# MSCS Seminar Calendar

Tuesday January 22, 2019

**Quantum Topology / Hopf Algebra Seminar**

Smooth Generic Position

Jonathan Schneider (UIC)

3:00 PM in 612 SEO

We generalize classical knot diagrams and moves to higher dimensions.
Smooth maps are generic when they cannot be fundamentally altered by small perturbations.
Codimension-1 generic maps may be decomposed into simple structures of finitely many types.
We catalog these structures for dimensions 0 through 3, and also catalog their moves.

Wednesday January 23, 2019

**Mathematics Education Colloquium**

Student perceptions of MyMathLab in Developmental Courses

Aida Alibek (UIC)

10:45 AM in 612 SEO

We will discuss a paper by D.Holt, W.Holt & R.Lumadue "At Cross-Purposes with a Developmental Mathematics
Course: Perceptions of Students on the Use of MyMathLab".
This is a discussion seminar, so although prior reading is recommended it is not required. Feel free to come and join the conversation!
Everyone is welcome!

**Special Colloquium**

Too much data!

John Stufken (Arizona State University)

3:00 PM in 636 SEO

The enormous amounts of data that are collected in applications in a wide variety of fields create challenges and opportunities for statisticians. One of the challenges is that traditional statistical methods for data of smaller size may no longer be applicable in the new “big data” environment, for computational reasons or otherwise. The corresponding opportunity lies in the need to develop methods that are applicable for big data. The simplest such methods, and often the most elegant ones, are based on innovations that allow familiar techniques to be applied in this new environment in a computationally feasible way. Adapting existing methods for this new environment can typically not be accomplished by putting “old wine in new bottles”, but requires clever innovations.
Traditionally, it goes against a statistician’s core principles to “discard” some of the data. Yet, some data sets are so large that exploration and analysis must proceed by using only some of the data. This leads to the idea of selecting subdata from big data and drawing conclusions from an analysis of the subdata. While this idea brings traditional statistical analysis methods potentially back into the picture, there are the immediate questions of how to select the subdata and, if needed, how to adjust analysis methods. Innovations to accomplish this are the focus of this presentation. We discuss subdata selection methods, with special emphasis on information-based subdata selection, as well as challenges and shortcomings associated with these methods.

**Graduate Algebraic Geometry Seminar**

Artin-Mumford’s “Some elementary examples of unirational varieties which are not rational” explanation

Fumiaki Suzuki (UIC)

3:00 PM in 712 SEO

We review Artin-Mumford’s construction of a 3-fold which is unirational and non-rational. We start from the motivation, give a construction, and explain it in terms of Severi-Brauer schemes

**Algebraic Geometry Seminar**

The stable cohomology of moduli spaces of sheaves on surfaces

Izzet Coskun (UIC)

4:00 PM in 427 SEO

Moduli spaces of Gieseker semistable sheaves on surfaces play a central role in mathematics and have many applications to cycles and linear systems on surfaces, Donaldson's 4-manifold invariants and mathematical physics. In this talk, I will describe a conjecture with Matthew Woolf on the cohomology of these moduli spaces. We conjecture that the Betti numbers of these moduli spaces stabilize as the discriminant tends to infinity and that the stable numbers are independent of the rank and the first Chern class. In particular, calculations of Gottsche determine the stable numbers. I will give some evidence for the conjecture. This is joint work with Matthew Woolf.

**Graduate Groups and Dynamics Seminar**

Introduction to the work of "7 samurais"

Alex Furman (UIC)

4:00 PM in 612 SEO

This semester we plan to discuss the recent work of Abert-Bergeron-Biringer-Gelander-Nikolov-Raimbault-Samet) and to
(hereafter 7s) that, among other things, discusses the asymptotic growth of the Betti numbers of compact locally symmetric manifolds
$b_i(M)/vol(M)$ as $vol(M)\to \infty$, where $M=\Gamma\backslash X$
are quotients of a fixed (higher rank) irreducible symmetric space.
To understand these results (and to put them in perspective) we need to discuss a variety of important and cool math topics:
- L^2-Betti numbers
- Luck's Approximation Theorem
- Benjaminy-Schramm convergence
- Invariant Random Subgroups
- Stuck-Zimmer theorem
- and more...
There is some topology, geometry, dynamics, and number theory in this all.
In this first talk we will give a general overview, and discuss soem organizational topics.

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.

Tuesday January 29, 2019

**Special Colloquium**

Individualized Multi-Directional Variable Selection

Dr. Annie Qu (UIUC)

3:00 PM in 636 SEO

In this paper we propose a heterogeneous modeling framework which achieves the individual-wise feature selection and the covariate-wise subgrouping simultaneously. In contrast to conventional model selection approaches,the key component of the new approach is to construct a separation
penalty with multi-directional shrinkages, which facilitates individualized modeling to distinguish strong signals from noisy ones and selects different relevant variables for different individuals. Meanwhile, the proposed model identifies subgroups among which individuals share similar covariates’ effects, and thus improves individualized estimation efficiency and feature selection accuracy. Moreover, the proposed model also incorporates within individual correlation for longitudinal data. We provide a general theoretical
foundation under a double-divergence modeling framework where the number
of individuals and the number of individual-wise measurements can both
diverge, which enables the inference on both an individual level and a population
level. In particular, we establish the population-wise oracle property
for the individualized estimator to ensure its optimal large sample property
under various conditions. Simulation studies and an application to HIV longitudinal
data are illustrated to compare the new approach to existing variable
selection methods.

Tea at 4:00-4:30 PM at SEO 300.

Wednesday January 30, 2019

**Graduate Analysis Seminar**

Introduction to the water wave problem of finite depth and modulated waves

Yannis Giannoulis

4:00 PM in 1227 SEO

We will discuss the derivation of the water wave equations for finite depth, their different features depending on the relation between their characteristic lengths, and the notion of modulated waves, and aim to give an outline of the proof of Lannes’s well-posedness result.

**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.

Thursday January 31, 2019

Monday February 4, 2019

Wednesday February 6, 2019

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

Monday April 1, 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

Friday April 5, 2019

Friday April 12, 2019

Monday April 15, 2019

Wednesday April 17, 2019

Friday April 19, 2019

**Algebraic Geometry Seminar**

Double ramification cycles for target varieties

Rahul Pandharipande (ETH)

2:00 PM in 427 SEO

A basic question in the theory of algebraic curves is whether a
divisor represents the zeros and poles of a rational function.
An explicit solution in terms of periods was given by the work of Abel
and Jacobi in the 19th century. In the past few years, a different
approach to the question has been pursued: what is the class
in the moduli of pointed curves of the locus of such divisors? The
answer in Gromov-Witten theory is given by Pixton's formula
for the double ramification cycle. I will discuss recent work
with F. Janda, A. Pixton, and D. Zvonkine which considers
double ramification cycles for target varieties X (where Pixton's
original question is viewed as the X=point case). I will also
discuss the associated relations studied by Y. Bae.

Monday April 22, 2019

Wednesday April 24, 2019

Friday April 26, 2019

Monday April 29, 2019

Wednesday May 1, 2019

Monday May 6, 2019

Monday September 9, 2019

Friday November 1, 2019