# MSCS Seminar Calendar

Monday February 20, 2017

**Geometry, Topology and Dynamics Seminar**

Arboreal Galois Representations and Odoni's Conjecture

Nicole Looper (Northwestern University)

3:00 PM in SEO 636

Since the mid-1980s, when the study of arboreal Galois representations first began,
most results have concerned the representations induced by quadratic rational maps.
In the higher degree case, by contrast, very little has been known.
I will discuss some recent results pertaining to higher degree polynomials over number fields.
This will include a partial solution to a conjecture made by R.W.K. Odoni in 1985.

**Analysis and Applied Mathematics Seminar**

Improved estimates for thermal fluid equations

Andrei Tarfulea (University of Chicago)

4:00 PM in SEO 636

We consider a model for three-dimensional fluid flow on the
torus that also keeps track of the local temperature. The momentum
equation is the same as for Navier-Stokes, however the kinematic viscosity
grows as a function of the local temperature. The temperature is, in turn,
fed by the local dissipation of kinetic energy. Intuitively, this leads to
a mechanism whereby turbulent regions increase their local viscosity and
dissipate faster. We prove a strong a priori bound (that would fall within
the Ladyzhenskaya-Prodi-Serrin criterion for ordinary Navier-Stokes) on
the thermally weighted enstrophy for classical solutions to the coupled
system.

Wednesday February 22, 2017

**Graduate Geometry, Topology and Dynamics Seminar**

Geodesic Laminations Part 3

Cloie McClellan

3:00 PM in SEO 612

In this talk, I will present the remainder of chapter 3 of Casson and Bleiler. The section covered begins by asking if the automorphism group of a closed hyperbolic surface acts naturally on the surface and then proceeds to present some partial results.

**Statistics Seminar**

Functional Coefficient Time Series Models with Trending Regressors

Tingting Cheng (Nankai University)

4:00 PM in SEO 636

We study a functional coefficient time series model with trending regressors, where the coefficients are unknown functions of time and random variables. We propose a local linear estimation method to estimate the unknown coefficient functions. An asymptotic distribution of the proposed local linear estimator is established under mild conditions. A test procedure is developed to test the null hypothesis that the functional coefficients take particular parametric forms. For practical use, we further propose a Bayesian approach to select bandwidths involved in this local linear estimator. Several numerical examples are provided to examine the finite sample performance of the proposed local linear estimator and the test procedure. The results show that the local linear estimator works well and the proposed test has satisfactory size and power. In addition, simulation studies show that the Bayesian bandwidth selection method is better than cross–validation method. Furthermore, we employ the functional coefficient model to study the relationship between consumption per capita and income per capita in U.S. and the results show that functional coefficient model with our proposed local linear estimator and Bayesian bandwidth selection method performs best in both in–sample fitting and out–of–sample forecasting.

**Algebraic Geometry Seminar**

Homomorphisms between Cremona groups

Christian Urech (University of Basel / University of Rennes 1)

4:00 PM in SEO 427

The Cremona group is the group of birational transformations of the projective space. While the plane Cremona group is well understood, many questions about Cremona groups in higher dimensions remain open. In this talk we will look at the question how the plane Cremona group can be embedded into Cremona groups in higher dimensions. In particular, I will give a classification of algebraic embeddings from the plane Cremona group to the group of birational transformations of a threefold and explain the geometry of some interesting examples in higher dimensions.

Thursday February 23, 2017

Friday February 24, 2017

**Departmental Colloquium**

Determining forms and data assimilation

Mike Jolly (Indiana University Bloomington)

3:00 PM in SEO 636

A determining form for a dissipative partial differential equation is an ordinary differential equation in a certain trajectory space where the solutions on the global attractor of the PDE are readily recognized. It is an ODE in the true sense of defining a vector field which is (globally) Lipschitz. We discuss two types of determining forms: one where solutions on the global attractor of the PDE are traveling waves, and another where they are steady states. Each determining form is related to a certain approach to data assimilation, i.e. the injection of a coarse-grain time series into the model in order to recover the matching full solution. Applications have been made to the 2D incompressible Navier-Stokes, damped-driven nonlinear Schrodinger, damped-driven Korteveg-de Vries and surface quasigeostrophic equations.

Monday February 27, 2017

**Computer Science Seminar**

Complete Derandomization of Identity Testing of Read-Once Formulas

Ilya Volkovich (University of Michigan)

2:00 PM in SEO 612

In this paper we study the identity testing problem of arithmetic read-once formulas (ROF) and some related models. A read-once formula is formula (a circuit whose underlying graph is a tree) in which the operations are {+, ×} and such that every input variable labels at most one leaf. We obtain the ﬁrst polynomial-time deterministic identity testing algorithm that operates in the black-box setting for read-once formulas, as well as some other related models. As an application, we obtain the ﬁrst polynomial-time deterministic reconstruction algorithm for such formulas. Our results are obtained by improving and extending the analysis of the algorithm of Shpilka-Volkovich 09’.
Joint work with Daniel Minahan.

