way.

The first part of the talk studies preconditioned SGD for nonconvex problems. I will present a local basin perspective showing that preconditioning can accelerate late-stage convergence, lower the effective noise floor, and improve stability near local minimizers. This framework helps explain when curvature-informed choices, including Fisher-type preconditioners, are beneficial in scientific machine learning.

The second part considers preconditioned truncated single-sample Krylov methods for scalable estimation of inverse quadratic forms and log-determinants. These quantities appear, for example, in Gaussian process training. I will show that preconditioning not only speeds up the underlying iterative methods but also reduces the variance introduced by stochastic truncation. Overall, the talk shows that preconditioning is a powerful organizing principle for scalable stochastic learning algorithms.

Time/Location: 2:30 - 3:30 pm Friday, March 6th / LeConte 440

Speaker: Sharon Crook, Arizona State University

Title: Data-driven modeling of the dynamics of cold-sensitive neurons

Abstract: The ability to perceive cold and warm temperatures is critical for life. In response to cold stimuli, cold-sensitive neurons in the peripheral nervous system exhibit patterned electrical activity, primarily driven by the transient receptor potential melastatin 8 (TRPM8) ion channel. The activation of this ion channel depends on the cell membrane potential, intracellular calcium, temperature, and chemical ligands such as menthol. We present a data-driven differential equations model of TRPM8 kinetics that incorporates these dependencies. We validate the model with novel data and demonstrate its ability to reproduce dynamic TRPM8 behavior. The TRPM8 model is then integrated into a conductance-based cold-sensory neuron model to investigate how TRPM8 influences firing dynamics and adaptation under complex stimuli, offering insight into the mechanisms of cold-sensory neuron dynamics. This talk will include an introduction to models of channel kinetics and neuron excitability so that it is accessible to a wide audience of mathematicians.

Time/Location: 2:30 - 3:30 pm Friday, Nov. 7th / LeConte 440

Speaker: Chengyue Wu,
Department of Imaging Physics, University of Texas MD Anderson
https://faculty.mdanderson.org/profiles/chengyue_wu.html

Title: Towards practical digital twins to predict and optimize TNBC treatment response

Abstract: Triple-negative breast cancer (TNBC) has the poorest prognosis among breast cancer subtypes due to its inherently aggressive clinical behavior and the absence of well-defined molecular targets. Achievement of pCR to neoadjuvant therapy has been widely recognized as a surrogate marker for improved long-term outcomes, including reduced risk of recurrence and enhanced overall survival. However, current neoadjuvant therapy stratification for TNBC is far from satisfying. With the conventional neoadjuvant chemotherapy (NAC), over half of TNBC patients do not achieve pCR and face poor prognoses. The new neoadjuvant chemoimmunotherapy (NACI) combined pembrolizumab with the NAC and has improved pCR and survival rates (by less than 10%), but also introduces substantial toxicity risks without reliable predictive methods to determine individual patient benefit. Currently, there is no method to reliably foretell whether an individual patient will response well to a specific therapeutic regimen, nor to practically guide optimization of therapy on a patient-specific basis. Digital twin techniques have gained emerging attention in this context, which offer great promise for precision management of TNBC by integrating real-time clinical and multi-modal data into virtual patient models to support decision-making. In this talk, we will present essential concepts of cancer digital twins, and show the team’s latest results on building image-guided mechanistic models to obtain personalized prediction of the triple-negative breast cancer growth and response to neoadjuvant therapy, which serve as the computational foundation of establishing patient-specific TNBC digital twins. Beyond prediction response to conventional therapies, these models are capable of identifying alternative treatment regimens designed to outperform the standard-of-care, so allowing for optimizing, and adjusting in near real-time, therapeutic interventions on a patient-specific basis.

Date/Location: 2:30 pm, Friday, Oct 31 / LeConte 440

Speaker: Deepanshu Verma, Clemson University

Title: Neural Network Approaches for Optimal Control: Implicit Hamiltonians and Transferable Policies

Abstract: This talk presents two neural network methodologies advancing optimal control beyond current limitations. First, we address implicit Hamiltonians in practical problems like space shuttle reentry, where existing methods fail without explicit feedback control formulas. Our end-to-end implicit deep learning approach directly parameterizes value functions to handle the underlying implicit structure while enforcing physical principles through the relationship between optimal control and value function gradients, bridging Pontryagin's Maximum Principle and Dynamic Programming. Using Jacobian-Free Backpropagation, we efficiently train the implicit networks for high-dimensional feedback controllers in previously intractable scenarios.

Second, we tackle the computational burden of re-solving problems when objectives change. Our function encoder framework learns reusable neural basis functions enabling zero-shot adaptation through offline-online decomposition: basis functions are learned once, while adaptation requires only lightweight coefficient estimation. Experiments demonstrate near-optimal performance across diverse dynamics with minimal overhead.

These approaches expand neural HJB applicability by handling structural complexity through implicit Hamiltonians and enabling operational flexibility through transferable policies for real-time deployment.