Department Colloquium, Spring
2007
| Colloquium |
Seminars |
Clec Lectures |
Public Lectures |
Distinguished Lectures |
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Date
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Speaker
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Title
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| Friday, January 12, 2:00 - 3:00 p.m., MP3314 |
Mel Henriksen, Harvey
Mudd College |
Removing sets from connected product
spaces while preserving connectedness
|
| Friday, January 26, 3:00 - 4:00 p.m.,
MP3314 |
Jian Yang,
Department of Industrial and Manufacturing Engineering, New Jersey
Institute of Technology |
Coordinated Dynamic Control of Marketing and
Production |
| Friday, February 2 , 3:00 - 4:00 p.m.,
MP3314 |
Linghai Zhang, Lehigh University |
Cauchy problems for some partial differential
equations: temporal decay estimates and spatial regularity |
| Friday, February 9, 3:00 - 4:00 p.m., MP3314 |
Gavin Seal, McGill University
(Canada) |
Galois
connections and monads |
| Friday, February, 16, 3:00 - 4:00 p.m.,
MP3314 |
Seung Wook Lee,
Korea Atomic Energy Research Institute and National
Institute of Standards and Technology, Gaithersburg, MD, USA |
Neutron imaging technique and applications at the
research reactors of KAERI and NIST |
| Friday, March 2, 3:00 - 4:00 p.m.,
MP3314 |
Lixin Yan, Zhongshan University and University of
Missouri-Columbia
|
Hardy and BMO spaces associated with
operators |
| Friday,March 9, 3:00 - 4:00 p.m.,
MP3314 |
Shigeki Akiyama, Niigata University (Japan) |
Discretized rotation and domain
exchange |
| March 12-16 |
--Spring break-- |
| Thursday, March 22, 3.30-4.30pm,
MP3314 |
Florian Potra, University of Maryland |
Modern Optimization Techniques in Bioinformatics |
| Friday, March 23, 3:00 - 4:00 p.m.,
MP3314 |
Xinping Sun, Missouri State |
Applications of Radial Basis Functions in Uniform Distribution and Discrepancy Estimates |
| Friday, March 30, 3:00 - 4:00 p.m.,
MP3314 |
Goran Lesaja, Georgia Southern U.
|
A New Class of Polynomial Interior-Point Algorithms for P*(k)-Linear Complementary
Problems
|
Thursday, April 5, 6:00-7:00 p.m., IT 1005
CLEC Lecture |
Raphael Sorkin, University of Syracuse |
Genealogy of spacetime |
| Friday, April 6, 3:00 - 4:00 p.m.,
MP3314 |
Raphael Sorkin, University of Syracuse |
Is spacetime a past-finite poset?
|
| Friday, April 13, 3:00- 4:00 p.m.,
MP3314 |
David Benko, Western Kentucky University |
A new solution to Hilbert's third problem |
Thursday, April 19, 6:00-7:00 p.m., IT 1004
Distinguished Lecture |
Gilbert Strang, M.I.T. |
Teaching and Learning Computational Science and
Engineering
|
| Friday, April 20, 2:00- 3:00 p.m.,
MP3314 |
Gilbert Strang, M.I.T. |
Maximum Area and Minimum Cuts with New Measures
of Perimeter |
| Friday, April 27, 3:00-
4:00 p.m., MP3314 |
TBA |
TBA |
Details of Spring 2007 lectures
1. Friday, January 12, 2pm-3pm, MP 3314
Speaker: Mel Henriksen, Harvey Mudd
College
Title: Removing sets from connected product spaces while
preserving connectedness
Abstract:
As
per the title, the nature of sets
that can be removed from a product of more
than one
connected, arcwise connected, or point arcwise
connected spaces
while preserving the appropriate kind
of connectedness is studied. This can
depend on the
cardinality of the set being removed or sometimes just
on
the cardinality of what is removed from one or two
factor spaces. Sometimes
it can depend on topological
properties of the set being removed or its trace
on
various factor spaces. Some of the results are
complicated to prove
while being easy to state.
