# MSCS Seminar Calendar

Monday September 26, 2016

**Graduate Analysis Seminar**

Oscillatory Integrals of the First Kind

Jack Arbunich (UIC)

12:00 PM in SEO 1227

Oscillatory integrals have been an integral part of Harmonic analysis from its
conception. The Fourier transform is a ripe example of such an
oscillatory integral. One main use of oscillatory integrals is to obtain
decay estimates for Fourier transforms of measures on surfaces.
In a sense, oscillatory integrals link geometric properties of manifolds and
the harmonic analysis related to them. We will prove a few basic yet
noteworthy results on the asymptotics of oscillatory integrals in 1D.

**Commutative Algebra Seminar**

Lech Conjecture: an overview

Wenliang Zhang (UIC)

2:00 PM in SEO 427

In 1960, Lech conjectured that, if R-->S is a flat local map between noetherian local rings, then the Hilbert-Samuel multiplicity of R is less than or equal to the one of S. This conjecture has been open in dimension 3 or higher since then. The purpose of this talk is to give an overview of this conjecture, especially the recent breakthrough made by Linquan Ma in dimension 3.

**Geometry, Topology and Dynamics Seminar**

Treating Limits as Colimits and Colimits as Limits ... with Applications!

Jordan Watts (University of Colorado Boulder)

3:00 PM in SEO 636

Actually, in this talk, we will restrict ourselves to treating subspaces as quotient spaces and quotient spaces as subspaces ... with applications. To elaborate, consider a manifold. Typically it is defined to be a certain gluing of open subsets of Euclidean space (a quotient space), although we know we can embed any manifold into some large Euclidean space (a subspace). Conversely, the level set of a regular value of a smooth real-valued function (a subspace) is a manifold (a quotient space).
This is all elementary, but when one starts treating singular spaces in this fashion, interesting math occurs! We will first focus on orbifolds, and show how this point-of-view leads to an essentially injective functor between orbifolds and differentiable (local) semi-algebraic varieties. As an application, we use this to prove that a symplectic reduced space of a Hamiltonian circle action is never diffeomorphic to an orbit space of a Lie group action, unless it is an orbifold. Moreover, it is only ever an orbifold if its dimension is at most 2, or if the reduction is performed at a regular value of the momentum map.

We will have lunch with the speaker 1-2 p.m. on Monday. Email schapos@uic.edu if you'd like to join.

Tuesday September 27, 2016

**Logic Seminar**

Ordinal definable subsets of singular cardinals

Dima Sinapova (UIC)

4:00 PM in SEO 427

A remarkable theorem of Shelah states that if $\kappa$ is a singular strong limit cardinal of uncountable cofinality, then there is a subset $x$ of $\kappa$, such that $HOD_x$ contains the powerset of $\kappa$. We show that in general this is not the case for countable cofinality. Using a version of diagonal supercompact extender Prikry forcing, we construct a generic extension in which there is a singular cardinal $\kappa$ with countable cofinality, such that $\kappa^+$ is supercompact in $HOD_x$ for all $x\subset\kappa$. This result was obtained during a SQuaRE meeting at AIM and is joint with Cummings, Friedman, Magidor, and Rinot.

Wednesday September 28, 2016

**Graduate Algebraic Geometry Seminar**

Applications of Kontsevich's space of stable maps

Dylan Moreland

3:00 PM in SEO 712

Two decades ago Kontsevich introduced the space of a stable maps in order to check enumerative predictions coming from string theory. We will sketch how to do this in the simplest possible example and, if time permits, mention some applications to birational geometry.
No food will be provided, but there will be plenty of waffling.

**Statistics Seminar**

Some Recent Developments on the Applications of Evolutionary Algorithm in the Statistical Optimization

Frederick Phoa (Academia Sinica, Taiwan R.O.C.)

