# MSCS Seminar Calendar

Monday April 24, 2017

**Geometry, Topology and Dynamics Seminar**

On word hyperbolic surface bundles

Autumn Kent (University of Wisconsin)

3:00 PM in SEO 636

There is a characterization of hyperbolicity of the
fundamental group of a surface bundle due to Farb-Mosher-Hamenstaedt,
namely that the bundle has hyperbolic fundamental group if and only if the fundamental group of the base is ``convex cocompact,'' a notion analogous to
the synonymous notion in Kleinian groups. I will discuss joint work
with Bestvina, Bromberg, and Leininger that gives a new
characterization of convex cocompactness, namely that the group is
purely pseudo-Anosov and undistorted in the mapping class group.

**Analysis and Applied Mathematics Seminar**

An algebraic reduction of the "scaling gap" in the Navier-Stokes regularity problem

Zoran Grujic (University of Virginia)

4:00 PM in SEO 636

It is shown--within a mathematical framework based on the suitably
defined scale of sparseness of the super-level sets of the positive
and negative parts of the vorticity components, and in the context of
a blow-up-type argument--that the ever-resisting "scaling gap" in the
3D Navier-Stokes regularity problem can be reduced by an algebraic
factor; all preexisting improvements have been logarithmic in nature,
regardless of the functional set up utilized. The mathematics
presented was inspired by morphology of the regions of intense
vorticity/velocity gradients observed in computational simulations of
turbulent flows. A joint work with Z. Bradshaw and A. Farhat.

**Algebraic Geometry Seminar**

Extension theorems for sections and cohomology classes under weak semipositivity conditions

Jean-Pierre DEMAILLY (Institut Fourier, Grenoble, FRANCE)

4:00 PM in SEO 427

We describe a generalization of an L2 extension theorem due to Ohsawa-Takegoshi: the
holomorphic sections or cohomology classes defined on an algebraic
subscheme (or a non necessarily reduced analytic subvariety) can be extended
under a weak semipositivity assumption.
This even works with singular hermitian metrics, and the ambient subvariety need
only be Kaehler and holomorphically convex, the total space of a projective morphism
over an affine base being a typical situation.

Tuesday April 25, 2017

**Quantum Topology / Hopf Algebra Seminar**

Knots and Infinitesimal Deformations

Ljubica S. Velimirovic (Faculty of Science and Mathematics, University of Nis, Serbia)

2:00 PM in SEO 612

In order to consider the shape of physical knots we study infinitesimal bending of knotted curves. Variations of the Willmore energy, the total curvature, the total torsion, as well as the total normalcy are obtained. Some examples are visualized.Higher order bending of knots is specified.
We discuss the results we have obtained in collaboration with Louis Kauffman, Marija Najdanovic and Svetozar Rancic.

**Logic Seminar**

Exponential Pregeometries and the Logical Complexity of Schanuel's Conjecture

Dave Marker (UIC)

4:00 PM in SEO 427

In it's natural formulation Schanuel's Conjecture is a $\Pi^1_1$-sentence. We show there is an equivalent $\Pi^0_3$-sentence.
The key to the proof is work on J. Kirby on natural pregeometries in exponential fields. Most of the talk will be devoted to
explaining Kirby's work.

Wednesday April 26, 2017

**Thesis Defense**

Intersection Theory on the Hilbert Scheme of Points in the Projective Plane

Alexander Stathis (UIC)

9:00 AM in SEO 612

I will discuss my results concerning the intersection product in the
Chow ring of the Hilbert scheme of points in the projective plane.
Specifically, I provide an explicit algorithm to compute the intersection
of elements of complementary codimension in a basis for the Chow groups
due to Mallavibarrena and Sols and an explicit algorithm to compute the
action of a natural divisor on the classes in this basis.
This is my thesis defense.

**Model Theory Seminar**

Definable Regularity for NIP Relations, Part II

Roland Walker (UIC)

10:00 AM in SEO 427

The Szemerédi Regularity Lemma (1976) has proven to be a very important tool in extremal graph theory with many applications to number theory and computer science as well. It basically says that the vertices of any finite graph can be partitioned in such a way that the edges between any pair of sets from the partition are uniformly (or randomly) distributed up to a requested nonzero margin of error $\varepsilon$. Furthermore, the size of partition needed to obtain such regularity depends only on $\varepsilon$, not on the size or complexity of the graph. However, in 1997, Timothy Gowers showed that the size of partition needed in the general case grows faster than an exponential tower of height polynomial in $1/\varepsilon $. Recently, many subcategories of hypergraphs, such as those with bounded VC dimension and those defined by semialgebraic sets of bounded complexity, have been shown to require only polynomial growth in terms of $1/\varepsilon $. We will be discussing the results of a paper by Artem Chernikov and Sergei Starchenko in which they develop and prove a model-theoretic analog of the regularity lemma for NIP hypergraphs, both finite and infinite, using finitely approximated Keisler measures. They also show that regular partitions are definable and, when VC dimension is bounded, their size can be bounded by a polynomial in $1/\varepsilon $. In addition, if the hypergraph is stable, all defective pairs can be eliminated. Alternatively, if the hypergraph is defined in a distal structure, there is a definable partition for which all pairs are homogenous in terms of the edge relation.

