# MSCS Seminar Calendar

Monday March 30, 2015

**Geometry, Topology and Dynamics Seminar**

Unimodal Maps and Inverse Limit Spaces

Lori Alvin (University of Denver)

3:00 PM in SEO 636

In this talk we investigate some of the continua (compact, connected
metric spaces) that occur as inverse limit spaces of unimodal bonding maps. The
inverse limit space of a single map $f:I\to I$ is
$$\lim_{\longleftarrow} {\bf f} = \{ x = (x_0, x_1, x_2, \ldots ) : x_n \in I \textrm{ and } f(x_{n+1}) = x_n \textrm{ for all } n\in \mathbb{N} \}$$
and has metric
$$d(x,y) = \sum_{i=0}^\infty \frac{|x_i-y_i|}{2^i}.$$
We begin by exploring the continua that arise as inverse limit spaces from a single
logistic map of the form $g_a(x) = ax(1-x)$, where $a\in [0,4]$. We are particularly
interested in drawing the inverse limits that arise from the family of logistic maps
seen within the classical period doubling bifurcation diagram. We then use the
period doubling bifurcation to gain an intuition for the inverse limit space of the
logistic map with parameter $a\approx 3.569945668$, also called the Feigenbaum
limit. This map, sometimes referred to as the $2^\infty$ map, is the unique
logistic map with period points of period $2^n$ for all $n\in \mathbb{N}$ and no
other periodic points; the action of $g|_{\omega(c,g)}$ is topologically conjugate
to a special type of map called an adding machine or odometer. We conclude by
discussing inverse limit spaces whose single bonding maps have embedded adding
machines.

**Applied Mathematics Seminar**

Probabilistic global well-posedness of the energy-critical defocusing nonlinear wave equation on euclidean spaces

Oana Pocovnicu (Princeton University)

4:00 PM in SEO 636

We consider the energy-critical defocusing nonlinear wave equation
(NLW) on $\mathbb{R}^d$, $d = 3, 4, 5$. In the deterministic setting, Christ,
Colliander, and Tao showed that this equation is ill-posed below the
energy space $H^1 × L^2$.
In this talk, we take a probabilistic approach. More precisely, we
prove almost sure global existence and uniqueness for NLW with rough
random initial data below the energy space. The randomization that we
use is naturally associated with the Wiener decomposition and with
modulation spaces. The proof is based on a probabilistic perturbation
theory and on probabilistic energy bounds.
If time allows, we will briefly discuss how the above strategy also
yields a conditional almost sure global well-posedness result below
the scaling critical regularity, for the defocusing cubic nonlinear
Schrödinger equation on euclidean spaces. This talk is partially
based on joint work with Tadahiro Oh, and on joint work with Árpád
Bényi and Tadahiro Oh.

Wednesday April 1, 2015

Friday April 3, 2015

Monday April 6, 2015

**Geometry, Topology and Dynamics Seminar**

Morse geodesics in torsion groups

Elisabeth Fink (Ecole Normale Superieure)

3:00 PM in SEO 636

A geodesic in a metric space is Morse, if quasi-geodesics connecting points on it stay uniformly close. In many cases, such geodesics come from an embedded cyclic subgroup, in other words from a so-called Morse element which generates this cyclic subgroup. By studying asymptotic cones, we will exhibit Morse geodesics in infinite torsion groups which are direct limits of hyperbolic groups. On the contrary, it will be shown that there exist many non-Morse geodesics in the same groups, which do not even contain arbitrarily large powers. I will also discuss related properties and possible consequences.

Wednesday April 8, 2015

Friday April 10, 2015

**Departmental Colloquium**

Interpolation for polynomials in several variables

Joe Harris (Harvard)

3:00 PM in SEO 636

An elementary theorem says that we can always find a polynomial $f(x)$ of degree $d$ or less having specified values at $d+1$ given points $x$. When we try to state (let alone prove) an analogue for polynomials in several variables, however, we run into immediate difficulties. In this talk, I’ll try to show that the difficulties lie in the geometry of the points, and suggest at least a conjectural answer to the problem.

Opening lecture: Midwest Algebraic Geometry Graduate Conference

Monday April 13, 2015

Tuesday April 14, 2015

Friday April 17, 2015

Wednesday April 22, 2015

Friday April 24, 2015

**Departmental Colloquium**

Some Examples of the use of nonstandard methods in continuum theory

Steven Leth (University of Northern Colorado)

3:00 PM in SEO 636

In this talk I will outline some applications of nonstandard methods to the
study of compact, connected subsets of the plane. Nonstandard models allow
for many complicated limiting properties of a set to be "actualized" in the nonstandard version of the set. This
can make objects such as "pseudo-arcs" and
other hereditarily indecomposable continua more intuitive to work with. Of
particular interest are possible applications to sub-questions of the

*plane fixed point problem*, which asks if every compact, connected subset of the plane that does not separate the plane has the fixed point property.Monday April 27, 2015

Tuesday April 28, 2015

Wednesday April 29, 2015

**Statistics Seminar**

Panel discussion

Stat faculty and students (UIC)

4:00 PM in SEO 636

This panel discussion will give students an opportunity to have questions about various things (e.g., advantages and disadvantages of
an academic career, general strategies for successful research, career opportunities outside of academia and how to prepare for them, etc)
answered by faculty and senior graduate students.

Friday May 1, 2015