Scalable Computational Framework for Cardiac Radiofrequency Ablation: Multiphysics Modeling and Domain Decomposition
Abstract: Radiofrequency ablation (RFA) is a cornerstone treatment for cardiac arrhythmias, yet its long-term efficacy is often limited by a lack of understanding regarding the biophysical mechanisms of lesion formation. Traditional models rely on thermal thresholds that fail to distinguish between reversible tissue stunning and the permanent functional block required for clinical success.
This dissertation introduces a high-fidelity computational framework that integrates cardiac electrophysiology (EP) directly into RFA assessment. By shifting the paradigm toward functional conduction block, this work establishes a new foundation for predictive ablation modeling.
The framework, implemented within the MFEM finite element library, comprises two pillars:
(I) A Multiphysics RFA Solver that couples electrostatics, bioheat transfer, and fluid dynamics using efficient domain decomposition.
(II) An Integrated EP Solver that utilizes an automated ODE code-generation pipeline to handle complex membrane kin…
Event Type: Dissertation. Research Area: Defense. Location: WH 206. Speaker Name: Leonardo Molinari. Speaker Institution: Emory University.
Thursday, March 19, 2026, 1:00 PM – 3:00 PM.
On the edge expansion of random polytopes
A \emph{$0/1$-polytope} in $\RR^n$ is the convex hull of a subset of $\{0,1\}^n$. The graph of a~polytope $P$ is the graph whose vertices are the zero-dimensional faces of $P$ and whose edges are the one-dimensional faces of~$P$. A conjecture of Mihail and Vazirani states that the edge expansion of the graph of every $0/1$-polytope is at least one. We study a random version of the problem, where the polytope is generated by selecting vertices of $\{0,1\}^n$ independently at random with probability $p\in (0,1)$. Improving earlier results, we show that, for any $p\in (0,1)$, with high probability the edge expansion of the random $0/1$-polytope is bounded from below by an absolute constant. This is joint work with Asaf Ferber, Michael Krivelevich and Wojciech Samotij.
Event Type: Seminar. Research Area: Discrete Math and Combinatorics. Location: MSC E408. Speaker Name: Dr. Marcelo Sales. Speaker Institution: University of California.
Friday, March 20, 2026, 4:00 PM – 5:00 PM.
First-Order PINNs and the Least-Squares Finite Element Method
Abstract: Physics-Informed Neural Networks (PINNs) have proven to be very useful for solving partial differential equations, particularly as a meshless alternative to the Finite Element Method. However, they can be difficult to train due to the non-convex loss landscape. In this dissertation, we draw a connection between the first-order formulation of PINN training and the Least-Squares Finite Element Method. We demonstrate cases where the first-order formulation leads to more accurate results than the second-order formulation and examine the impacts of various first-order formulations. Then we show that using a norm-equivalent loss function for PINN training improves performance and use the norm-equivalence to obtain an error decomposition for the first-order formulation of PINNs. Finally, we leverage a connection between the Least-Squares Finite Element Method and stabilized Finite Element Methods and use data from a stabilized finite element solution to improve PINN performance in advection-dominated prob…
Event Type: Dissertation. Research Area: Defense. Location: WH 200. Speaker Name: Benjamin Yellin. Speaker Institution: Emory University.
Wednesday, March 25, 2026, 11:30 AM – 1:00 PM.
The Harnack inequality without convexity for the Curve Shortening Flow
Abstract: Everything I will discuss is joint work with P. M. Topping. In 1995, Hamilton introduced a Harnack inequality for convex solutions of the Mean Curvature Flow. Hamilton’s Harnack Inequality has played an important role in the theory of the Curve Shortening Flow (CSF), for example in the classification of convex ancient solutions (Daskalopoulos, Šešum & Hamilton, 2010; Wang, 2011; Bourni, Langford & Tinaglia, 2020). In this talk I will introduce an alternative Harnack inequality for the CSF which does not require any assumption of convexity. Our Harnack inequality is related to previous work in Lagrangian MCF (Neves, 2013), and to work in the Ricci Flow, cf. (Topping & Yin, 2017). Given an initial smooth properly embedded curve in the plane whose ends are radial lines but which is otherwise arbitrarily wild, our Harnack inequality will give a precise time after which the CSF of said curve will become graphical, with an explicit gradient bound. This gives a new instance of delayed parabolic regularity.
Event Type: Seminar. Research Area: Analysis and Differential Geometry. Location: MSC W301. Speaker Name: Arjun Sobnack. Speaker Institution: UT Austin.
Friday, March 27, 2026, 11:00 AM – 12:00 PM.