# MSCS Seminar Calendar

Monday October 15, 2018

**Geometry, Topology and Dynamics Seminar**

Galois groups and Cantor actions

Olga Lukina (UIC)

3:00 PM in 636 SEO

In this paper, we study the actions of profinite groups on Cantor sets which arise from representations of Galois groups of certain fields of rational functions. Such representations are associated to polynomials, and they are called profinite iterated monodromy groups. We are interested in a topological invariant of such actions called the asymptotic discriminant. In particular, we give a complete classification by whether the asymptotic discriminant is stable or wild in the case when the polynomial generating the representation is quadratic. We also study different ways in which a wild asymptotic discriminant can arise.

**Mathematical Computer Science Seminar**

List Coloring Cartesian Products of Graphs: Criticality and the List Color Function

Hemanshu Kaul (IIT)

3:00 PM in 427 SEO

The list chromatic number of the Cartesian product of graphs is not well understood. The best result is by Borowiecki, Jendrol, Kral, & Miskuf (2006) who proved that the list chromatic number of the Cartesian product of two graphs can be bounded in terms of the list chromatic number and the coloring number of the factors, implying a bound exponential in the list chromatic number of the factors.
We show how the knowledge of the list color function (list coloring analogue of the chromatic polynomial) can be applied to list coloring of Cartesian products. We introduce the notion of strongly chromatic choosable graphs, that includes odd cycles, cliques, many more infinite families of graphs, and the join of a clique with any other such graph, as a notion of color-criticality in the context of chromatic-choosability. This leads to improved bounds on choosability of Cartesian product of certain large classes of graphs and to classes of chromatic-choosable Cartesian products of graphs. This is joint work with Jeffrey Mudrock.

**Analysis and Applied Mathematics Seminar**

Boundary Layers in Kinetic-fluid Coupling

Qin Li (University of Wisconsin–Madison)

4:00 PM in 636 SEO

Many kinetic equations have the corresponding fluid limit. In the zero limit of the Knudsen number, one derives the Euler equation out of the Boltzmann equation and the heat equation out of the radiative transfer equation. While there are good numerical solvers for both kinetic and fluid equations, it is not quite well-understood when the two regimes co-exist. In this talk, we model the layer between the fluid and the kinetic using a half-space equation, study the well-posedness, design a numerical solver, and utilize it to couple the two sets of equations that govern separate domains.

Tuesday October 16, 2018

**Logic Seminar**

Random query learning and model theory

James Freitag (UIC)

3:30 PM in 427 SEO

In this talk, we will describe the work of Angluin and Dohrn (2017) where a variation on equivalence query learning is analyzed. Specifically, the teacher chooses counterexamples from a fixed (but arbitrary) probability distribution. Angluin and Dohrn show that the number of expected queries for exactly identifying a target concept grows linearly in the $log (n)$ where $n$ is the size of the domain of the concepts. They also show that no better upper bound can be achieved in terms of the VC-dimension of the concept class. Even when the VC-dimension is one, the upper bound can be achieved.
We will show that the number of expected queries grows linearly in the Littlestone dimension. In many set systems, this produces better bounds than those of Angluin and Dohrn, since the Littlestone dimension is bounded from above by $log(n)$, but in general concept classes, $n$ may be arbitrarily large with fixed Littlestone dimension. Many examples are provided by formulas in stable theories (a formula is stable if and only if it has finite Littlestone dimension).
This is joint work with Hunter Chase.

Wednesday October 17, 2018

**Mathematics Education Colloquium**

Inquiry Based Learning in college Calculus

Aida Alibek (UIC)

12:00 PM in 612 SEO

We will discuss the Padraig & McLoughlin paper presented at the 2009 JMM that looks into the implementation of Inquiry Based Learning in Calculus.
Prior reading of the paper is not necessary and all are welcome! Faculty and graduate students involved in Calculus teaching at UIC are encouraged to join!

