2025 Faculty and Student Summer Talks | Department of Mathematical Sciences

Date	Day	Speaker, Title, and Abstract
June 2	M	Dr. Roy Goodman A MATLAB disaster (or, why not to blindly trust your numerics) Prof. Goodman will give an example of a short talk that succeeds in its objectives (in his opinion). He will then discuss some pitfalls to avoid when speaking about your research. Time permitting, he may also discuss another important issue: managing numerical experiments.
June 9	M	Michael Storm Spectral Stability of the Swift-Hohenberg Equation with Computer Assisted Proofs The Swift-Hohenberg equation is a partial differential equation noted for its use in modeling pattern formation. In this talk we consider the problem of determining the spectral stability of standing pulse solutions. A difficulty in determining spectral stability is that the point spectrum can be challenging to compute. To deal with this, we count a related object called conjugate points, which have a 1-1 correspondence with unstable eigenvalues. We discuss the numerics involved in counting conjugate points and how computer assisted proofs can be applied to give a rigorous proof of the spectral stability/instability of a pulse solution.
June 12	R	Zheng Zhang Information-theoretic Limits for Testing Community Structure of Bipartite Network
June 16	M	Matthew Illingworth On Correlating Topology and Performance of Membrane Filter Pore Networks Membrane filtration is an important and ubiquitous process in industrial applications, and there is a growing body of mathematical models that capture this complex process. Previous theoretical work models the internal structure of membrane filters as a network of cylindrical pores whose radii are drawn from a uniform distribution, with fouling modeled as an adsorption process; i.e. the gradual accretion of fouling particles on the inner walls of the pores. Simulation-based approaches are used to measure membrane filter performance, using metrics such as total throughput and accumulated foulant concentration. In the present work, we investigate the correlation between the performance of these networks and their topological properties, in order to discover optimal pore topologies for membrane filter design. We use persistent homology as our principal tool for quantifying topological features, where the radii of a network’s pores are represented by a collection of two-dimensional points known as a persistence diagram. The data encoded in these persistence diagrams are then statistically correlated with the performance metrics, particularly with total throughput. A purely topological effect on total throughput will be presented, along with the temporal evolution of filter topology over the lifetime of the filter.
June 19	R	Souaad Lazergui Analysis of Multiple Scattering In High Frequency Regime for Dirichlet and Neumann Problems We analyze an asymptotic method for solving electromagnetic and acoustic scattering problems using boundary integral equations, which remain computationally efficient in the high-frequency regime, and it avoids the typical increase in numerical cost. In the case of a single convex obstacle, we employ an integral representation where the unknown surface densities are constructed in a way that allows the application of the stationary phase method, effectively capturing the dominant contributions of the scattered wave field. For multiple scattering configurations involving several well-separated convex obstacles, we develop an iterative framework that accounts for successive wave reflections between the objects. In this setting, the scattered field is represented as a series where each term corresponds to a specific sequence of reflections, allowing us to capture the complex interactions among obstacles while maintaining high accuracy and efficiency. To illustrate this, we focus more on the two-dimensional convex obstacles. We demonstrate that the iterated solution can be expressed as a sum over periodic ray paths—trajectories in which waves reflect repeatedly in a fixed pattern among the obstacles. This decomposition not only provides a physically intuitive picture of the wave interaction but also offers a rigorous understanding of the structure of the scattered field in complex geometric settings. The framework highlights how geometric optics and wave phenomena interplay in high-frequency regimes, making it especially valuable for applications in radar, sonar, and other wave-based imaging or detection technologies.
June 23	M	Mark Fasano Modeling Drops Driven by Surface Acoustic Waves (SAWs) We present a theoretical study, supported by simulations and simple experiments, on the spreading of a silicone oil drop under MHz-frequency SAW excitation in the underlying solid substrate. Our time-dependent theoretical model uses the long wave approach and considers interactions between fluid dynamics and acoustic driving. For the macroscopic silicon oil drops in this study, acoustic forcing arises from Renolds stress variations in the liquid due to changes in the intensity of the acoustic field leaking from the SAW beneath the drop and the viscous dissipation of the leaked wave. Both experiments and simulations show that after an initial phase where the oil drop deforms to accommodate acoustic stress, it accelerates, achieving nearly constant speed over time, leaving a thin wetting layer. Our model indicates that the steady speed of the drop results from the quasi-steady shape of its body. The drop’s shape and speed are further clarified by a simplified traveling wave-type model that highlights various physical effects. In the second half of the talk, we discuss an extension of this model that describes the dynamics of SAW-driven drops covering solid obstacles. The solid obstacle contributes to both the gravitational and capillary terms in the evolution equation for the drop height consistent with the literature. Numerical results show that for both bump and ramp shaped obstacles qualitative trends with respect to the SAW amplitude are captured by the simulations consistent with experiments.
June 26	R	Atul Anurag Title/Abstract Forthcoming
June 30	M	Joseph D'Addesa Title/Abstract Forthcoming
July 3	R	Andrew White Title/Abstract Forthcoming ***** Bryan Currie Title/Abstract Forthcoming**
July 7	M	Patrick Grice Title/Abstract Forthcoming * Justin Maruthanal Title/Abstract Forthcoming**
July 10	R	Nan Zhou Title/Abstract Forthcoming ***** Elizabeth Tootchen Title/Abstract Forthcoming**
July 14	M	Matthew Cassini Title/Abstract Forthcoming
July 17	R	Philip Zaleski Title/Abstract Forthcoming
July 21	M	Luc Brancheau Title/Abstract Forthcoming ***** Gabriel Masarwa Title/Abstract Forthcoming**
July 24	R	José Pabón Title/Abstract Forthcoming
July 28	M	Joseph Canavatchel Title/Abstract Forthcoming * Ellison O'Grady Title/Abstract Forthcoming**
July 31	R	Xiaotian Mu Title/Abstract Forthcoming

Updated: May 29, 2025