4:00 PM in SEO 636

Nature-inspired metaheuristic methods, like the particle swarm optimization and many others, enjoys fast convergence towards optimal solution via a series of inter- particle communication. Such methods are common for the optimization problem in engineering, but few in statistics problem. It is especially difficult to implement in some fields of statistics as the search spaces are mostly discrete, while most natural heuristic methods require continuous search domains. This talk introduces a new method called the Swarm Intelligence Based (SIB) method for optimization in statistics problems, featuring the searches within discrete space. Such fields include experimental designs, community detection, change-point analysis, variable selection, etc. The SIB method is a nature-inspired metaheuristic method that includes several operations. This method is advantageous over the traditional particle swarm optimization and many other heuristic approaches in the sense that it is ready for the search of both continuous and discrete domains, and its global best particle is guaranteed to monotonically move towards the optimum. The SIB method is demonstrated in several examples. Several extensions from the standard framework are also discussed at the end of this talk.

**Algebraic Geometry Seminar**

Vector Bundles of Conformal Blocks-- Rank One and Finite Generation

Natalie Hobson (University of Georgia)

4:00 PM in SEO 427

Given a simple Lie algebra \g, a positive integer l and an n-tuple of dominant integral weights for \g at level l, one can define a vector bundle on the moduli space of curves known as a vector bundle of conformal blocks. These bundles are nef in the case that the genus is zero and so this family provides potentially an infinite number of elements in Nef(M_0,n\bar) to analyze.
It is natural to ask how this infinite family of conformal blocks divisors lives in Nef(M_0,n\bar). Is the subcone generated by conformal blocks divisors polyhedral? In this talk, we give several results to this question for specific cases of interest. To show our results, we use a correspondence of the ranks of these bundles with computations in the quantum cohomology of the Grassmannian.

Friday September 30, 2016

**Homotopy Theory Seminar**

On Brauer groups, purity and topology

Xing Gu (UIC)

12:30 PM in SEO 1227

In this talk I will introduce Brauer groups for schemes and topological spaces and the purity problem. Following a paper by B. Antieau and B. Williams, I will discuss purity for PGL_n torsors on complex varieties and their methods of generating counter examples in this case.

**Departmental Colloquium**

Hitting questions for stochastic processes and stochastic PDE

Carl Mueller (University of Rochester)

3:00 PM in SEO 636

Hitting questions play a central role in the theory of stochastic processes. For example, we could consider our wealth as a random process and think of “striking it rich” as an example of this random process hitting the set of rich values. Here is a purely mathematical example. It is well known that Brownian motion hits points in one dimension, but not in higher dimensions. For a general Markov process, we can determine whether the process hits a given set in terms of potential theory. There has also been a huge amount of work on the related question of when a process has multiple points.
For stochastic partial differential equations (SPDE), much less is known, but there has been a growing number of papers on the topic in recent years. Potential theory provides an answer in principle. But unfortunately, solu- tions to SPDE are infinite dimensional processes, and the potential theory is intractible. As usual, the critical case is the most difficult.
We will give a brief survey of known results, followed by a discussion of an ongoing project with R. Dalang, Y. Xiao, and S. Tindel which promises to answer questions about hitting points and the existence of multiple points in the critical case.

**Math for the Real World**

Transitioning from Academia to Industry & Math in Finance

Paul Reschke, PhD and Recruiter (SBB Research Group)

4:30 PM in SEO 636

All are invited to hear a talk given by UIC math PhD alum Paul Reschke. Paul completed his PhD in 2013 and his advisor was Laura DeMarco. After graduating, he became an Assistant Professor at the University of Michigan. He is now working as a Tactics Associate at an investment management company, SBB Research Group (http://www.sbbrg.com/). He will be speaking about his transition from academia to industry and how he uses math in his current position.

There will be a recruiter present. Please bring your resume if you are interested in internships, part-time, or full-time positions. SBB Research Group is located in Northbrook, IL. Position descriptions are here: http://www.sbbrg.com/careers/.

There will be a recruiter present. Please bring your resume if you are interested in internships, part-time, or full-time positions. SBB Research Group is located in Northbrook, IL. Position descriptions are here: http://www.sbbrg.com/careers/.