**Graduate Geometry, Topology and Dynamics Seminar**

Poset persistent homology

Jānis Lazovskis (UIC)

4:00 PM in 612 SEO

This talk builds on part one from the previous week. I will describe zigzag persistence and generalized persistence modules as functors from posets. Using the right filtration functor of Carlsson and de Silva I will introduce a method to compare two persistence modules connected by a path in the universal persistent homology space.

**Statistics Seminar**

Modeling Non-stationary Multivariate Time Series of Counts via Common Factors

Fangfang Wang (University of Wisconsin at Madison)

4:00 PM in 636 SEO

In this talk, a new parameter-driven model for multivariate time series of counts is discussed. The time series is not necessarily stationary. The mean process is modelled as the product of modulating factors and unobserved stationary processes. The former characterizes the long-run movement in the data, while the latter is responsible for rapid fluctuations and other unknown or unavailable covariates. The unobserved stationary processes evolve independently of the past observed counts, and might interact with each other. We express the multivariate unobserved stationary processes as a linear combination of possibly low-dimensional factors that govern the contemporaneous and serial correlation within and across the observed counts. Regression coefficients in the modulating factors are estimated via pseudo maximum likelihood estimation, and identification of common factor(s) is carried out through eigenanalysis on a positive definite matrix that pertains to the autocovariance of the observed counts at nonzero lags. Theoretical validity of the two-step estimation procedure is presented. We also provide numerical results that corroborate the theoretical findings. Finally, we illustrate the use of the proposed model through an application to the numbers of National Science Foundation funding awarded to seven research universities from January 2001 to December 2012.

Thursday October 18, 2018

**Louise Hay Logic Seminar**

Anti-Choice Axioms and the Dual of $\ell^\infty$

Noah Schoem

4:00 PM in 427 SEO

In most functional analysis courses, $\ell^1$ is often an example of a
Banach space that is not reflexive; that is, $(\ell^1)^*$, the dual space of $\ell^1$, is $\ell^\infty$,
but $(\ell^\infty)^*\supsetneq \ell^1$.
However, this argument requires the Axiom of Choice.
In fact, we will show that under a certain anti-choice axiom, that $(\ell^\infty)^*=\ell_1$.

Friday October 19, 2018

Monday October 22, 2018

**Geometry, Topology and Dynamics Seminar**

Taut sutured handlebodies as twisted homology products

Margaret Nichols (University of Chicago)

3:00 PM in 636 SEO

A basic problem in the study of 3-manifolds is to determine when geometric objects are of 'minimal complexity'. We are interested in this question in the setting of sutured manifolds, where minimal complexity is called ‘tautness’.
One method for certifying that a sutured manifold is taut is to show that it is homologically simple - a so-called 'rational homology product'. Most sutured manifolds do not have this form, but do always take the more general form of a 'twisted homology product', which incorporates a representation of the fundamental group. The question then becomes, how complicated of a representation is needed to realize a given sutured manifold as such?
We explore some classes of relatively simple sutured manifolds, and see one class is always a rational homology product, but that the next natural class contains examples which require twisting. We also find examples that require twisting by a representation which cannot be 'too simple’.

**Analysis and Applied Mathematics Seminar**

Sign-changing solutions of the nonlinear heat equation with positive initial value

Fred Weissler (Universite de Paris Nord)