Sometimes proofs for different kinds of
connectedness
are similar, but different enough to require
separate
proofs. Many examples are given to show that part of
the
hypotheses of theorems cannot be dropped, and some
examples describe results
about spaces whose
connectedness can be established directly but not
with
the help of our results. A large number of examples
are given for
such purposes.
2.Friday, January 26, 3pm-4pm, MP3314
Speaker: Jian Yang, New Jersey
Institute of Technology
Title: Coordinated Dynamic Control of Marketing and Production
Abstract:
We study the dynamic profit
maximization problem for a firm which exercises control on both marketing and
production. The firm's marketing effort impacts the demand it faces through both
multiplicative and additive terms, and the current-period demand in turn affects
future demand in a dissipating fashion. Under linear-cost and zero-leadtime
assumptions, we show that the firm should follow base-point policies for both
marketing and production, whereas trends of the base points reflect the
complementarity between marketing and production. For the special case where
demand is uncorrelated and purely additive, we establish several trends under
which optimal policy forms change with problem parameters. Our computational
study points out directions in which both marketing and production efforts
should follow when parameters for the problem setting change. We also find
two-point characterizations for the special-demand case when leadtimes are
nonzero.
3. Friday, February 2 , 3:00 - 4:00 p.m.,
MP3314
Speaker: Linghai Zhang, Lehigh University
Title: Cauchy problems for some partial
differential equations: temporal decay estimates and spatial
regularity
Abstract.
Motivated by many very interesting
results, we will establish ex-
act limits for the L2 -norm multiplied by the
sharp rate of decay of the global
solutions, as time approaches positive
infinity, of the Cauchy problems for an
abstract dissipative partial
differential equation in n-dimensional space, where
n ≥ 1. The model
includes the one-dimensional cubic Korteweg-de Vries-
Burgers equation, the
one-dimensional cubic Benjamin-Ono-Burgers equation,
the two-dimensional
nonlocal quasi-geostrophic equation, the n-dimensional
incompressible
Navier-Stokes equations and the n-dimensional magnetohydro-
dynamics
equations as particular examples.
The main ideas in the analysis are Fourier
transform, time-dependent de-
composition of frequency space and lower limit
and upper limit estimates. For
certain other model equations (for example,
the fluid dynamics equations in
geophysics, the quasi-geostrophic equations
with fractional-order derivative,
the Cahn-Hilliard equation, the
non-degenerate system of filtration type, and
the Kuramoto-Sivashinsky
equation), which are not covered by the aforemen-
tioned abstract
differential equation, we can apply the same idea as above to
obtain the
exact limit of the L2 -norm of the global solutions.
4. Friday, February 9 , 3:00 - 4:00 p.m.,
MP3314
Speaker: Gavin Seal, McGill University (Canada)
Title: Galois connections and
monads
Abstract.
Finding their origin in Galois
theory, Galois connections have made
their way into many areas of
mathematics, where they reveal how not
necessarily isomorphic ordered
structures may nonetheless be closely
related. For example, the existence of
a Galois connection between an
ordered set X and its powerset can be used to
determine whether X is a
complete lattice or not. This fact can be further
exploited to reveal
the deep algebraic nature of certain ordered
sets.
5. Friday, February 16 ,
3:00 - 4:00 p.m., MP3314
Title:
Neutron imaging technique and applications at
the research reactors of KAERI and NIST
Speaker: Seung Wook Lee,
Korea Atomic
Energy Research Institute and
National Institute of Standards and
Technology
Abstract:
The
neutron imaging is complementary to x-ray imaging and only available at the very
expensive neutron sources around the world. In this talk, techniques and
activities mainly at the two neutron facilities will be introduced, which are
HANARO of the KAERI, Korea and NIST Center for Neutron Research, MD. The
traditional application area of neutron imaging lies in the non-destructive
testing of nuclear fuel, aircraft components, explosive detection, and so on.
Owing to the digital detectors and image processing techniques developed for the
last decade, three dimensional tomographic imaging, dynamic quantitative
imaging, and phase imaging are now being
routinely available for many
scientific communities. One of the hottest
application areas of the neutron
imaging at the moment is visualizing water inside the operating fuel cell that
is the key component for the hydrogen economy. Special emphasis will be given on
this together with the on-going research on the phase imaging using the silicon
grating method.