**Refreshments will be provided, so please sign up to attend!**
SIGN-UP HERE: https://goo.gl/forms/chNYs7QzNApCvsh62

Monday October 3, 2016

**Graduate Analysis Seminar**

Asymptotic Values of Functions with Polynomial Schwarzian Derivative

Charles Alley (UIC)

12:00 PM in SEO 1227

It is a classical result of Rolf Nevanlinna that an entire
function whose Schwarzian derivative is a polynomial of degree $d$ has
exactly $d+2$ asymptotic values. In this talk I will sketch a proof of this
result and remark on the role of Stokes' phenomenon in understanding the
set of asymptotic values.

**Graduate Student Colloquium**

The Story of Geometric Groups Part II

Edgar A. Bering IV (UIC)

1:00 PM in SEO 636

Continuing the theme of the first talk, I will introduce the classical Banach Tarski paradox, its algebraic origins, and the geometry of non-paradoxical groups.
This talk will conclude with a map of the universe of finitely generated groups, as sketched in these two talks. The map to-date contains much uncharted territory.

**Computer Science Seminar**

Approximating the rectilinear crossing number

Andrew Suk (UIC)

2:00 PM in SEO 612

A straight-line drawing of a graph $G$ is a mapping which assigns to each vertex a point in the plane and to each edge a straight-line segment connecting the corresponding two points. The rectilinear crossing number of a graph $G$, $\overline{cr}(G)$, is the minimum number of pairs of crossing edges in any straight-line drawing of $G$. Determining or estimating $\overline{cr}(G)$ appears to be a difficult problem, and deciding if $\overline{cr}(G)\leq k$ is known to be NP-hard. In fact, the asymptotic behavior of $\overline{cr}(K_n)$ is still unknown.
In this talk, we present a deterministic $n^{2+o(1)}$-time algorithm that finds a straight-line drawing of any $n$-vertex graph $G$ with $\overline{cr}(G) + o(n^4)$ pairs of crossing edges. Together with the well-known Crossing Lemma due to Ajtai et al.~and Leighton, this result implies that for any dense $n$-vertex graph $G$, one can efficiently find a straight-line drawing of $G$ with $(1 + o(1))\overline{cr}(G)$ pairs of crossing edges. This is joint work with Jacob Fox and Janos Pach.

**Geometry, Topology and Dynamics Seminar**

Counting commensurability classes of hyperbolic manifolds

Arie Levit (Weizmann Institute, Rehovot Israel)

3:00 PM in SEO 636

An interesting direction in the study of hyperbolic manifolds is counting questions.
By a classical result of Wang, in dimension > 3 there are finitely many isometry classes of hyperbolic manifolds up to any finite volume V. More recently, Burger, Gelander, Lubotzky and Mozes showed that this number grows like V^V.
In this talk we focus on the number of commensurability classes of hyperbolic manifolds. Two manifolds are commensurable if they admit a common finite cover. We show that in dimension > 3 this number grows like V^V as well.
Since the number of arithmetic commensurability classes grows ~ polynomially, our result implies that non-arithmetic manifolds account for “most" commensurability classes.
We will explain the ideas involved in the proof, which include a mixture of arithmetic, hyperbolic geometry and some combinatorics.
This is a joint work with Tsachik Gelander.

Wednesday October 5, 2016

**Algebraic Geometry Seminar**

Rational Curves on Complete Intersections in Positive Characteristic

Matthew Woolf (UIC)

4:00 PM in SEO 427

In this talk, I will discuss joint work with Eric Reidl showing that a general Calabi-Yau or general type complete intersection over a field of positive characteristic is not uniruled. I will also discuss applications of this work to deducing bounds on the dimension of complete intersections containing too many rational curves.

**Statistics Seminar**

New Approaches to Fast Approximate Bayesian Nonparametric Inference

George Karabatsos (UIC)

