Events

Past Event

Applied Mathematics Colloquium with Franca Hoffmann, Caltech

February 21, 2023
2:45 PM - 3:45 PM
America/New_York
Mudd Hall, 500 W. 120 St., New York, NY 10027 214

Speaker: Franca Hoffmann, Caltech

Title: Covariance-modulated Optimal Transport and Gradient Flows

Abstract: We present a variant of the dynamical optimal transport problem in which the energy to be minimized is modulated by the covariance matrix of the current distribution.​
Such transport metrics arise naturally in mean-field limits of certain ensemble Kalman methods for solving inverse problems.​

We show that the transport problem splits into two coupled minimization problems up to degrees of freedom given by rotations: one for the evolution of mean and covariance of the interpolating curve, and one for its shape.​

Similarly, on the level of the gradient flows a similar splitting into the evolution of moments and shapes of the distribution can be observed. ​

Those show better convergence properties in comparison to the classical Wasserstein metric in terms of exponential convergence rates independent of the Gaussian target.​

Bio: Franca Hoffmann obtained her masters in mathematics from Imperial College London (UK) and holds a PhD from the Cambridge Centre for Analysis at University of Cambridge (UK). She held the position of von Kármán instructor at Caltech from 2017 to 2020 before joining University of Bonn (Germany) as Junior Professor, and Quantum Leap Africa (AIMS Rwanda) as AIMS-Carnegie Research Chair in Data Science. In 2022, she moved to the CMS department at Caltech as Assistant Professor. Franca Hoffmann's research interests lie at the interface of model-driven and data-driven approaches. She works on the development and application of mathematical tools for PDE Analysis and Data Analysis. Broadly, Franca's interests in the area of partial differential equations revolve around non-linear drift-diffusion equations, kinetic theory, many particle systems and their mean-field limits, gradient flows, entropy methods, optimal transport, functional inequalities, parabolic and hyperbolic scaling techniques and hypocoercivity.

For now, only CU-ID holders are welcome at in-person talks. Everyone else is invited to participate remotely. Please email [email protected] ahead of time for the Zoom link.

Contact Information

APAM Department