**Algebraic Geometry Seminar**

Jet differentials and algebraic hyperbolicity properties

Jean-Pierre DEMAILLY (Institut Fourier, Grenoble, FRANCE)

11:00 AM in SEO 427

On a projective variety of general type, one can prove the existence of sections of
certain jet bundles of sufficiently high order and degree, and even evaluate the growth of
their cohomology groups. New algebraic concepts of "strong general type"
and "jet algebraic hyperbolicity" can be derived from there, that imply
hyperbolicity properties for transcendental entire curves.
Related techniques have been used recently by Damian Brotbek to
confirm a version of the Kobayashi conjecture on the generic hyperbolicity of hypersurfaces of large degree.

**Mathematical Computing Laboratory**

Spring Research Expo

MCL Members (University of Illinois at Chicago)

1:00 PM in SEO 709

The end-of-semester research expo is the MCL’s main public event, where student research teams present posters and demonstrations of their work from the preceding semester. Faculty and graduate students who will be sponsoring upcoming MCL projects will also be on hand to answer questions. Attending the expo is a great way for UIC students to find out about undergraduate mathematical research opportunities.

Pizza will be served.

**Departmental Colloquium**

Asymptotics for magnetostrophic turbulence in the Earth's fluid core

Susan Friedlander (University of Southern California)

3:00 PM in SEO 636

We consider the three dimensional magnetohydrodynamics (MHD) equations in
the presence of stochastic forcing as a model for magnetostrophic
turbulence. For scales relevant to the Earth's fluid core this MHD system
is very rich in small parameters. We discuss results concerning the
asymptotics of the stochastically forced PDEs in the limit of vanishing
parameters. In particular we establish that the system sustains ergodic
statistically steady states thus providing a rigorous foundation for
magnetostrophic turbulence.
This is joint work with Juraj Foldes, Nathan Glatt-Holtz and Geordie
Richards.

**Statistics Seminar**

P-SVM: Efficient Parameter Selection for Support Vector Machines with Gaussian Kernels

Prof. Hsin-Hsiung Huang (University of Central Florida)

4:00 PM in SEO 636

Support Vector Machines (SVM) classifier is a popular classification method.
However, most users may not well take tuning parameters selection because
this step is time consuming. In practice, the tuning parameters are chosen
by evaluating parameter candidates via cross validation. It is shown that
the performance of SVM is sensitive to the values of tuning parameters. In
some cases, SVM performs poorly due to the values of tuning parameters.
However, selection of parameter values for SVM often relies on inefficient approaches
such as extensive cross validation. To get around the problem, users
may resort to anecdotal methods or default values set by software developers.
However, these methods may compromise performance of classification accuracy.
In this research, we propose an efficient algorithm called P-SVM for
selecting the parameter pair, (gamma,C), of SVM with Gaussian kernels on metric
data. P-SVM searches only a handful of percentiles of the squared Euclidean
distances of data points to select the best pair of parameter values. Our motivation
case study of business intelligence categorization demonstrates that
P-SVM achieved a signi cant improvement in precision, recall, F-measure,
and AUC from the default parameter values settled in Weka, a widely used
data mining software. Applications of both simulation and publicly-available
datasets also demonstrate that P-SVM achieves substantial improvement in
computational time without loss of much classification accuracy.

Thursday April 27, 2017

**Teaching and Learning Community**

Active Learning in Algebra through Calculus Courses

Martina Bode, Tim Boester, Jenny Ross, Brooke Shipley (UIC)

2:00 PM in SEO 636

Active Learning is trending, what is the buzz about?
MSCS is participating in a national study on Student Engagement in Mathematics through an Institutional Network for Active Learning (SEMINAL): http://www.aplu.org/projects-and-initiatives/stem-education/seminal/
This presentation will look at how we are incorporating active learning into the lecture and discussion portions of calculus, pre-calculus, and algebra courses. You will hear about and from Peer Leaders and their role in in lectures and in the learning center. We will also discuss our Teaching Assistant training, and the role of TAs in active learning.

**Graduate Computational Algebraic Geometry Seminar**

Enumerating Zonotope Vertices for Correlation Clustering

Nate Veldt (Purdue University)

3:00 PM in SEO 1227

A zonotope is the linear projection of a high dimensional hypercube into a lower-dimensional space. Many combinatorial optimization problems can be solved by enumerating vertices of this special kind of convex polygon. In this talk I will give a general introduction to zonotopes, and then demonstrate how sampling vertices of the so-called signing-zonotope leads to a fast method for the task of correlation clustering on low-dimensional datasets.

Friday April 28, 2017

Wednesday May 3, 2017

Monday November 6, 2017