MSCS Seminar Calendar

Monday April 24, 2017
pdf * 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.

pdf * 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.

pdf * 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
pdf * 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.

pdf * 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
pdf * 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.

pdf * 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.

pdf * 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.

pdf * 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.

pdf * 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.

pdf * 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.

pdf * Algebraic Geometry Seminar
Tommaso de Fernex (University of Utah)
4:00 PM in SEO 427
Thursday April 27, 2017
pdf * Quantum Topology / Hopf Algebra Seminar
Knotoids and Their invariants ( joint work with Lou Kauffman)
Neslihan Gugumcu (National Technical University, Athens, Greece)
2:00 PM in SEO 612
The theory of knotoids, introduced by V.Tureav in 2012, extends the theory of classical knots. A knotoid is defined in analogy to an open-ended knot diagram, that is, as an image of the unit interval in an oriented surface under an immersion with finitely many transversal double points endowed with under/over-data and two distinct endpoints. But for knotoids we allow the endpoints to be in different regions of the diagram.
In this talk, we first go through the basic notions of knotoids in S^2 and R^2 and review basic notions from virtual knot theory. We introduce the virtual closure map and show that it is a non-injective and non-surjective map. We then introduce some invariants of knotoids including the height of a knotoid, the affine index polynomial and the arrow polynomial. We show both the affine index polynomial and the arrow polynomial are used to determine the type of a knotoid. We also present a proof for a conjecture by Turaev, concerning the height of minimal diagrams of knot-type knotoids.

pdf * 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):
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.

pdf * 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.

pdf * Louise Hay Logic Seminar
Large Numbers: A Survey
Noah Schoem
4:00 PM in SEO 427
Although mostly an idle curiosity, the quest to name large natural numbers gives rise to, and requires substantial use of, tools from mathematical logic. We begin with elementary attempts and conclude with state-of-the-art techniques that go beyond $ZFC$.
Friday April 28, 2017
pdf * Departmental Colloquium
Height Zeta Functions
Yuri Tschinkel (NYU and Simons Foundation )
3:00 PM in TBA
Atkin Memorial Lecture
Wednesday May 3, 2017
pdf * Statistics Seminar
Recent advances in crossover designs and related studies
Prof. Wei Zheng (Indiana University – Purdue University Indianapolis)
4:00 PM in SEO 636
Crossover design is a design of experiments, where a subject receives a sequence of various treatment over a period of time points. While it provides the within subject comparison between treatment effects, the potential carryover effect in the model makes the study of optimal crossover designs quite complicated. Such study was initiated by Hedayat and Afsarinejad (1978), and many researchers have contributed to the general theory for optimal designs. Among them, Kushner (1997) developed very elegant results for the optimality conditions in the approximate design theory. My talk will mainly focus on this approach and talk about some recent progress as well as future challenges. I will also share some of my own thoughts of how to tackle these problems.
Monday November 6, 2017
pdf * Geometry, Topology and Dynamics Seminar
Andrea Tirelli (Imperial College London )
3:00 PM in SEO 636
Monday November 13, 2017
pdf * Geometry, Topology and Dynamics Seminar
Ngo Bao Chau (University of Chicago)
3:00 PM in SEO 636
The talk is part of the 2-day meeting "Current trends on spectral data for Higgs bundles III"
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