# MSCS Seminar Calendar

Monday February 8, 2016

**Graduate Analysis Seminar**

The Schwarzian Derivative

Charles Alley (UIC)

2:00 PM in SEO 612

In this talk I will introduce the Schwarzian derivative and
give a survey of some of its properties and related results. The
Schwarzian derivative is a quadratic differential operator on the space of
locally injective holomorphic functions which is distinguished by the
property $S(f)=0$ if and only if $f$ is a linear fractional transformation.

**Set Theory Seminar**

Fine structure, part I

Sherwood Hachtman (UIC)

3:00 PM in SEO 427

Jensen invented the fine structure theory in order to make a detailed analysis of Godel's constructible universe, $L$. Today the fine structure theory is fundamental to an understanding of inner models for large cardinals. We aim to develop the basic theory for $L$ and use it to prove some of the earliest applications, including that $\square_\kappa$ holds in $L$ for all cardinals $\kappa$, and Jensen's Covering Theorem: If $0^{\#}$ does not exist, then every uncountable set of ordinals is contained in a constructible set of the same size.

**Analysis and Applied Mathematics Seminar**

Numerical Optimal Transportation Using the Monge-Ampere Equation

Brittany Froese (New Jersey Institute of Technology)

4:00 PM in SEO 636

The problem of optimal transportation, which involves finding the most cost-efficient mapping between two measures, arises in many different applications. However, the numerical solution of this problem remains extremely challenging. We describe a numerical method for the widely-studied case when the cost is quadratic. The solution is obtained by solving the Monge-Ampere equation, a fully nonlinear elliptic partial differential equation (PDE), coupled to a non-standard implicit boundary condition. Expressing this problem in terms of weak (viscosity) solutions enables us to construct a monotone finite difference approximation that computes the correct solution. A range of challenging computational examples demonstrate the effectiveness of this method, including the recent application of this method to problems in beam shaping and seismic inversion.

**Graduate Algebraic Geometry Seminar**

Geometric Complexity and the Permanent

Jeremy Kun (UIC)

4:00 PM in SEO 712

I will discuss the relationship between algebraic geometry and computational complexity, give a short outline of Mulmuley's Geometric Complexity Program, and illustrate the ideas specifically for the determinant versus permanent problem.

Tuesday February 9, 2016

**Logic Seminar**

Indestructible guessing models

Sean Cox (Virginia Commonwealth University)

4:00 PM in SEO 427

By results of Viale-Weiss, stationarity of the class of "guessing models" is responsible for many of the consequences of the Proper Forcing Axiom (PFA), including the Tree Property at $\omega_2$ and failure of square. I will discuss joint work with Krueger about the stronger notion of "indestructible guessing models". Stationarity of such models captures even more consequences of PFA (e.g. Suslin's Hypothesis, SCH, and a theorem of Todorcevic), but on the other hand doesn't decide the value of the continuum.

**Graduate Computational Algebraic Geometry Seminar**

Conditional Probabilistic Knowledge Bases using Gröbner Bases

Jon Yaggie (UIC)

4:00 PM in SEO 1227

Under the circumstances where conditional knowledge is associated
with rational probabilities, the maximum entropy principle can be used
to generate a set of polynomial equations.
These polynomial equations can then be used to check consistency and
infer probabilities for new information via Gröbner bases computations
(Kern-Isberner, Wilhelm, Beierle).
I will review these theoretic results and demonstrate
an implementation using Sage.

**Graduate Statistics Seminar**

A discussion on the performance of the Coordinate-Exchange Algorithm

Tian Tian (UIC)

4:00 PM in SEO 636

The use of discrete choice experiments (DCEs) for modeling real marketplace choices, in both fundamental and applied research, has gained much attention recently. To construct proper choice designs, one needs the help of efficient
search algorithms, among which the coordinate-exchange algorithm (CEA) has shown itself to
work very well under the widely used multinomial logit discrete choice model. However, due to
the discrete nature of choice designs, there are no computationally feasible ways to verify
the real performance of the resulting designs. In this talk, I'll discuss an approach of evaluating the
performance of the CEA.
Empirical study was conducted to show that the CEA is indeed highly efficient for deriving homogeneous optimal designs.