4:00 PM in SEO 636

Dirichlet process (DP) mixture models, as well as models
with mixture distribution assigned a general Bayesian nonparametric (BNP)
prior distribution on the space of probability measures, are
widely-applied and flexible models that can provide reliable statistical
inferences complex data. For such Bayesian mixture models, in practice,
posterior inferences are usually conducted using MCMC, which however, is
prohibitively slow for large data sets. Also for such models, prior
specification can be non-trivial in practice. As alternatives to MCMC, I
consider two new approaches to fast and approximate BNP inference for
large data sets. First, I show that if the ordinary least-squares (OLS)
estimator of the linear regression coefficients is specified as a
functional of the DP posterior distribution, then this functional has
posterior mean given by an observation-weighted ridge regression
estimator, with ridge (coefficient shrinkage) parameter given by the DP
precision parameter;
and has a heteroscedastic-consistent posterior covariance matrix.
This result is based on the multivariate delta method applied to
prior-informed bootstrap distribution approximation to the DP posterior.
Second, I consider an approximation to the BNP (infinite) mixture model
that I introduced and studied in several articles, defined by ordinal
regression mixture weights.The approximate model is defined by a (large)
finite mixture, with each component distribution multiplied by a histogram
bin indicator function. I show that posterior inference with this
approximate BNP model can be conducted by iteratively-reweighted least
squares estimation for the mixture weight parameters, and least-squares
estimation for the component densities, all involving computations that
are orders of magnitude faster that MCMC-based inference of the original
mixture model. This is also true for a version of the approximate model
that is defined by an ordinal regression of DPs. I illustrate the two
approximate BNP methods through the analysis of real data sets.

TBA

Monday October 10, 2016

**Graduate Analysis Seminar**

Stokes' Phenomenon

Charles Alley (UIC)

12:00 PM in SEO 1227

In this talk I will describe the classical Stokes' phenomenon.
This topic in complex analysis deals with the nature of asymptotic series
expansions of meromorphic functions in a neighborhood of a singularity.
In particular, we will discuss why and how the dominant term in such a
series expansion changes as one moves along different paths in the complex
plane.

**Combinatorics Seminar**

New developments in hypergraph Ramsey theory

Dhruv Mubayi (UIC)

2:00 PM in SEO 612

I will describe lower bounds (i.e. constructions) for several hypergraph Ramsey problems. These
constructions settle old conjectures of Erdos-Hajnal on classical Ramsey numbers as well as more
recent questions due to Conlon-Fox-Lee-Sudakov and others on generalized Ramsey numbers and
the Erdos-Rogers problem. Most of this is joint work with Andrew Suk.

Wednesday October 12, 2016

**Algebraic Geometry Seminar**

The Miyaoka-Yau inequality for minimal models of general type and uniformization.

Behrouz TAJI (Northwestern University.)

4:00 PM in SEO 427

By proving Calabi's conjecture, Yau proved that the Chern classes of a compact manifold with
ample canonical bundle encode the symmetries of the Kahler-Einstein metric via a simple inequality
-- the so-called Miyaoka-Yau inequality. Furthermore it was shown that in the case of equality, the
universal cover is the ball. Later, Tsuji established the MY inequality for smooth minimal models of general
type by constructing singular Kahler-Einstein metrics. The singularity of these metrics are usually a major
obstacle towards uniformization; a problem that has not yet been resolved via analytic methods. In a joint
project with Greb, Kebekus and Peternell, we take a different approach, via Hermitian-Yang-Mills theory and
Simpson's groundbreaking work on complex variation of Hodge structures, and we prove the MY inequality
for minimal models of general type and establish a uniformization result for their canonical models.

Friday October 14, 2016

Monday October 17, 2016

Wednesday October 19, 2016

**Statistics Seminar**

Model-based approaches to learn partitions from data

Dongxiao Zhu (Wayne State University)

3:00 PM in SEO 636

In multi-class classification, different classes may relate to different feature groups. In this
talk, I will present a class-conditional regularization of the multinomial logistic model to enable the
discovery of class-specific feature groups. I will also present an efficient cyclic block coordinate descent
based algorithm to solve the model. In another work, I will introduce a novel joint mixture model framework
to estimate cluster size distribution, particularly for over-dispersed (high variance) ones, together with
cluster compactness (density). Our methods are sufficiently flexible and general to be applied to multiple
application domains, such as social networks, image segmentation, natural language processing and
bioinformatics.

**RTG Workshop on the Geometry and Physics of Higgs bundles I**

Introduction to Higgs bundles

Laura P. Schaposnik (UIC)

5:30 PM in SEO 430

For more information on the schedule, and social plans see the website:
http://schapos.people.uic.edu/Higgs-2016.html
If you would like to register, email schapos@uic.edu

Saturday October 22, 2016

**RTG Workshop on the Geometry and Physics of Higgs bundles I**

8:30 a.m. - 7 p.m.

Mini-courses by Marina Logares (Oxford) & Steven Rayan (Saskatchewan)

8:30 AM in SEO 430

For more information on the schedule, and social plans see the website:
http://schapos.people.uic.edu/Higgs-2016.html
If you would like to register, email schapos@uic.edu

Sunday October 23, 2016

**RTG Workshop on the Geometry and Physics of Higgs bundles I**

8:30 a.m. - 1 p.m.

Mini-courses by Marina Logares (Oxford) & Steven Rayan (Saskatchewan)

8:30 AM in SEO 430

For more information on the schedule, and social plans see the website:
http://schapos.people.uic.edu/Higgs-2016.html
If you would like to register, email schapos@uic.edu

Monday October 24, 2016

**Geometry, Topology and Dynamics Seminar**

Quivers, hyperpolygons, and Hitchin systems

Steven Rayan (Saskatchewan)

3:00 PM in SEO 636

I will discuss three closely-related moduli problems: moduli of representations of star-shaped quivers, moduli of hyperpolygons, and moduli of parabolic Higgs bundles. One theme that weaves these three problems together is complete integrability. I will discuss recent results on the topology of these moduli spaces (joint work with Jonathan Fisher) and then pose questions on the relationship between stability for Higgs bundles and stability for hyperpolygons, and also speculate on mirror symmetry for hyperpolygon spaces.

We will be going for lunch on Monday 12-1, have some tasty treats for tea at 4 p.m. in the common room and we will go for drinks at 5 p.m. (and then dinner). Come join us!

Wednesday October 26, 2016

Monday October 31, 2016

**Commutative Algebra Seminar**

Cartier modules and crystals

Nicholas Switala (UIC)

1:00 PM in SEO 427

The goal of this talk is to introduce the categories of Cartier modules and Cartier crystals introduced by M. Blickle and G. Boeckle in their 2011 Crelle paper, as well as the basic finiteness results proved there.

**Geometry, Topology and Dynamics Seminar**

Molino theory for laminations

Olga Lukina (UIC)

3:00 PM in SEO 636

A foliation of a compact manifold can be considered as a
generalized dynamical system, in the sense of Smale. The study of the
dynamical properties of foliations has been an active area of research for
the past 40 years. A smooth foliation is Riemannian, if the normal bundle
of the foliation admits a Riemannian metric invariant under the action of
the holonomy pseudogroup of the foliation. Riemannian foliations are very
rigid geometric structures, and they are completely classified by Molino
theory.
Ghys asked in 1988 whether Molino theory can be generalized to a
topological setting. In this setting, one considers foliations of compact
topological spaces, which do not admit normal bundles, and where the
transversals need not be locally connected. The condition analogous to the
existence and invariance of a Riemannian metric in this non-differentiable
setting, is the assumption of equicontinuity of the holonomy pseudogroup
of the foliation. Alvarez Lopez, Candel, and Moreira Galicia gave a
version of a Molino-like theory for foliated spaces under the additional
assumption that the closure of the holonomy pseudogroup is strongly
quasi-analytic, that is, it satisfies the condition of local generation.
In this talk, we consider foliated spaces with totally disconnected
transversals, which we call matchbox manifolds, and use the methods of
topological dynamics and continuum theory to develop a Molino-like
classification of all such spaces. We show that for matchbox manifolds,
the Molino sequence need not be well-defined, and specify the conditions
under which it is well-defined. We outline the classes of matchbox
manifolds, for which the local generation condition holds or does not
hold, and study other properties of these spaces. Inspired by the result
of Lubotzky about the existence of torsion in profinite completions of
torsion-free groups, we construct a class of examples with well-defined
non-trivial Molino sequences, where the non-triviality of the Molino
sequence cannot be explained by the holonomy properties of leaves in the
matchbox manifold. The examples that we construct and study show that this
class of dynamical systems is far from being completely classified.

Monday November 7, 2016

Friday November 11, 2016

Wednesday November 16, 2016

Monday November 28, 2016

Wednesday November 30, 2016