# MSCS Seminar Calendar

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

**Set theory workshop**

Iterated forcing and the Continuum Hypothesis, part 3

Justin Moore (Cornell)

9:30 AM in SEO 636

One of the great successes in set theory in the 1970s and 80s has been the isolation of an optimal hypothesis for iterating forcings while preserving uncountablity. It turns out that while there is a well developed theory of iterating forcings which do not introduce new reals, this theory is necessarily more ad hoc in nature. This tutorial will discuss Shelah's preservation theorems for not adding reals as well as recently discovered examples which illustrate that these results are, in some sense, sharp.

**Set theory workshop**

Integer cost and ergodic actions

Anush Tserunyan (UIUC)

11:00 AM in SEO 636

A countable Borel equivalence relation $E$ on a probability space can always be generated in two ways: as the orbit equivalence relation of a Borel action of a countable group and as the connectedness relation of a locally countable Borel graph, called a $\it{graphing}$ of $E$. Assuming that $E$ is measure-preserving, graphings provide a numerical invariant called $\it{cost}$, whose theory has been largely developed and used by Gaboriau and others in establishing rigidity results. A well-known theorem of Hjorth states that when $E$ is ergodic, treeable (admits an acyclic graphing), and has integer or infinite cost $n \le \infty$, then it is generated by an a.e. free measure-preserving action of the free group $\mathbf{F}_n$ on $n$ generators. We give a simpler proof of this theorem and the technique of our proof, combined with two other new tools, yields a strengthening of Hjorth's theorem: the action of $\mathbf{F}_n$ can be arranged so that each of the $n$ generators acts ergodically. This is joint work with Benjamin Miller.

**Set theory workshop**

Applications of descriptive set theory to classical dynamical systems, part 1

Matt Foreman (UC Irvine)

1:30 PM in SEO 636

In 1932 von Neumann proposed the project of classifying smooth measure preserving transformations. As part of the project he raised the question of whether every ergodic measure preserving transformation of the unit interval is isomorphic to a diffeomorphism of a manifold.
Despite deep progress on both questions, they remained open until recently. The lecture presents joint work with B. Weiss that shows that the classification problem is impossible to solve--because the associated equivalence relation is not Borel (and moreover is strictly more complicated than any $S^\infty$-action). Along the way the authors made progress on the second problem, by showing that a quasi-generic class of transformations can be realized as diffeomorphisms of the 2-torus. This class is the source of the complexity of the classification problem.

**Set theory workshop**

Applications of descriptive set theory to classical dynamical systems, part 2

Matt Foreman (UC Irvine)

2:45 PM in SEO 636

In 1932 von Neumann proposed the project of classifying smooth measure preserving transformations. As part of the project he raised the question of whether every ergodic measure preserving transformation of the unit interval is isomorphic to a diffeomorphism of a manifold.
Despite deep progress on both questions, they remained open until recently. The lecture presents joint work with B. Weiss that shows that the classification problem is impossible to solve--because the associated equivalence relation is not Borel (and moreover is strictly more complicated than any $S^\infty$-action). Along the way the authors made progress on the second problem, by showing that a quasi-generic class of transformations can be realized as diffeomorphisms of the 2-torus. This class is the source of the complexity of the classification problem.

**Set theory workshop**

Weak Squares and Very Good Scales

Maxwell Levine (UIC)

4:00 PM in SEO 636

The combinatorial properties of large cardinals tend to clash with those satisfied by G\"odel's constructible universe, especially the square property (denoted $\square_\kappa$) isolated by Jensen in the seventies. Strong cardinal axioms refute the existence of square, but it is possible with some fine-tuning to produce models that exhibit some large cardinal properties together with weakenings of square. In this talk we will exhibit some results along these lines and will outline the techniques used to produce them.

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

**Set theory workshop**

Applications of descriptive set theory to classical dynamical systems, part 3

Matt Foreman (UC Irvine)

10:00 AM in SEO 636

In 1932 von Neumann proposed the project of classifying smooth measure preserving transformations. As part of the project he raised the question of whether every ergodic measure preserving transformation of the unit interval is isomorphic to a diffeomorphism of a manifold.
Despite deep progress on both questions, they remained open until recently. The lecture presents joint work with B. Weiss that shows that the classification problem is impossible to solve--because the associated equivalence relation is not Borel (and moreover is strictly more complicated than any $S^\infty$-action). Along the way the authors made progress on the second problem, by showing that a quasi-generic class of transformations can be realized as diffeomorphisms of the 2-torus. This class is the source of the complexity of the classification problem.

**Set theory workshop**

Space decomposition techniques in Borel dynamics

Kostyantyn Slutskyy (UIC)

11:30 AM in SEO 636

In recent years a substantial progress has been achieved in the field of Borel dynamics. A part of this progress is due to the development of space decomposition methods. The goal of the talk is to make an overview of the old and new results that have been proved along this path. In particular, we will discuss in various degrees of details the following: Dougherty-Jackson-Kechris classification of hyperfinite Borel equivalence relations, Multi-Tower Rokhlin Lemma for Borel automorphisms and regular cross sections of Borel flows, Lebesgue orbit equivalence of multidimensional flows, and Hochman's proof of existence of finite generators for compressible automorphisms.

