Fall 2010
Colloquium Schedule
Department of Mathematics
Fall 2010 Colloquia (and other events)
Schedule:
Except as noted, all talks are on Monday, from 4:00 to 4:50pm,
in Avery Hall 115,
preceded by refreshments at 3:30 pm in Avery Hall 348.
Here is a
discussion of
what to expect at Colloquium talks and
here
is a discussion of what might make a good colloquium talk.
Go here
for information on scheduling a future colloquium
and eventually
here
for
Spring 2011
Colloquia schedule.
Go here
for tentative
scheduling for colloquia next semester.
Mon Aug 23:
First
Day of classes
Aug 23: No colloquium
Aug 30:
Speaker: David Pitts
Affiliation:UNL
Local host:
Title:
Norming Algebras
and Isomorphisms of Operator Algebras
Abstract: An operator algebra is a closed subalgebra of the algebra of all continuous linear
operators
on a Hilbert space. Such an algebra can be viewed in the category of Banach
algebras (where the maps
are bounded homomorphisms). But one can change the family of maps
from bounded homomorphisms
to "completely bounded'' homomorphisms to get a new category,
which turns out to be an extremely
useful viewpoint.
In this talk, I'll discuss a condition which ensures that every bounded homomorphism is
completely
bounded. This condition has implications for an old, unsolved question of Richard
Kadison, which
asks whether every bounded representation of a C*-algebra on a Hilbert space is
similar to a
*-representation. Time permitting, I will also give several applications.
(Sample application: a new
proof of a 1965 theorem of Gardner, which gives the structure of
any isomorphism between two
C*-algebras.)
Mon
Sep 6: Labor Day/no colloquium
Sept 13:
Speaker: Gro Hovhannisyan
Affiliation: Kent State University, Ohio
Local hosts: Lynn Erbe and Allan Peterson
Title:
Asymptotic Behavior of a Planar Dynamic System on a Time Scale
Abstract: We establish asymptotic representations of solutions of
planar dynamic systems on a time
scale
by using a new version of Levinson's asymptotic theorem with the error estimates given in terms
of phase functions and characteristic functional.
In the paper (J. Math. Phys. 2009,50,123507) we
used these representations to study Dirac's non-autonomous equation.
Results of this work will be
used in the forthcoming paper to study discrete Dirac's equation.
Sept 20:
Speaker: Lucas Sabalka
Affiliation: Binghamton University
Local hosts: Allan Donsig and Susan Hermiller
Title:
Braid Groups on Graphs
Abstract:
One class of groups of great importance is Artin's
classical and much studied braid groups.
These groups may be defined
topologically, in terms of configurations of points on a disk. A natural
generalization of classical braid groups is to replace the disk with other
spaces. This leads us to
consider braid groups on graphs. In this talk, we
will discuss the definition of graph braid groups and
give a survey of some
known results. In particular, we will discuss the relationship between
graph
braid groups and right-angled Artin groups, and possibly the
isomorphism problem for certain tree
braid groups.
Sept 27:
Speaker:
Kyle Fey
Affiliation:UNL
Local host: Mikil Foss
Title:
Young measures associated with sequences in Morrey spaces
Abstract:
Given a weakly convergent sequence of functions, its weak limit describes the limiting
behavior of the averages of those functions. Young measures are parametrized probability measures
that provide a way to capture the oscillatory behavior of weakly convergent sequences of functions as
well as their average behavior. After spending some time discussing weak convergence in L^p
spaces and introducing Young measures, I will present results that characterize those
Young
measures that are generated by sequences bounded in Morrey (or Sobolev-Morrey) spaces. An
application of this result to variational problems allows one to use information about a minimizing
Young measure to determine how much Morrey (or Sobolev-Morrey) regularity one can expect a
minimizing sequence to possess.