Wednesday February 10, 2016

**Dylon Chow Lecture Series in Derived Algebraic Geometry**

On $\infty$-operads

Tasos Moulinos (UIC)

1:00 PM in SEO 612

We define the notion of an operad in the $\infty$-categorical setting and relate it to the classical notion of a colored operad. We discuss what it means for an $\infty$-category to be symmetric monoidal and give several examples along the way.

**Graduate Geometry, Topology and Dynamics Seminar**

Topologies on Transformation Groups of a Compact Manifold

Jake Herndon

3:00 PM in SEO 612

We'll discuss Kathryn Mann's new proof that the group of piecewise linear homeomorphisms of a compact piecewise linear manifold does not have a Polish group topology.

**Algebraic Geometry Seminar**

Interpolation and vector bundles on curves

Atanas Atanasov (Citadel)

4:00 PM in SEO 427

We aim to address the following: When is there a (smooth) curve of degree $d$ and genus $g$ passing through $n$ general points in $\mathbb{P}^r$. Generalizations ask for the dimension of such curves, or replace the point incidence conditions with higher dimensional linear spaces. We will start by relating these statements to a property of the normal bundle of curves in projective space. Next, we will show how to address these questions for $r = 3$ and $d >= g + 3$. The demonstrated techniques generalize significantly and lead to an answer to our question for $d >= g + r$. This is joint work with E. Larson and D. Yang.

Thursday February 11, 2016

**Graduate Homotopy Theory Seminar**

K-theory with Reality and its Anderson dual

Lennart Meier (Bonn)

2:00 PM in SEO 612

We will first prove a universal coefficient sequence for complex K-theory by a method called Anderson duality. There is a C2-equivariant cohomology theory called K-theory with Reality that combines real and complex K-theory. We will discuss how we can copy our method from complex K-theory to obtain the Anderson dual of K-theory with Reality and deduce a universal coefficient sequence for real K-theory.

Friday February 12, 2016

**Departmental Colloquium**

All Roads Lead to Rome, and Many Models Lead to Taylor's Power Law of Fluctuation Scaling

Professor Joel E. Cohen (Rockefeller University & Columbia University)

3:00 PM in SEO 636

"Taylor's law" asserts that, in sets of samples of a nonnegative quantity
(e.g., insect population abundance), the sample variance is approximately
proportional to some power of the sample mean. Taylor's law has been verified
for hundreds of species and in many fields beyond ecology, including physics
and finance. As scientific motivation, I will show some empirical examples of
Taylor's law from my own work. The main focus of my talk is the different
mathematical interpretations of Taylor's law and the great diversity of
theoretical models (from stochastic processes, differential equations,
and number theory, among other areas of mathematics) that lead to Taylor's law.

Tea at 300 SEO at 4:15PM

Monday February 15, 2016

**Algebraic Geometry Seminar**

Interpolation of Projective Varieties

Aaron Landesman (Harvard University)

2:00 PM in SEO 1227

In this talk, we discuss interpolation of projective varieties through points.
It is well known that one can find
a rational normal curve in $\mathbb P^n$
through $n+3$ general points. More recently, it
was shown that one can always find nonspecial curves
through the expected number of general points.
We consider the generalization of this question
to varieties of all dimensions and explain why
rational normal scrolls satisfy interpolation.
We'll also discuss joint work
with Anand Patel on interpolation for del Pezzo surfaces
and present several interesting open interpolation problems.
We'll place particular emphasis on explaining the standard techniques used
to solve interpolation:
deformation theory, specialization, degeneration, and association.