**Geometry, Topology and Dynamics Seminar**

Universal acylindrical actions

Carolyn Abbott (University of Wisconsin, Madison)

3:00 PM in SEO 636

Given a finitely generated group, one can look for an acylindrical action on a hyperbolic space in which all elements that are loxodromic for some acylindrical action of the group are loxodromic for this particular action. Such an action is called a universal acylindrical action and, for acylindrically hyperbolic groups, tends to give a lot of information about the group. I will discuss recent results in the search for universal acylindrical actions, describing a class of groups for which it is always possible to construct such an action as well as an example of a group for which no such action exists.

**Analysis and Applied Mathematics Seminar**

A priori upper bounds for the inhomogeneous Landau equation

Stanley Snelson (University of Chicago)

4:00 PM in SEO 636

We consider the Landau equation, an integro-differential kinetic model from plasma physics that describes the evolution of a particle density in phase space. It arises as the limit of the Boltzmann equation when grazing collisions predominate. I will give an overview of prior work on the regularity theory of the Landau equation, and describe how to prove a priori upper bounds that decay polynomially in the velocity variable. The technical tools include precise bounds on the coefficients, and tracking how local estimates scale as the velocity grows. I will also explain why the polynomial decay cannot be improved to exponential decay. This talk is based on joint work with Stephen Cameron and Luis Silvestre.

Tuesday February 28, 2017

**Logic Seminar**

A Tale of Two Liouville Closures

Allen Gehret (UIUC)

4:00 PM in SEO 427

$H$-fields are ordered differential fields which serve as an abstract generalization of both Hardy fields (ordered differential fields of germs of real-valued functions at $+\infty$) and transseries (ordered valued differential fields such as $\mathbb{T}$ and $\mathbb{T}_{\log}$). A \emph{Liouville closure} of an $H$-field $K$ is a minimal real-closed $H$-field extension of $K$ that is closed under integration and exponential integration. In 2002, Lou van den Dries and Matthias Aschenbrenner proved that every $H$-field $K$ has exactly one, or exactly two, Liouville closures, up to isomorphism over $K$. Recently (in arxiv.org/abs/1608.00997), I was able to determine the precise dividing line of this dichotomy. It involves a technical property of $H$-fields called $\lambda$-freeness. In this talk, I will review the 2002 result of van den Dries and Aschenbrenner and discuss my recent contribution.

Wednesday March 1, 2017

Monday March 6, 2017

**Analysis and Applied Mathematics Seminar**

A damped Newton algorithm for semi-discrete optimal transport

Jun Kitagawa (Michigan State University)

4:00 PM in SEO 636

We consider a damped Newton algorithm to calculate the transport map of semi-discrete optimal transport problems, where the initial measure is absolutely continuous while the target measure is discrete. For costs satisfying standard conditions arising in the regularity theory of optimal transport, and initial measures with Hölder continuous density and support satisfying some mild connectivity conditions, we show this algorithm enjoys global linear and local superlinear convergence. A key ingredient in the proof comes from PDE theory, and involves Loeper’s geometric interpretation of the Ma-Trudinger-Wang conditions. This is joint work with Quentin Mérigot and Boris Thibert.

Tuesday March 7, 2017

Friday March 10, 2017

Tuesday March 14, 2017

**Logic Seminar**

The relation of embeddability between torsion-free abelian uncountable groups

Filippo Calderoni (Università di Torino)

4:00 PM in SEO 427

We will discuss the problem of determining the Borel complexity of the analytic quasi-order of embeddability between torsion-free abelian groups in both the settings of the classical and generalized Descriptive Set Theory. Then we will see how we can slightly modify a categorical construction by Przezdziecki to prove that, for every uncountable $\kappa$ such that $\kappa^{<\kappa}=\kappa$, the embeddability between $\kappa$-sized torsion-free abelian groups is as complicated as possible among the analytic quasi-orders defined on the generalized Baire space on $\kappa$.

Wednesday March 15, 2017

Monday March 27, 2017

Wednesday March 29, 2017

Friday March 31, 2017

Monday April 3, 2017

Wednesday April 5, 2017

Friday April 7, 2017

Monday April 10, 2017

Wednesday April 12, 2017

Thursday April 13, 2017

Friday April 14, 2017

Monday April 17, 2017

Wednesday April 19, 2017

Friday April 21, 2017

Monday April 24, 2017

Wednesday April 26, 2017

Friday April 28, 2017