Oct 4: Math movie: "Hard Problems"
Local host: Steve Dunbar
Title:
Hard Problems
Abstract:
"Hard Problems" is the MAA-produced documentary about the extraordinarily gifted
students who represented the United States in 2006 at the world's toughest math
competition—the
International Mathematical Olympiad (IMO). "Hard Problems" focuses
on the dedication to
mathematics shown by the coaches and team members, as well
as the importance of the support of the
student's parents. The film also gives
the general public a glimpse of the hard work and pressure that
the students face at the IMO.
Oct. 11: No colloquium
Oct. 18-19: October break/no colloquium
Oct. 25:
Speaker: Jean-Paul Zolesio
Affiliation: CNRS-INLN, Sophia
Antipolis, France
Local host: Lorena Bociu
Title:
The Shape Derivative in Partial Differential Equations
Abstract:
In the first part of the talk I will introduce the notions of moving domain,
flow map and
shape derivative, and use the solution to the Laplace-Neumann
boundary value problem as an
example. Then I will discuss the extension of
derivative of functionals that are like a double
integral,
where the first integral is from 0 to tau, and the next is over Omega_t, of y^2_t dx dt,
by introducing the new concept of "transverse vector field". Such functional derivatives
are used
in the linearization of time depending coupled fluid-structure problem (joint work with L.Bociu).
This colloquium is funded by the
UNL Research Council.
Nov. 1:
Fourth Annual Pi Mu Epsilon Lecture
Speaker:
Prof. James A.
Sellers
Affiliation: Pennsylvania State University
Local host: Stephen Hartke, Petronela Radu
Title:
Revisiting What Euler and the Bernoullis Knew About Convergent
Infinite Series
Abstract:
All too often in first-year calculus classes, conversations
about infinite series stop with
discussions about convergence or
divergence. Such interactions are, unfortunately, not often
illuminating or intriguing. Interestingly enough, Jacob and Johann
Bernoulli and Leonhard Euler (and
their contemporaries in the early 18th
century) knew quite a bit about how to find the *exact* values of
numerous families of convergent infinite series. In this talk, I will
show you two sets of *exact* results
in this vein. The talk will be
accessible to anyone interested in mathematics, so bring a friend!
Nov. 8:
Speaker:
Terry Loring
Affiliation:University of New Mexico
Local host: David Pitts
Title:
Topological Insulators and Joint Approximate Diagonalization of Matrices
Abstract:
Only commuting families of self-adjoint matrices can be jointly diagonalized,
but that does
not stop physicists and electrical engineers from trying.
Settling for a unitary change of basis that brings
all the matrices
``close'' to diagonal is often good enough. In signal processing,
joint approximate
diagonalization has led to effective algorithms
for blind source separation. In quantum chemistry, joint
approximate
diagonalization can find a basis of low-energy space consisting of
localized electron
states.
There are limits to joint approximate diagonalization, some of which
can be explained by K-theory.
The choice of scalar field is surprisingly
important. Theorems regarding almost commuting unitary
matrices cannot
be translated properly to results on almost commuting orthogonal matrices
unless one
takes care with the distinction between KO and KU
groups.
Much of the talk will be on joint work with Matt Hastings on topological
insulators. These are
intriguing states of matter where a sample is
conducting on the boundary, yet insulating in the interior.
Numerical
models of topological insulators suggest that fast algorithms to distinguish
topological
insulators from ordinary insulators can be found based
on the K-theory obstructions to joint
approximate diagonalization.
This colloquium is funded by the
UNL Research Council.
Nov. 9: UNL Math Day
Nov. 12:
UNL Masters Week Special Seminar
Speaker:
Therese McGuire
Affiliation:Northwestern University
Local host: John Meakin
Title:
Tobin Meets Oates: Solidarity and the Optimal Fiscal Federal Structure
Abstract:
A longstanding question in public economics is whether the delivery of
publicly provided
goods and services is more efficient if undertaken largely
by the national government (i.e., in a
centralized system) or largely by
fiscally-empowered sub-national units of government (i.e., in a
decentralized system). For the two largest components of public spending in
the U.S. - education and
health care - the theory would seem to point to
decentralized provision (Oates, 1972). We specify a
model with a central
government and n regional governments and use constrained maximization to
search for the optimal system. We are unable to derive closed-form solutions
and turn to simulations.