6. Friday, March 2, 3:00 - 4:00 p.m.,
MP3314
Speaker: Lixin Yan, Zhongshan University and
University of Missouri-Columbia
Title: Hardy
and BMO spaces associated with operators
Abstract:
In this talk, we will discuss some
Hardy and BMO spaces associated
with operators, which are characterized by
relevant estimates of
generators of semigroups with suitable heat kernel
bounds. Depending
on the assumptions of these generators, we will obtain
characterizations
of the classical Hardy and BMO spaces or obtain new Hardy
and BMO
spaces associated with operators.
7. Friday, March 9, 3:00-4:00 p.m.,
MP3314
Speaker: Shigeki
AKIYAMA
Title:
Discretized rotation and domain
exchange.
Abstract:
We
study a simple recursion on $\mathbb{Z}^2$ defined by
an inequality $0\le
a_{n+2}+\lambda a_{n+1}+a_n<1$ with $|\lambda|<2$.
This is a kind of
discrete rotation and all orbits are expected to be
eventually periodic. We
prove in some cases this conjecture using domain
exchange dynamics.
8. Thursday, March 22, 3.30-4.40pm, MP3314
Speaker: Florian Potra, University of Maryland
Title: Modern Optimization Techniques in Bioinformatics
Abstract:
In the post-genomic era, proteomics has become one of the most
important research topics of modern science, opening new doors and
potentially influencing medical science for years to come. By
separating, cataloging, and comparing proteins from normal and
diseased cells and tissues we gain invaluable knowledge about the
changes taking place in complex biological systems at the molecular
level, which in turn leads to better diagnostics and therapeutics. Two
dimensional gel (2D Gel) electrophoresis, used in conjunction with a
protein identification method such as mass spectrometry (MS), could
provide the front end for a high-throughput analysis tool capable of
comparing protein expression between large collections of samples.
However the lack of reliable automated techniques for gel alignment,
forms an important bottleneck to the large scale comparative studies
that are necessary for fulfilling the potential of proteomics. In the
talk we show that modern optimization techniques may be able to
remove this bottleneck. We present new algorithms for image alignment
of two-dimensional polyacrylamide electrophoresis (2D-PAGE) gels. In
contrast with previous approaches that considered only pairwise
alignment, we consider algorithms for the alignment of a whole
collection of gels. A synthetic gel, containing some "ideal landmarks"
is constructed together with a family of transformations, so that for
each gel from the collection there is a unique transformation that
maps that gel into the synthetic gel in such a way that the gel's
landmarks are mapped into a very small neighborhoods of the
corresponding ideal landmarks. Both the ideal landmarks and the family
of transformations are obtained as the solution of a large-scale
quadratic optimization problem which can be efficiently solved by
interior-point methods.
9. Friday, March 23, 3.00 pm-4.00 pm
Speaker: Xinping Sun, Missouri State
Title: Applications of Radial Basis Functions in Uniform Distribution and Discrepancy Estimates
Abstract:
The uniform distribution of a large number of points in
a domain or a manifold is an important problem in many areas of mathematics
and statistics. The quantitative measurement for uniform distribution
of points is referred to as "discrepancy estimates". In this talk, we
will explore the applications of radial basis functions in some aspects
of uniform distribution and discrepancy estimates.
10. Friday, March 30, 3.00 pm-4.00 pm
Speaker: Goran Lesaja, Georgia Southern University
Title: A New Class of Polynomial Interior-Point Algorithms for P*(k)-Linear Complementary
Problems
Abstract:
11. Thursday, April 5, 6.00 pm-7.00 pm: CLEC LECTURE in IT 1005
Speaker: Raphael Sorkin, University of Syracuse
Title: Genealogy of Spacetime
Abstract:
Among the various ideas put forward in the search for a theory
of quantum gravity, the causal set hypothesis is distinguished
by its logical simplicity and by the fact that it incorporates
the assumption of an underlying spacetime discreteness
organically and from the very beginning.
