Wednesday 15:30 -16:20, https://ucr.zoom.us/j/97606227247
Organizers : Weitao Chen / Yat Tin Chow / Qixuan Wang / Jia Gou / Mykhailo Potomkin / Yiwei Wang / Maziar Raissi / Siting Liu / Thomas Bury
Past Organizers : Mark Alber / James Kelliher / Amir Moradifam / Heyrim Cho
Archives: Fall 2019 / Winter 2020 / Spring 2020 / Fall 2020 / Winter 2021 / Spring 2021 / Fall 2021 / Winter 2022 / Spring 2022 / Fall 2022 / Winter 2023 / Spring 2023 / Fall 2023 / Winter 2024 / Spring 2024 /Fall 2024 / Winter 2025 / Spring 2025 / Fall 2025 / Winter 2026
Links : Interdisciplinary Center for Quantitative Modeling in Biology (ICQMB) seminar
In Winter 2026, the PDE & Applied Math seminar will be held through Zoom or in person (Skye 361). Specific information about the format of each talk will be provided in the email announcement and posted below. If you're interested in attending the seminar, please contact Dr. Thomas Bury (tbury@ucr.edu) and Dr. Weitao Chen (weitaoc@ucr.edu).
Winter 2026 Schedule
Jan 07 15:30 (Wed) Organizational meeting
Jan 20 10:00 (Tue) Nusrat Molla, Princeton University (note time difference) (recording)
Jan 28 15:30 (Wed) Thomas Anderson, Rice University
Feb 04 15:30 (Wed) Maliha Ahmed, MIT (in person talk)
Feb 11 15:30 (Wed) Jiajie Chen, University of Chicago
Feb 18 15:30 (Wed) Marissa Renardy, GSK
Feb 25 15:30 (Wed) Charles Puelz, University of Houston
Mar 02 15:30 (Mon) Ming Zhong, University of Houston (note time difference)
Mar 11 15:30 (Wed) Franziska Weber, University of California, Berkeley
Upcoming Talks:
Feb 11, 2026, 3:30 PM - 4:50 PM PT
Dr. Jiajie Chen (University of Chicago)
Title: Singularities in Fluids and Related Equations
Abstract: In this talk, we will discuss recent developments on singularity formation in fluids and show how singularities in the Euler equations can be lifted to construct singularities in related equations.
Past Talks:
Jan 28, 2026, 3:30 PM - 4:50 PM PT
Dr. Thomas Anderson (Rice University)
Title: Integral equation methods for inhomogeneous problems: discretizations and solvers
Abstract: Methods based on Green's functions have long been a workhorse for homogeneous boundary value problems, as they lead to integral equations posed on the boundary of a region of interest, with additional special advantages accruing for exterior problems. Persistent challenges include the need to evaluate singular integrals with kernels that decay slowly and require special care for efficient computations of long-range interactions. But even more fundamentally, the methods have not seen success for inhomogeneous problems for which methods typically involve one or several volume integral operators (VIOs). We will discuss a class of numerical methods for VIOs that rely on analytic regularization: they use Green's identities to regularize the singular kernels in the volume integrals and lead to high-order accuracy even with the use of standard, singularity-oblivious triangle/tetrahedral quadratures. A complete error analysis, over 2D and 3D meshes possibly containing curved elements, for several key VIOs of progressively increasing singularity strength that arise in applications will be discussed. Numerical examples will be presented in the context of (1) IMEX time-stepping methods for nonlinear PDEs and (2) variable-coefficient scattering problems arising in inhomogeneous media. For the latter, a key challenge involves the incorporation of efficient volume preconditioners into iterative solvers, while retaining high-order accuracy in the presence of material discontinuities.
Jan 20, 2026, 10:00 AM - 11:00 AM PT
Dr. Nusrat Molla (Princeton)
Title: A Dynamical Systems Perspective on the Resource Curse
Abstract: The resource curse is a long-studied problem in which resource extraction-dependent economies face poor socio-economic outcomes. This talk presents a low-dimensional nonlinear dynamical systems model of the dynamics leading to the resource curse, focusing on feedbacks between extractive activity, institutional quality, and human and social capital. The resulting system of ordinary differential equations produces multiple stable equilibria corresponding to a diversified and extraction-dominated economic states. As parameters such as commodity prices vary, the diversified equilibrium loses stability in a saddle-node bifurcation while the resource curse never loses stability, leading to an irreversible transition to the resource curse. A generalized version of the model shows that these qualitative behaviors are robust to changes in functional form but depend critically on endogenous institutional dynamics. Removing institutional dynamics causes bifurcations to disappear, indicating that socio-political dynamics are necessary for the emergence of irreversible development traps.
Feb 4, 2026, 3:30 PM - 4:50 PM PT
Dr. Maliha Ahmed (MIT) (in person talk)
Title: The Fate of Absence Seizures in Neurosteroid-Modulated Thalamocortical Networks
Abstract: Childhood absence epilepsy (CAE) is a pediatric generalized epilepsy characterized by brief periods of impaired consciousness and a 2.5-5 Hz spike–wave discharge pattern on electroencephalography. Although CAE often remits spontaneously during adolescence, the mechanisms underlying remission, and non-remission, remain poorly understood. We use conductance-based thalamocortical network models to investigate how neurosteroid modulation influences absence seizure dynamics. Allopregnanolone, a progesterone metabolite that enhances GABAergic inhibition, has been proposed as a potential remission factor, yet clinical observations suggest that hormonal modulation alone cannot fully explain seizure outcomes. To explore this discrepancy, we introduce an enhanced thalamocortical model incorporating layered cortical structure, regional heterogeneity, and genetically motivated neuronal perturbations. Within this multi-scale framework, we examine how network architecture, intrinsic connectivity, and cell-type composition shape seizure trajectories and recovery. These results highlight the role of network structure in determining the fate of absence seizures and illustrate how computational models can provide insights into spontaneous transitions in pathological brain dynamics.