Through simulations, we are able to demonstrate
that, if people have a preference for providing equal
access to goods and
services that determine life chances, services that arguably include
education and
health care, the optimal fiscal federal structure is neither
centralization nor decentralization, but a
system whereby the central
government guarantees a minimum level of expenditure across all regions,
and
regions can choose to tax themselves to finance a level of spending above
the guaranteed minimum.
This guaranteed minimum system dominates the two
polar systems of complete decentralization
and complete centralization for a
wide range of preferences for specific egalitarianism (Tobin, 1970),
or
solidarity.
The seminar will be from 4:00-4:50pm on Friday, November 12 in Avery 106.
There will be a
reception preceding the seminar from 3:30-4:00 in Avery 348.
Therese McGuire will be at UNL as the College of Arts and Sciences Master for masters' week.
She is an alumna of UNL, with dual majors in math and economics. She went on to do a PhD in
economics at
Princeton and to have a distinguished career at Northwestern.
Nov. 15: No colloquium
Speaker:
Affiliation:
Local host:
Title:
TBA
Abstract:
Nov. 22:
Speaker:
Zoran Sunik
Affiliation: Texas A&M University
Local host: Susan Hermiller
Title: Hanoi Twin Towers
Abstract:
We present results related to a certain self-similar group of rooted tree automorphisms
modeling
the classical Hanoi Towers Problem. Some of the results concern the structure of the group,
while
some represent applications of our understanding of this structure back to the combinatorial
world
(e.g., we solve the Hanoi Twin Towers Problem).
Fri
Nov. 26:
Thanksgiving break/no colloquium
Nov. 30: Special Lecture, 2 pm, Room 19 Avery Hall
Speaker:
Joerg Kliewer
Affiliation: New Mexico State University
Local host:Christine Kelley
Title:
Coding Strategies for the Wiretap Channel and for Secure Network Coding
Abstract:
In this talk we consider two related aspects of information theoretic secrecy
which recently
have gained some attention in the community: First, we consider
transmission over Wyner's wiretap
channel where both the main and the wiretapper's
channel are binary erasure channels. We show that
the recently proposed class of
polar codes asymptotically can achieve capacity on a degraded version
of this channel,
and for finite blocklength compare these codes with a new construction based on
bilayer
LDPC codes. In the second part we then consider secure network coding over networks with
link erasures and unequal link capacities in the presence of a wiretapper that can
wiretap any subset of
k links. In contrast to the case with equal link capacities,
we show that for unequal link capacities, the
secrecy capacity is not the same in
general when the location of the wiretapped links is known or
unknown. An example
is given to show that when the location of the wiretapped links is unknown the
cut-set bound is not achievable. We give achievable strategies where random keys
are canceled at
intermediate non-sink nodes or injected at intermediate non-source
nodes.
Dec. 6:
Speaker:
Paul Sacks
Affiliation:Iowa State University
Local host: Daniel Toundykov
Title:
The Singular Inverse Sturm-Liouville Problem
Abstract:
We consider inverse eigenvalue problems associated with the
Sturm-Liouville operator
Alφ = - φ″ + (V(x)+ (l (l +1) ⁄ x2) ) φ , 0<x<1,
with domain D(Al)
suitably defined to incorporate boundary conditions. Here l is a
nonnegative
integer.
In a typical problem one is given certain information
about the eigenvalues and
eigenfunctions of D(Al) and seeks to determine the
potential V. I will review some of the classical
results in the
regular (l =0) case, and
then discuss some more recent work on the singular (l ≥ 1)
case.
Mon Dec 13:
First
Day of Fall Semester Final Exams
Dec. 13: OPEN
Speaker:
Affiliation:
Local host:
Title:
TBA
Abstract:
Later.
Current Schedule of
Open Dates for Spring 11
eventually
2011: Friday April 1
Rowlee Lecture
Speaker: David Eisenbud
Affiliation: University of California, Berkeley
Local Host:Lucho Avramov and Roger Wiegand
Title: To be announced
Abstract: