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# Departmental Colloquia

Our department is proud to host weekly colloquium talks featuring research by leading mathematicians from around the world. Most colloquia are held on Fridays at 4pm in Parker Hall, Room 250 (unless otherwise advertised) with refreshments preceding at 3:30pm in Parker Hall, Room 244.

DMS Colloquium: Matthias Heikenschloss

Apr 26, 2019 04:00 PM

Speaker: Matthias Heikenschloss, Rice University

Title: Risk averse PDE constrained optimization

Abstract: Optimal control and optimal design problems governed by partial differential equations (PDEs) arise in many engineering and science applications. In these applications one wants to maximize the performance of the system subject to constraints. When problem data, such as material parameters, are not known exactly but are modeled as random fields, the system performance is a random variable. So-called risk measures are applied to this random variable to obtain the objective function for PDE constrained optimization under uncertainty. Instead of only maximizing expected performance, risk averse optimization also considers the deviation of actual performance below expected performance. The resulting optimization problems are difficult to solve, because a single objective function evaluation requires sampling of the governing PDE at many parameters. In addition, risk averse optimization requires sampling in the tail of the distribution.

This talk demonstrates the impact of risk averse optimization formulations on the solution and illustrates the difficulties that arise in solving risk averse optimization. New sampling schemes are introduced that exploit the structure of risk measures and use reduced order models to identify the small regions in parameter space which are important for the optimization. It is shown that these new sampling schemes substantially reduce the cost of solving the optimization problems.

Brief Bio and Research Summary
Matthias Heinkenschloss joined the Rice faculty in 1996 after serving for three years as an assistant professor in the Department of Mathematics at Virginia Polytechnic Institute and State University. He rose through the ranks at Rice, and is now the Noah G. Harding Chair and Professor of Computational and Applied Mathematics. He served as department chair for six years. Matthias began his academic career at the University of Trier in the Federal Republic of Germany, where he was from 1988 to 1993.

Matthias Heinkenschloss’ research interests are in the design and analysis of mathematical optimization algorithms for nonlinear, large-scale (often infinite dimensional) problems and their applications to science and engineering problems. Research areas include large-scale nonlinear optimization, model order reduction, optimal control of partial differential equations (PDEs), optimization under uncertainty, PDE constrained optimization, iterative solution of KKT systems and domain decomposition in optimization.
Hosts: Yanzhao Cao and Hans-Werner van Wyk

DMS Colloquium: Frédéric Holweck

Apr 19, 2019 04:00 PM

Speaker: Frédéric Holweck, Université de Technologie de Belfort-Montbéliard (France)

Title: Projective duality and quantum information

Abstract: Quantum Information is a nascent science which intends to use the properties of quantum physics to produce new computational paradigms. Quantum phenomena, like entanglement, are non-classical resources that need to be classified. Interestingly in the early 2000’s the old idea of projective duality regained new interest in the quantum physics literature as a potential tool for studying entanglement.

In this talk, after explaining the motivations from quantum physics, I will recall some classical notions regarding projective duality and introduce more recent results obtained with Luke Oeding about the calculation of hyperdeterminants from the $$E_8$$-discriminant.

Faculty host: Luke Oeding

DMS Colloquium: Youssef Marzouk

Apr 12, 2019 04:00 PM

Speaker: Youssef Marzouk,  MIT​

Title: Nonlinear filtering and smoothing with transport maps

Abstract: Bayesian inference for non-Gaussian state-space models is a ubiquitous problem, arising in applications from geophysical data assimilation to mathematical finance. We will present a broad introduction to these problems and then focus on high dimensional models with challenging nonlinear dynamics and sparse observations in space and time. While the ensemble Kalman filter (EnKF) yields robust ensemble approximations of the filtering distribution in this setting, it is limited by linear forecast-to-analysis transformations. To generalize the EnKF, we propose a methodology that transforms the non-Gaussian forecast ensemble at each assimilation step into samples from the current filtering distribution via a sequence of local nonlinear couplings. These couplings are based on transport maps that can be computed quickly using convex optimization, and that can be enriched in complexity to reduce the intrinsic bias of the EnKF. We discuss the low-dimensional structure inherited by the transport maps from the filtering problem, including decay of correlations, conditional independence, and local likelihoods. We then exploit this structure to regularize the estimation of the maps in high dimensions and with a limited ensemble size.

We also present variational methods---again based on transport maps---for smoothing and sequential parameter estimation in non-Gaussian state-space models. These methods rely on results linking the Markov properties of a target measure to the existence of low-dimensional couplings, induced by transport maps that are decomposable. The resulting algorithms can be understood as a generalization, to the non-Gaussian case, of the square-root Rauch--Tung--Striebel Gaussian smoother.

This is joint work with Ricardo Baptista, Daniele Bigoni, and Alessio Spantini.

Faculty hosts: Yanzhao Cao and Xiaoying Han

DMS Colloquium: Emanuele Ventura

Apr 05, 2019 04:00 PM

Speaker: Emanuele Ventura, Postdoc Texas A&M; Ph.D., Aalto University (Helsinki, Finland) 2017

Title: Tensors and their symmetry groups

Abstract: Tensors (multi-dimensional matrices) appear in many areas of pure and applied mathematics. I will discuss their use in algebraic complexity theory. Matrix multiplication is a tensor and its complexity is encoded in its tensor rank. To analyze the complexity of the matrix multiplication tensor, Strassen introduced a class of tensors that vastly generalize it, the tight tensors. These tensors have continuous symmetries. Pushing Strassen’s ideas forward, with A. Conner, F. Gesmundo, and J.M. Landsberg, we investigate tensors with large symmetry groups and classify them under a natural genericity assumption. Our study provides new paths towards upper bounds on the complexity of matrix multiplication.

DMS Colloquium: Ferenc Fodor

Mar 22, 2019 04:00 PM

Speaker: Ferenc Fodor, University of Szeged (Hungary)

Title: On the $$L_p$$ dual Minkowsi problem

Abstract: We will mainly discuss the solution of the existence part of the $$L_p$$ version of the $$q$$th dual Minkowski problem for $$p>1$$ and $$q>0$$. The $$L_p$$ dual Minkowski problem, formulated by Lutwak, Yang, and Zhang, provides a unification of several other variants of the question. We will concentrate on the more geometric parts of the argument and especially on the discrete case. We will also describe some regularity properties of the solution with the help of the corresponding Monge–Ampère equation. This is joint work with Károly J. Böröczky (MTA Rényi Institute, Budapest, and Central European University, Budapest, Hungary).

Faculty host: Andras Bezdek

DMS Colloquium CANCELED

Mar 20, 2019 04:00 PM

CANCELED

Last Updated: 09/11/2015