NDSU Applied Mathematics Seminar - Spring 2010
**Loyola University Chicago **

Department of Mathematics and Statistics

ANALYSIS SEMINAR
**Time: 4:00PM-4:50PM**** **

Location: **BVM Hall - Room 1102****
(6349 N. Kenmore Avenue, Chicago, IL 60626)** [map]

**FALL 2015
SCHEDULE**

**AUGUST 2015**

Tuesday,
August 25 - ROBERT
JENSEN **(Loyola University Chicago)** - *The Vibrating Inverted Pendulum*

Abstract:
Click here.

**SEPTEMBER
2015**
**Thursday, September 10 - ****DANIEL SPECTOR** **(National
Chiao Tung University, Taiwan)** - ** ***A new embedding
theorem in "Sobolev" spaces*

*Abstract:
*Specialists
in PDEs and Harmonic Analysis oftentimes have
different perspectives on the same question.
In this talk I will discuss some of these viewpoints
in the context of embedding theorems. In particular,
I will present a new result in this area which is
surprising in several ways, raising fundamental
questions regarding what we understand about
integration.

**NOVEMBER 2015**
Tuesday,
November 10 - **RAFAL
GOEBEL** **(Loyola University
Chicago)** -
**A (mildly biased) survey of mathematical
models of hybrid systems**

*Abstract:** *Classical
approach to dynamical systems categorizes each dynamical
system as a continuous-time dynamical system or a
discrete-time dynamical system. For example, systems of
planets that evolve under Newton's laws or biological systems
where populations of species grow or decay exponentially are
continuous-time systems and have solutions parameterized by
time. Your savings account balance that increases every month,
recursively-defined sequences, binary values in an algorithm,
etc. are examples of discrete-time systems and have solutions
parameterized by natural numbers that count the number of
transitions. Broadly understood, hybrid dynamical systems are
dynamical systems that exhibit features characteristic of
continuous-time dynamical systems and features characteristic
of discrete-time systems. Modeling of cyber-physical systems
that combine analog and digital components; of mechanical
systems with impacts, where velocities may change
instantaneously; of biological systems with impulses; etc.
motivate the interest in hybrid systems in control theory and
control engineering literature. There, one can find piecewise
affine systems, complementarity systems, differential or
hybrid automata, dynamical systems on time scales, hybrid
inclusions, impulsive differential equations, measure-driven
differential equations, switched systems, etc., all of which
have hybrid features. The talk will present several of these
modeling frameworks, discuss some concepts of solutions to the
models, and relate selected frameworks to hybrid inclusions.

Tuesday,
November 17 - **CHARLES SMART**
**(University of Chicago)** - **Rates of convergence for the
random conductance model****
**

Abstract:* *I
will survey some of the recent work on the homogenization of
the random conductance model. This will include some
work of mine with Armstrong and some work of
Armstrong-Kuusi-Mourrat and Gloria-Otto. There are now
two approaches to obtaining optimal rates in for random
elliptic equations in divergence form. The first
obtains Green's function estimates by appealing to the
Efron-Stein concentration inequality. The second uses
regularity theory to localize the dependence of the solution
on the coefficients. I will discuss both of these
methods.