**Computer Science Seminar**

Learning Weakly-Labeled and Cross-modal Semantics for Structured NLP

Mohit Bansal (Toyota Technological Institute at Chicago)

3:00 PM in SEO 612

For artificial intelligent agents to function autonomously in our homes
and workplaces, they must be able to effectively understand natural
language for instructions and conversational dialog. For this, it is
necessary to resolve the various deep semantic and pragmatic ambiguities
that exist in everyday natural language, a challenging goal that involves
two fundamental requirements. First, we need diverse, external world
knowledge which is simply not present in the standard training datasets
used for supervised NLP tasks. Second, we need to develop appropriate
machine learning models that can extract the precise disambiguation cues
lying latent in such diverse, large-scale knowledge datasets. My research
addresses both these requirements by learning novel weakly-labeled and
cross-modal semantic representations with accurate, well-formulated
disambiguation methods. We model world knowledge via unlabeled Web-scale
features, weakly-supervised language embeddings, and grounding cues from
vision and speech, and harness these in both structured and neural
network based learning methods to achieve the state-of-the-art on various
core NLP tasks and multimodal applications.

**Analysis and Applied Mathematics Seminar**

Evolutionary system, global attractor, trajectory attractor, and applications

Songsong Lu (Sun Yat-sen University)

4:00 PM in SEO 636

I will review some resent results on the long-time behavior of the nonautonomous 3D Navier-Stokes equations and general nonautonomous reaction-diffusion systems. The method is based on a new framework of evolutionary systems that deals directly with the notion of a uniform global attractor due to Haraux, and with which a trajectory attractor can be defined for the original system under consideration. The notion of a trajectory attractor was previously established for a system without uniqueness by considering a family of auxiliary systems including the original one. I will also expound on the existence of a strongly compact strong trajectory attractor when the system is asymptotically compact, and how we view the global and trajectory attractors in a unified way. Part of the results of the talk is a joint work with Cheskidov.

Tuesday February 16, 2016

**Dynamical Systems Working Seminar**

The dynamical Mordell-Lang conjecture

John Lesieutre (UIC)

3:00 PM in SEO 712

Suppose that phi is an endomorphism of a smooth complex
algebraic variety, p is a point on X, and V is a subvariety of X. The
dynamical Mordell-Lang conjecture predicts that the set of n for which
phi^n(p) lands in V is the union of finitely many arithmetic
progressions and a finite set. (This is already interesting when phi is
just a matrix acting on CP^n!) I'll give a general introduction to the
conjecture: where does it come from, what are some interesting cases,
and what sorts of techniques come into play?

**Graduate Statistics Seminar**

Gibbs Models for Identification of Image Boundaries

Nick Syring (UIC)

4:00 PM in SEO 636

I will introduce the problem of identifying boundaries in images observed with random noise. I will present a Gibbs model solution, which combines elements of machine learning and Bayesian statistics. I have produced a proof that the proposed model converges at the minimax rate, and I show through simulations the competitive performance of the Gibbs model. If there is sufficient interest, I may share the details of the proof at a later date.

**Logic Seminar**

Menger compacta and projective Fraisse limits

Aristotelis Panagiotopoulos (UIUC)

4:00 PM in SEO 427

In every dimension $n$, there exists a canonical compact, metrizable space called the $n$-dimensional Menger space. For $n=0$, it is the Cantor space and for $n=\infty$, it is the Hilbert cube. On the first part of the talk I will illustrate how basic notions of classical descriptive set theory naturally generalize into higher homotopical dimensions. In the second part of the talk I show how projective Fraisse machinery can be employed in the study of the Menger compacta.
This is a joint work with Slawomir Solecki.

Wednesday February 17, 2016

Friday February 19, 2016

**Departmental Colloquium**

Obliquely reflected Brownian motion

Zhen-Qing Chen (University of Washington, Seattle, WA)

3:00 PM in SEO 636

Boundary theory for one-dimensional diffusions is now well understood. Boundary theory for multi-dimensional diffusions is much richer and remains to be better understood. In this talk, we will be concerned with the construction and characterization of obliquely reflected Brownian motions in all bounded simply connected planar domains, including non-smooth domains,
with general reflection vector field on the boundary.
We show that the family of all obliquely reflected Brownian motions in a given domain can be characterized in two different ways, either by the field of angles of oblique reflection on the boundary or by the stationary distribution and the rate of rotation of the process about a reference point in the domain. We further show that Brownian motion with darning and excursion reflected Brownian motion can be obtained as a limit of obliquely reflected Brownian motions.
Based on joint work with K. Burdzy, D. Marshall and K. Ramanan.

