epshteyn (at) math.utah.edu)January 11, Friday (Special Seminar), Room LCB 219. Time 3pm - 4pm
Speaker:
William Feldman, Department of Mathematics, University of Chicago
Title: Recent developments in stochastic homogenization of Hamilton-Jacobi
equations
Abstract: I will describe some background and some new developments in the theory
homogenization of Hamilton-Jacobi equations in random environments. The
primary difficulties in this field have been around understanding the
roles of convexity and coercivity (controllability). Many interesting
problems, especially involving interface motions, lack one or both of
these properties. I will discuss some positive results and some
counter-examples where homogenization does not hold.
January 18, Friday (Special Seminar), Room LCB 215. Time 4pm - 5pm.
Speaker:
Ian Tobasco, Department of Mathematics, University of Michigan,
Ann Arbor
Title: Optimal design of wall-bounded heat transport
Abstract: Flowing a fluid is a familiar and efficient way to cool: fans cool electronics,
water cools nuclear reactors, and
the atmosphere cools the surface of the Earth. In this talk, we discuss a class of
problems from fluid dynamics
which ask for the design of incompressible wall-bounded flows
achieving optimal rates of heat transport for a given
flow intensity budget. Guided by a perhaps unexpected connection between
this optimal design problem and various
"energy-driven pattern formation" problems from materials science, we construct
flows achieving
nearly optimal rates of heat transport in their scaling with respect to a prescribed
intensity budget. The
resulting flows share striking similarities with self-similar elastic wrinkling
patterns, such as can be seen in
the shape of a hanging drape or nearby the edge of a torn plastic sheet. They also
remind of (carefully designed
versions) of the complex multi-scale patterns seen in turbulent fluids.
Nevertheless, we prove that in certain
cases natural buoyancy-driven convection is not capable of achieving optimal rates
of cooling. This is joint work
with Charlie Doering.
March 1, Time 3pm, Room LCB 219, Joint Stochastics and Applied
Math seminar
Speaker:
Greg Rice, Department of Statistics and Actuarial Science,
University of Waterloo
Title: Change point analysis with functional time series
Abstract: We consider methods for detecting and dating changes in both the
level and variability of a time series of curves or functional data
objects. Regarding level shifts, we propose a new detection and dating
procedure that is ``fully functional", in the sense that it does not rely
on dimension reduction techniques. To test for changes in variability, we
consider methods based on measuring the fluctuations of eigenvalues of the
sequential estimates of the empirical covariance operator. A thorough
asymptotic theory is developed for each procedure that highlights their
relative strengths and weaknesses when compared to existing methods. An
application to annual temperature curves illustrates the practical use of
the proposed methods.
March 4
Speaker: Piotr Kokoszka, Department of Statistics, Colorado State University
Title: Fundamental concepts of functional data analysis
and an application to global cooling
Abstract: The talk will consist of two parts. In the first part I
will review the basic concepts of functional data analysis (FDA), mostly
by showing relevant graphical displays. In FDA, a single observation is
a curve rather than a number. The curves exist as mathematical objects,
but are never fully observed. For example, a child has a height at
any time point, but it is generally recorded about once a year.
In the second part of the talk, I will focus on the problem of testing
if there is a global cooling trend in the ionosphere.
It has been conjectured almost 30 years ago that green house
gases should radiate heat into space once they enter the ionosphere.
This should result in its thermal contraction. The height of
the ionosphere can be approximately measured only directly over a terrestrial
observatory. These observatories are unevenly spaced and have operated
over different time periods. I will explain how the data collected by
them can be used to test the conjecture of the thermal contraction of the ionosphere.
The talk will be accessible to anyone with an undergraduate
background in statistics.
April 1 (reserved)
Speaker: TBA
Title: TBA
Abstract: TBA
April 8
Speaker:
Petia Vlahovska, School of Engineering, Northwestern University
Title: Electrohydrodynamic fluid instabilities: droplet tumbling, surface
vortices, equatorial streaming
Abstract: A classic result due to G.I.Taylor is that a weakly conducting drop bearing
zero net charge placed in a uniform electric field adopts a prolate or
oblate spheroidal shape, the flow and shape being axisymmetrically aligned
with the applied field. In this talk, I will discuss some intriguing
symmetry--breaking instabilities related to the Quincke rotation effect:
drop steady tilt or tumbling, and appearance of vortices along the drop
equator. If time permits I will also present a related instability - the
streaming from the drop equator that creates visually striking
"Saturn-rings" around the drop.
April 15
Speaker
Christian Kern, Institute of Applied Physics, KIT
Title: On the Hall Effect in Composites
Abstract: The Hall effect describes the appearance of a transversal voltage, the so-called Hall voltage, in a
current-carrying slab of material that is subject to a magnetic field. The corresponding material
property, which relates the Hall voltage to the current, magnetic field, and thickness of the slab,
is the so-called Hall coefficient. In composites, very unusual values of the effective Hall
coefficient can be realized by tailoring their microscopic structure.
In this talk, based on the work of Marc Briane and Graeme Milton, I will show that the effective
Hall coefficient of a single-constituent porous composite can be sign-inverted with respect to
the Hall coefficient of the constituent material and how we were able to demonstrate this
effect experimentally. Furthermore, I will discuss structures with lower symmetry, which are
described by a rank-two tensor instead of a scalar Hall coefficient. Finally, I will elaborate on
corresponding bounds and show how the theory can be extended to account for non-trivial
distributions of the magnetic permeability.
Joint work with Graeme Milton, Muamer Kadic, and Martin Wegener.
June 12, Room LCB 222, Time 4pm - 5pm
Speaker Robert Viator, Department of Mathematics, Southern Methodist University
Title: Perturbation of Steklov Eigenvalues in Nearly-Circular Domains
Abstract: We will explore the shape-perturbation of Steklov eigenvalues in
nearly-circular domains. The shape perturbation is determined by a
perturbation parameter epsilon > 0 and a perturbation function, rho,
defined on the circle. Analyticity in the parameter epsilon will be shown
provided rho is smooth enough, and the resulting expressions for the first
and second order corrections in epsilon will be provided. We will also
discuss the consequences of these calculations, particularly isoperimetric
and local optimization results for certain Steklov eigenvalues.
epshteyn (at) math.utah.edu).
Past lectures: Fall 2018, Spring 2018, Fall 2017, Spring 2017, Spring 2016, Fall 2015, Spring 2015, Fall 2014, Spring 2014, Fall 2013, Spring 2013, Fall 2012, Spring 2012, Fall 2011, Spring 2011, Fall 2010, Spring 2010, Fall 2009, Spring 2009, Fall 2008, Spring 2008, Fall 2007, Spring 2007, Fall 2006, Spring 2006, Fall 2005, Spring 2005, Fall 2004, Spring 2004, Fall 2003, Spring 2003, Fall 2002, Spring 2002, Fall 2001, Spring 2001, Fall 2000, Spring 2000, Fall 1999, Spring 1999, Fall 1998, Spring 1998, Winter 1998, Fall 1997, Spring 1997, Winter 1997, Fall 1996, Spring 1996, Winter 1996, Fall 1995.