4:00 PM in 636 SEO

We consider the nonlinear heat equation $u_t - \Delta u = |u|^\alpha u$ on ${\mathbb R}^N$, where
$\alpha >0$. It is well known that the Cauchy problem is locally well-posed in a variety of spaces. For
instance, for every $\alpha >0$, it is well-posed in the space $C_0 ( {\mathbb R}^N )$ of continuous
functions that converge to $0$ at infinity. It is also well-posed in $L^p({\mathbb R}^N )$ for $p\ge 1$,
$p>\frac {N\alpha } {2}$, but not well-posed in $L^p$ for $1\le p< \frac {N\alpha } {2}$ if
$\alpha >\frac {2} {N}$. In particular, for such $p$ there exist positive initial values $u_0 \in L^p$ for
which there is no local in time positive solution. Also, if one considers the initial value
$u_0 (x)= c |x|^{-\frac {2} {\alpha }}$ for all $x\in {\mathbb R}^N \setminus \{0\}$, with $c>0$,
it is known that if $c$ is small, there exists a global in time (positive) solution with $u_0$ as initial
value, and in fact this solution is self-similar.
On the other hand, if $c$ is large, there is no local in time positive solution, self-similar or otherwise.
We prove that in the range $0 < \alpha <\frac {4} {N-2}$, for every $c>0$, there exist infinitely many self-similar solutions to the Cauchy problem with initial value $u_0 (x)= c |x|^{-\frac {2} {\alpha }}$. Of course, these solutions are all sign-changing if $c$ is sufficiently large. Also, in the range $\frac {2} {N}< \alpha <\frac {4} {N-2}$, we
prove the existence of local in time sign-changing solutions for a class of nonnegative initial values $u_0 \in L^p$, for $1\le p< \frac {N\alpha } {2}$, for which no local in time positive solution exists.
This is joint work with T. Cazenave, F. Dickstein and I. Naumkin.

Wednesday October 24, 2018

**Algebraic K-Theory Seminar**

The Frobenius in higher algebra

Allen Yuan (MIT)

3:00 PM in 1227 SEO

In classical algebra, the Frobenius provides a natural endomorphism of every ring in which p=0; this determines an action of the circle on the category of F_p algebras. In higher algebra, one can do away with the characteristic p assumption and define a Frobenius map for every E-infinity ring spectrum. In this talk, I will explain the analog of the circle action. The construction of the action features equivariant homotopy theory and a calculation of a non-group-complete variant of the K theory of F_p.

**Statistics Seminar**

Estimation and Inference for Differential Networks

Mladen Kolar (University of Chicago)

4:00 PM in 636 SEO

We present a recent line of work on estimating differential networks and conducting statistical inference about parameters in a high-dimensional setting. First, we consider a Gaussian setting and show how to directly learn the difference between the graph structures. A debiasing procedure will be presented for construction of an asymptotically normal estimator of the difference. Next, building on the first part, we show how to learn the difference between two graphical models with latent variables. Linear convergence rate is established for an alternating gradient descent procedure with correct initialization. Simulation studies illustrate performance of the procedure. We also illustrate the procedure on an application in neuroscience. Finally, we will discuss how to do statistical inference on the differential networks when data are not Gaussian.

**Algebraic Geometry Seminar**

The normalized volume of a singularity is lower semi-continuous

Yuchen Liu (Yale)

4:00 PM in 427 SEO

Motivated by work in differential geometry, Chi Li introduced the normalized volume of a klt singularity as the minimum normalized volume of all valuations centered at the singularity. This invariant carries some interesting geometric/topological information of the singularity. In this talk, we show that in a Q-Gorenstein flat family of klt singularities, normalized volumes are lower semicontinuous with respect to the Zariski topology. As an application, we show that K-semistability is a very generic or empty property in a Q-Fano family. If time permits, I will discuss related results in positive characteristic. This talk is partly based on joint work with Harold Blum.

Friday October 26, 2018

Monday October 29, 2018

**Analysis and Applied Mathematics Seminar**

On the variational properties of KdV multisolitons

John Albert (University of Oklahoma)

4:00 PM in 636 SEO

We characterize 2-soliton solutions of the Korteweg-de Vries equation as global minimizers for a constrained
variational problem. In particular this gives a nice proof of their stability. The proof uses the so-called profile
decomposition or bubble decomposition of a bounded sequence in Sobolev space.

**Statistics Seminar**

Applying Mathematics and Statistics to Characterize the Effectiveness of a Pharmaceutical Product

Yi-Lin Chiu (Abbvie)

4:00 PM in 636 SEO

This presentation addresses the basic science for clinical pharmacology: effective and safe drug administration. We use basic mathematics and statistics to introduce the applications to pharmacology, including characterizing the drug concentration, dose selection, and dosing strategy. The utility of clinical pharmacology will be explained: We will show how drugs work, rather than asking the audience to memorize information about individual drugs. Therefore, we can understand why drugs are given, as well as when they should be given, and come up with a better way to improve the effectiveness of drug administrations.

Friday November 2, 2018

Monday November 5, 2018

**Mathematical Computer Science Seminar**

Principles of Active Learning

Steve Hanneke (TTI-C)

3:00 PM in 427 SEO

In many machine learning applications, the effort required to manually
label the massive data sets necessary to train machine learning
systems to a high accuracy presents a major hurdle. One promising
approach to reducing the required training sample size is active
learning, a technique in which the learning algorithm participates in
interactively selecting examples to be labeled for training, in order
to focus the human expert's efforts on labeling only informative and
non-redundant examples. Active learning holds great potential for
dramatically reducing the number of labeled training examples needed
for learning. However, despite decades of research on the subject, the
most popular active learning algorithms in the applications literature
are known to be unreliable and sensitive to violations of modeling
assumptions, which has held back the widespread applicability of
active learning in practice. At the root of this problem, it seems we
have lacked a complete understanding of the basic principles that
should underlie the design of good active learning algorithms. Such a
situation calls for a careful theoretical approach to the problem.
In this talk, I will articulate essential principles for the design of
effective active learning algorithms, distilled from over a decade of
research on the theory of active learning. Moreover, I will describe a
general active learning strategy based on these principles, which is
provably near-optimal, in the sense that the number of labeled
training examples sufficient to achieve a given accuracy guarantee
cannot be significantly reduced by any other active learning
algorithm. In the process, I will discuss the fundamental trade-offs
and general complexity measures intrinsic to the active learning
setting, and present formulas expressing the minimum number of labeled
examples sufficient and necessary for an optimal active learning
algorithm to achieve a given accuracy guarantee.

Wednesday November 7, 2018

**Statistics Seminar**

MULTILAYER TENSOR FACTORIZATION WITH APPLICATIONS TO RECOMMENDER SYSTEMS

Annie Qu (UIUC)

4:00 PM in 636 SEO

Recommender systems have been widely adopted by electronic commerce and entertainment industries for individualized prediction and recommendation, which benefit consumers and improve business intelligence. In this article, we propose an innovative method, namely the recommendation engine of multilayers (REM), for tensor recommender systems. The proposed method utilizes the structure of a tensor response to integrate information from multiple modes, and creates an additional layer of nested latent factors to accommodate between-subjects dependency. One major advantage is that the proposed method is able to address the “cold-start" issue in the absence of information from new customers, new products or new contexts. Specifically, it provides more effective recommendations through sub-group information. To achieve scalable computation, we develop a new algorithm for the proposed method, which incorporates a maximum block improvement strategy into the cyclic block-wise-coordinate-descent algorithm. In theory, we investigate both algorithmic properties for global and local convergence, along with the asymptotic consistency of estimated parameters. Finally, the proposed method is applied in simulations and IRI marketing data with 116 million observations of product sales. Numerical studies demonstrate that the proposed method outperforms existing competitors in the literature. This is joint work with Xuan Bi and Xiaotong Shen.

Friday November 9, 2018

Monday November 12, 2018

Friday November 16, 2018

Monday November 19, 2018

Monday November 26, 2018

Wednesday November 28, 2018

Friday November 30, 2018

Monday December 3, 2018

**Analysis and Applied Mathematics Seminar**

Interfacial dynamics of dissolving objects in fluid flow

Christopher Rycroft (Harvard University)

4:00 PM in 636 SEO

An advection–diffusion-limited dissolution model of an object being eroded by a two-dimensional potential flow will be presented. By taking advantage of conformal invariance of the model, a numerical method will be introduced that tracks the evolution of the object boundary in terms of a time-dependent Laurent series. Simulations of several dissolving objects will be shown, all of which show collapse to a single point in finite time. The simulations reveal a surprising connection between the position of the collapse point and the initial Laurent coefficients, which was subsequently derived analytically.

Wednesday January 23, 2019

Monday January 28, 2019

Monday February 11, 2019

Wednesday February 13, 2019

Wednesday February 20, 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

Wednesday April 10, 2019

Friday April 12, 2019

Wednesday April 17, 2019

Monday April 22, 2019

Wednesday April 24, 2019