Faculty Research Talks - Spring 2025
Talks will be held at 2:30PM on every other Monday (M) at 2:30PM in CULM 611 unless otherwise noted.
February 3
Location: CULM 611
Title and Abstract Forthcoming
February 17
Location: CULM 611
Title and Abstract Forthcoming
March 3
Location: CULM 611
Title and Abstract Forthcoming
March 31
Location: CULM 611
Integral Equation Methods for Flexural-Gravity Waves (or, a Song of Ice and Water)
I'll present some results from two recent pre-prints on flexural and flexural-gravity waves (https://arxiv.org/abs/2409.19160 and https://arxiv.org/abs/2501.00887). These models are commonly used to understand the waves that propagate along the interface between ice floes and sea water. Perhaps surprisingly, this problem can be reduced from three dimensions to a tractable, second-kind integral equation defined on the interface alone. I'll discuss the derivation, analysis, and numerical solution of this integral equation --- soup to nuts --- which touches on a lot of the mathematics from our first year courses. Finally, I'll present some of the interesting numerical experiments that these tools enable and some open projects. This is joint work with Manas Rachh (Flatiron Institute) and Jeremy Hoskins, Peter Nekrasov, and Tim Su (U.Chicago).
April 14
Location: CULM 611
Inference of Phylogenetic Networks
Phylogenetic networks are a generalization of phylogenetic trees allowing for the representation of speciation and reticulate evolutionary events such as hybridization or horizontal gene transfer. The inference of phylogenetic networks from biological sequence data is a challenging problem, with many theoretical and practical questions still unresolved. In this talk, I will give an overview of the state of the art in phylogenetic network inference. I will then discuss a novel divide-and-conquer approach for inferring level-1 networks under the network multispecies coalescent model. I will end by discussing some open problems and avenues for future research.
April 28
Location: CULM 611
Numerical methods for the magnetophoretic transport and assembly of paramagnetic particles
I will present recent numerical methods for the problem of the magnetophoretic transport of magnetic liquids (ferrofluids). I will discuss the extension of the numerical framework to include the fluid-structure interactions based on direct solutions of the fully three-dimensional governing (Navier-Stokes) equations, coupled with the solution of Maxwell equations for the magnetic field and the magnetic stress calculations. Complex geometries are treated with an adaptive Cartesian embedded boundary using the volume-of-fluid method for piecewise linear reconstruction of the particle geometries. I will then discuss the self-assembly of particles at fluid-fluid interfaces, which is of considerable interest for studying the collective behavior of colloidal suspensions at small scales, and then the future work to study the spatial arrangement and clustering of paramagnetic particles on fluid-fluid interfaces.