# MSCS Seminar Calendar

Tuesday January 15, 2019

**Logic Seminar**

Very discrete groups

Sam Corson (University of the Basque Country)

3:30 PM in 427 SEO

Some groups are so discrete that abstract homomorphisms from many of the standard continuous topological groups to such a group always have open kernel. It was known classically that any homomorphism from a completely metrizable group to a free group has open kernel. I'll talk about the history of such results and give a plethora of new examples. Joint work with Greg Conner.

Thursday January 24, 2019

Monday January 28, 2019

**Analysis and Applied Mathematics Seminar**

Interaction of modulated water waves of finite depth

Yannis Giannoulis (University of Ioannina, Greece)

4:00 PM in 636 SEO

In this talk we consider the water wave problem of finite depth as a nonlinear dispersive system. Motivated by this feature, we are interested in the macroscopic dynamics of the envelopes of small, macroscopically amplitude-modulated fixed carrier waves, the latter being plane wave solutions of the linearized problem. More specifically, we want to know whether some sort of interaction of different (modulated) carrier waves can be observed macroscopically. For pure gravity waves such a macroscopic interaction can be observed only for the next-to-leading order corrections of the macroscopic amplitudes and a relevant system of modulation equations is derived. This system is then justified by employing the stability of the original water wave problem, as established by Lannes in his 2013 book. Time permitting, we discuss also the completely different situation in the case of capillary-gravity water waves, where for resonant carrier waves macroscopic interactions can be observed for the leading order amplitudes and where a stability result for the original water wave problem has to take into account the second-order differential operator of the surface tension.

Wednesday January 30, 2019

**Statistics Seminar**

Sufficient dimension folding via distance covariance

Wenhui Sheng (Marquette University)

4:00 PM in 636 SEO

We propose a new sufficient dimension folding method using distance covariance for regression in which the predictors are matrix- or array-valued. The
method works efficiently without strict assumptions on the predictor. It is
model-free and neither smoothing techniques or selection of tuning parameters
is needed. Moreover, it works for both univariate and multivariate response
cases. We use two approaches to estimate the structural dimensions: bootstrap
method and a new method of local search. Simulations and real data analysis
support the efficiency and effectiveness of the method.

Monday February 4, 2019

**Analysis and Applied Mathematics Seminar**

On a dissipative Gross-Pitaevskii-type model for exciton-polariton condensates

Ryan Obermeyer (University of Illinois at Chicago)

4:00 PM in 636 SEO

We study a generalized dissipative Gross-Pitaevskii-type model
arising in the description of exciton-polariton condensates. We derive rigorous
existence and uniqueness results for this model posed on the one dimensional
torus and derive various a-priori bounds on its solution. Then, we analyze
in detail the long time behavior of spatially homogenous solutions and their
respective steady states. In addition, we will present numerical simulations in
the case of more general initial data. We also study the corresponding adiabatic
regime which results in a single damped-driven Gross-Pitaveskii equation and
compare its dynamics to the one of the full coupled system.
Joint work with C. Sparber, P. Antonelli, P. Markowich, and J. Sierra

Monday February 11, 2019

Wednesday February 13, 2019

Monday February 18, 2019

**Analysis and Applied Mathematics Seminar**

Simulating Multilayer Plasmonic Devices with Domain Decomposition Methods: High-Order Perturbation of Surfaces Implementations

David Nicholls (University of Illinois at Chicago)

4:00 PM in 636 SEO

The faithful modeling of the propagation of linear waves in a layered,
periodic structure is of paramount importance in many branches of the
applied sciences, in particular, in the simulation and design of
multilayer plasmonic devices. In this talk we present a novel
numerical algorithm for the simulation of such problems which is free
of the artificial singularities present in related approaches. We
advocate for a non-overlapping domain decomposition method (DDM)
phrased in terms of Impedance-Impedance Operators that are immune to
the Dirichlet eigenvalues which plague the Dirichlet-Neumann Operators
that appear in classical formulations. We demonstrate a High-Order
Spectral algorithm to simulate these operators based upon a High-Order
Perturbation of Surfaces methodology which is rapid, robust, and
highly accurate. We demonstrate the validity and utility of our
approach with a sequence of numerical simulations.

Wednesday February 20, 2019

Monday February 25, 2019

Wednesday February 27, 2019

Friday March 1, 2019

Monday March 4, 2019

Monday March 11, 2019

Wednesday March 13, 2019

Friday March 15, 2019

Monday March 18, 2019

Wednesday March 27, 2019

Friday April 12, 2019

Wednesday April 17, 2019

Monday April 22, 2019

Wednesday April 24, 2019

Friday April 26, 2019

Wednesday May 1, 2019

Wednesday May 8, 2019