Monday February 22, 2016

Tuesday February 23, 2016

Wednesday February 24, 2016

Thursday February 25, 2016

**WISEST Leadership Seminar**

Taking Stock

Ingrid Daubechies (Duke University)

3:00 PM in Cardinal Room 329 in Student Center East.

In her presentation, Daubechies will mix her personal perspective
(``taking stock'' in her career of over 35 years, and counting), her international experience (as past President of the International Mathematical Union) and her hopes for the near future, in the context of women in STEM.

Professor Daubechies is the 2015-2016 UIC WISEST Distinguished Visiting Scholar.
A reception will follow her leadership lecture. The lecture and reception are taking place in Cardinal Room 329
on the 3rd floor of Student Center East, accessible by two escalators.

Friday February 26, 2016

**Departmental Colloquium**

Mathematicians Helping Art Historians and Art Conservators

Ingrid Daubechies (Duke University)

3:00 PM in Cardinal Room 329 of Student Center East

Mathematics can help Art Historians and Art Conservators in studying and understanding art works,
their manufacture process and their state of conservation. The presentation will review several instances of
such collaborations in the last decade or so, and then focus on one particular example: virtual cradle removal.
Between the 12th to the 17th century, European artists typically painted on wooden boards. To remediate or
prevent structural or insect damage, conservators in the 19th and first half of the 20th century first thinned
the panels to a few mm, and then strengthened the much thinner wood structures by (permanently) attaching
to their backs hardwood lattices called cradles. These cradles are highly visible in X-ray images of the paintings.
X-rays of paintings are a useful tool for art conservators and art historians to study the condition of a painting, as well as the techniques used by the artist and subsequent restorers. The cradling artifacts obstruct a clear ``reading'' of the X-rays by these experts.
These artifacts can be removed, using a variety of mathematical tools, including Bayesian algorithms.

Professor Daubechies is the 2015-2016 UIC WISEST Distinguished Visiting Scholar.
A reception will follow her scientific lecture. The lecture and reception are taking place in Cardinal Room 329
on the 3rd floor of Student Center East, accessible by two escalators.

Monday February 29, 2016

**Geometry, Topology and Dynamics Seminar**

Almost homogeneous solenoids

Olga Lukina (UIC)

3:00 PM in SEO 636

Matchbox manifolds are compact foliated spaces whose transversals are
totally disconnected. In the case when the pseudogroup holonomy dynamical
system on the transversals is equicontinuous, the matchbox manifold is
homeomorphic to a solenoid. This means that the pseudogroup action on
the transversal can be obtained as a restriction of a group action.
In the talk, we are interested in almost homogeneous solenoids, that is,
those which admit a finite-to-one cover by a solenoid which is also
a topological group. We give conditions on the action of the Ellis semigroup of the pseudogroup transverse dynamical system,
and on the growth of leaves, under which a solenoid is almost homogeneous. Joint work with Jessica Dyer and Steve Hurder.

Wednesday March 2, 2016

**Statistics Seminar**

Modeling between- and within-subject variances using mixed-effects location scale models for intensive longitudinal data

Donald Hedeker (University of Chicago)

4:00 PM in SEO 636

Intensive longitudinal data are increasingly encountered in many research areas. For example, ecological momentary assessment and/or experience sampling methods are often used to study subjective experiences within changing environmental contexts. In these studies, up to 30 or 40 observations are usually obtained for each subject over a period of a week or so. Because there are so many measurements per subject, one can characterize a subject's mean and variance and can specify models for both. In this presentation, we focus on an adolescent smoking study using ecological momentary assessment where interest is on characterizing changes in mood variation. We describe how covariates can influence the mood variances and also extend the statistical model by adding a subject-level random effect to the within-subject variance specification. This permits subjects to have influence on the mean, or location, and variability, or (square of the) scale, of their mood responses. These mixed-effects location scale models have useful applications in many research areas where interest centers on the joint modeling of the mean and variance structure.