In the way that it has developed, the causal set hypothesis has
given rise to a mathematical framework (the "dynamics of
sequential growth") in which time is an active process of
"becoming" that can be identified with the continual birth of
new elements of the causal set.
12. Friday, April 6, 3.00 pm-4.00 pm
Speaker: Raphael Sorkin, University of Syracuse
Title: Is spacetime a past-finite poset?
Abstract:
The causal set -- mathematically a locally finite ordered set or
``poset'' -- is a candidate discrete substratum for spacetime.
I will introduce this idea and describe some aspects of causal
set kinematics, dynamics, and phenomenology, including, as time
permits, a notion of fractal dimension, a stochastic growth
dynamics, and an idea for explaining some of the puzzling large
numbers of cosmology. I will also mention some questions of
mathematical interest that have arisen in this connection.
13. Friday, April 13, 3.00 pm-4.00 pm
Speaker: David Benko, Western Kentucky University
Title: A new solution to Hilbert's third problem
Abstract:
In his correspondence Gauss has expressed his regret to
F. Bolyai and Gerling that the definition of the volume of polyhedra
depends upon the method of exhaustion, i.e., on a method which uses a
limit process. In 1900 Hilbert reiterated the question in his
celebrated list of 23 problems. He suspected that there exist two
polyhedra having the same volume which are not equidecomposable, and so
the exhaustion method cannot be avoided. Dehn confirmed this in
1902 by showing that the regular tetrahedron and the cube are not
equidecomposable. That is, one cannot decompose the regular
tetrahedron into a finite number of polyhedra which can be
rearranged to form the cube. We will give a simple new proof of
this theorem which was overlooked for a century.
14. Thursday, April
19, IT 1005, Distinguished Lecture
Room IT 1005
Speaker: Gilbert Strang, M.I.T.
Title: Teaching and Learning Computational Science and
Engineering
Abstract.
I would like to discuss (together
with the audience!) how we can
go forward with computational science and
engineering. Getting students
involved has to be the key -- they will
develop new ideas later (and better
use of software). It is a fascinating
and creative subject that combines
applied mathematics with scientific
computing.
One question is how to present both of those essential
parts. My goal
is that each lecture discusses a model problem and a code to
solve it.
This MIT course is popular with engineering students and their
departments,
who want exposure to ideas and also to software (especially
MATLAB).
The main sections of the course are Applied Linear Algebra,
Differential Equations, Finite Differences and Finite Elements,
Fourier
Methods, Analytical Methods, Large Sparse Systems, and Optimization.
The
starting point is to understand the second difference matrices (entries
1,
-2, 1) that appear everywhere in scientific computing and
simulation.
The need to move beyond the older courses in engineering
mathematics,
and connect directly to computing, is widely recognized. A
pure
software course misses the foundations for understanding new problems.
The combination of analysis with computational science and engineering
is powerful.
The lecture will be less solemn than this
abstract.
15. Friday, April 20 , 2:00 - 3:00 p.m., MP3314
Speaker: Gilbert Strang, M.I.T.
Title: Maximum Area and Minimum Cuts with New
Measures of Perimeter
Abstract.
The oldest competition for an
optimal shape (area-maximizing)
was won by the circle. But if the fixed
perimeter is measured by
the line integral of |dx| + |dy|, a square would
win. Or if the
boundary integral of max(|dx|,|dy|) is given, a diamond has
maximum area.
For any norm in R^2, we show that when the integral of
||(dx,dy)||
around the boundary is prescribed, the area inside is maximized
by
a ball in the dual norm. When || || is the l^2 norm, that ball is a
circle. Our proof comes directly from the calculus of variations.
This isoperimetric problem has application to computing minimum cuts and
maximum flows in a plane domain. There the key is Cheeger's
isoperimetric
problem with shape inside a fixed set. The problem arises in
medical imaging.
Department Colloquium Archives
Please direct questions or comments regarding the
colloquium to Frederic
Mynard
( Last updated: April 3,
2007.)