Monday October 24, 2016

**Graduate Student Colloquium**

Circle Packings and Complex Projective Surfaces

Ellie Dannenberg (UIC)

1:00 PM in SEO 636

The Koebe-Andreev-Thurston Circle Packing Theorem says that given a triangulation $\tau$ of a surface $S$, there is a unique pair $(g,P)$, where $g$ is a constant curvature Riemannian Metric on $S$. $P$ is a circle packing of circles with respect to $g$ and combinatorics given by $\tau$. If, instead of constant curvature Riemannian metrics on $S$, we consider complex projective structures on $S$, there is a deformation space of complex projective circle packings with fixed combinatorics.
In this talk, I'll discuss circle packings and complex projective structures on surfaces. I'll then discuss the deformation space of complex projective circle packings with combinatorics given by $\tau$. Much is still unknown about this space.

**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 1-2, have some tasty treats for tea at 3 p.m. right before the talk.

**Analysis and Applied Mathematics Seminar**

Existence of large-amplitude steady stratified water waves

Ming Chen (University of Pittsburgh)

4:00 PM in SEO 636

We consider 2D steady water waves with heterogeneous density. The presence
of stratification allows for a wide variety of traveling waves, including
fronts, so-called generalized solitary waves with ripples in the far
field, and even fronts with ripples! Among these many possible wave
patterns, we prove that for any smooth choice of upstream velocity and
monotone streamline density function, there always exists a continuous
curve of solitary waves with large amplitude, which are even and
decreasing monotonically on either side of a central crest. As one moves
along this curve, the horizontal fluid velocity comes arbitrarily close to
the wave speed.
We will also discuss a number of results characterizing the qualitative
features of solitary stratified waves. In part, these include bounds on
the Froude number from above and below that are new even for constant
density flow; an a priori bound on the velocity field and lower bound on
the pressure; a proof of the nonexistence of monotone bores for stratified
surface waves; and a theorem ensuring that all supercritical solitary
waves of elevation have an axis of even symmetry. This is a joint work
with Samuel Walsh and Miles Wheeler.

Tuesday October 25, 2016

**Logic Seminar**

The Hanf number for Extendability

John Baldwin (UIC)

4:00 PM in SEO 427

We construct a complete $L_{\omega_1,\omega}$-sentence $\phi$ such that $(\textbf{R},\subseteq)$ is an abstract elementary class
with a proper class of models.

**Theorem.**There is a maximal model $M \in \textbf{R}$ of cardinality $\lambda$ if there is no measurable cardinal $\rho$ with $\rho \leq \lambda$, $\lambda = \lambda^{< \lambda}$, and there is an $S \subseteq S^{\lambda}_{\aleph_0}$, that is stationary non-reflecting, and $\diamond_S$ holds. Thus in the absence of a measurable, $\phi$ has arbitrarily large maximal models. But in the presence of measurables there are maximal models cofinally in the first measurable and never again. I hope to say something about the removal of the set-theoretic hypotheses.Wednesday October 26, 2016

**Algebraic Geometry Seminar**

Correspondences between convex geometry and complex geometry

Jian Xiao (Northwestern University)

4:00 PM in SEO 427

We present several (new) correspondences between convex bodies and the theory of holomorphic line bundles on smooth projective varieties or Kähler manifolds, thus extending the dictionary between convex geometry and complex geometry. An important ingredient is a refined structure of the movable cone of curves. This is joint work with Brian Lehmann.

**Statistics Seminar**

Design and Analysis of Clinical Studies using Restricted Mean Survival Time

Lihui Zhao (Northwestern University)

4:00 PM in SEO 636

For a study with an event time as the endpoint, its survival function contains all the information
regarding the temporal, stochastic profile of this outcome variable. The survival probability at a
specific time point, say t, however, does not transparently capture the temporal profile of this
endpoint up to t. An alternative is to use the restricted mean survival time (RMST) at time t to
summarize the profile. The RMST is the mean survival time of all subjects in the study population
followed up to t, and is simply the area under the survival curve up to t. The advantages of using
such a quantification over the survival rate have been discussed in the setting of a fixed-time
analysis. In this research, we generalize this approach by considering a curve based on the RMST over
time as an alternative summary to the survival function. Inference, for instance, based on
simultaneous confidence bands for a single RMST curve and also the difference between two RMST curves
are proposed. The latter is informative for evaluating two groups under an equivalence or
noninferiority setting, and quantifies the difference of two groups in a time scale. In addition, we
extend RMET to the setting of multiple endpoints, which includes classical competing risks and
semi-competing risks. The methods are illustrated with the data from two clinical trials.

**Commutative Algebra Seminar**

F-signature of non-local rings

Thomas Polstra (University of Missouri)

1:00 PM in SEO 427

The F-signature of a local ring, a numerical invariant shown to exist by Tucker, is the asymptotic measurement of the number of Frobenius splittings for which a local ring of prime characteristic admits. The F-signature serves as a measurement of singularities. Most notably, the F-signature of a local ring is 1 if and only if the ring is regular, by work of Huneke and Leuschke, and the F-signature of a local ring is positive if and only if the ring is strongly F-regular, by work of Aberbach and Leuschke. We will discuss how the notion and existence of F-signature extends to all rings which are F-finite but not necessarily local. Our methods our made meaningful by extending Huneke's and Leuschke's and Aberbach's and Leuschke's theorems to the non-local case. This is based on joint work with Alessandro De Stefani and Yongwei Yao.

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.

Wednesday November 2, 2016

**Statistics Seminar**

Overlaps and Pathwise Localization in the Anderson Polymer Model

Mike Cranston (UCI)

4:00 PM in SEO 636

We consider large time behavior of typical paths under the Anderson polymer measure. If $P^x_\kappa$ is the measure induced by rate $\kappa,$ simple, symmetric random walk on $\mathbb{Z}^d$ started at $x,$ this measure is defined as
\[d\mu^x_{\kappa,\beta,T}T(X)={Z_{\kappa,\beta,T}}^{-1} \exp\left\{\beta\int_0^T dW_{X(s)}(s)\right\}dP^x_\kappa(X)\]
where $\{W_x:x\in \mathbb{Z}^d\}$ is a field of $iid$ standard, one-dimensional Brownian motions, $\beta>0, \kappa>0$ and
$Z_{\kappa,\beta,t}(x)$ the normalizing constant.
We establish that the polymer measure gives a macroscopic mass to a small neighborhood of a typical path as $T \to \infty$, for parameter values outside the perturbative regime of the random walk, giving a pathwise
approach to polymer localization, in contrast with existing results. The localization becomes complete as $\frac{\beta^2}{\kappa}\to\infty$ in the sense that the mass grows to 1.
The proof makes use of the overlap between two independent samples drawn under the Gibbs measure $\mu^x_{\kappa,\beta,T}$,
which can be estimated by the integration by parts formula for the Gaussian environment.
Conditioning this measure on the number of jumps, we obtain a canonical measure which already shows scaling
properties, thermodynamic limits, and decoupling of the parameters. This talk is based on joint work with Francis Comets.

**Departmental Colloquium**

Numerical Investigation of Crouzeix’s Conjecture

Michael Overton (Courant Institute, NYU)

3:00 PM in SEO 636

Crouzeix's conjecture is among the most intriguing developments in matrix theory in recent years.
Made in 2004 by Michel Crouzeix, it postulates that, for any polynomial p and any matrix A,
||p(A)|| <= 2 max(|p(z)|: z in W(A)), where the norm is the 2-norm and W(A) is the field
of values (numerical range) of A, that is the set of points attained by v*Av for some
vector v of unit length. Remarkably, Crouzeix proved in 2007 that the inequality above
holds if 2 is replaced by 11.08. Furthermore, it is known that the conjecture holds in a
number of special cases, including n=2. We use nonsmooth optimization to investigate
the conjecture numerically by attempting to minimize the “Crouzeix ratio”, defined as the
quotient with numerator the right-hand side and denominator the left-hand side of the
conjectured inequality. We present numerical results that lead to some theorems and
further conjectures, including variational analysis of the Crouzeix ratio at conjectured global minimizers.
All the computations strongly support the truth of Crouzeix’s conjecture.
This is joint work with Anne Greenbaum and Adrian Lewis.

Tea starts at 4:15 PM in 300 SEO

Monday November 7, 2016

Tuesday November 8, 2016

Friday November 11, 2016

Wednesday November 16, 2016

Monday November 21, 2016

Monday November 28, 2016

Wednesday November 30, 2016

**Algebraic Geometry Seminar**

Pushforwards of pluricanonical bundles and morphisms to abelian varieties

Christian Schnell / David Yang (Stonybrook / MIT)

4:00 PM in SEO 427

In the past few years, people working on the analytic side of algebraic geometry have obtained two important new results: a version of the Ohsawa-Takegoshi extension theorem with sharp estimates (Blocki, Guan-Zhou), and the existence of canonical singular hermitian metrics on pushforwards of relative pluricanonical bundles (Berndtsson, Paun, Takayama, and others). In this talk, I will explore some consequences of this work for the study of morphisms to complex abelian varieties, including the recent proof of Iitaka's conjecture over abelian varieties (Cao-Paun). The talk will be understandable without any background in analysis.

Monday December 5, 2016

Monday January 23, 2017

Monday February 6, 2017

Monday March 6, 2017

Friday April 21, 2017

Wednesday April 26, 2017