Monday March 7, 2016

**Algebraic Geometry Seminar**

Regular cell complexes in total positivity

Patricia Hersh (North Carolina State)

2:00 PM in SEO 1227

Sergey Fomin and Michael Shapiro conjectured that certain topological spaces of totally nonnegative real matrices stratified according to which minors are positive and which are 0 are regular CW complexes homeomorphic to closed balls having the (lower) intervals of Bruhat order as their posets of closure relations. We will survey this area, including connections to Lusztig's theory of canonical bases, to electrical networks, and to cluster algebras, and we will discuss how combinatorics and topology were combined in somewhat non-standard ways to obtain a proof of this conjecture. This talk will not assume familiarity with these areas.

**Analysis and Applied Mathematics Seminar**

Some numerical aspects of Quasiconvexity and Rank-one convexity

Romeo Awi (Institute for Mathematics and its Applications)

4:00 PM in SEO 636

This talk is concerned with some numerical aspects of Morrey's Conjecture in dimension
2x2. The problem is to know whether there exists a rank-one convex
function defined on 2x2 matrices that is not quasiconvex. The conjecture
is first cast as a minimization problem. The later problem is
approximated by minimization problems over families of affine piecewise
functions. Two methods that could lead to finding counter-examples are
suggested.

Tuesday March 8, 2016

Friday March 11, 2016

Monday March 14, 2016

Tuesday March 15, 2016

Friday March 18, 2016

Monday March 28, 2016

**Analysis and Applied Mathematics Seminar**

On special regularity properties of solutions to a class of dispersive equations

Gustavo Ponce (University of California, Santa Barbara)

4:00 PM in SEO 636

In a joint work with P. Isaza and F. Linares we show that solutions of the IVP
for the $k$-generalized KdV equation
\begin{equation}
\begin{cases}
\begin{aligned}
\label{aaa}
&\partial_t u + \partial_x^3 u +u^k\partial_x u=0,\;\;\;\;\;t,\;x\in\mathbb R,\;\;k\in\mathbb Z^+,\\
&u(x,0)=u_0(x)
\end{aligned}
\end{cases}
\end{equation}
preserve some smoothness of the initial data $u_0$ and that this regularity moves with infinite speed to its left as time evolves.

Tuesday March 29, 2016

Monday April 4, 2016

Wednesday April 6, 2016

Thursday April 7, 2016

Monday April 11, 2016

Friday April 15, 2016

Monday April 18, 2016

Wednesday April 20, 2016

**Statistics Seminar**

A Flexible Bayesian nonparametric credibility model

Liang Hong (Robert Morris University)

4:00 PM in SEO 636

We propose a flexible Bayesian nonparametric model for modeling insurance losses. The model extends the current credibility theory literature in that (i) it does not assume any particular parametric form of the loss distribution, providing greater flexibility and (ii) it yields a full posterior distribution for the loss density that can be computed numerically, allowing practitioners to estimate any desired features of the loss distribution, such as Value-at-Risk and
conditional tail expectations. We will also use actuarial examples to demonstrate the benefit of our model compared to others in the credibility theory literature.

Wednesday April 27, 2016

**Statistics Seminar**

Panel Discussion

Stat faculty and students (UIC)

4:00 PM in SEO 636

This panel discussion will give students an opportunity to have questions about various things (e.g., advantages and disadvantages of an academic career, general strategies for successful research, career opportunities outside of academia and how to prepare for them, etc) answered by faculty and senior graduate students.

Friday April 29, 2016

Monday August 29, 2016