January
===
Date:: 30, 2007 (Tuesday)
Title:: Self-avoiding walks, connective constants, and generatingfunctionology
Speaker:: Jason Bode
Email:: [e-mail]
From:: Cornell University
Time:: 3:30 pm
Location:: NH 276
Status:: confirmed (TJ)
Misc::
Dinner:: personnel committee
Abstract:: We begin by examining random walks and self-avoiding walks.
Both will be defined and illustrated on a simple graph. We will encounter
the need for connective constants, with the focus of the talk on using
generatingfunctionology to calculate the connective constant of a
particular graph. Finishing the talk will be an undeniably beautiful
result, coupled with an open question.
===
Date:: February 1, 2007
Title:: General Outlier Detection for the Recurrent Event Setting
Speaker:: Jonathan Quiton
Email:: [e-mail]
From:: University of South Carolina
Time:: 3:40 pm
Location:: NH 276
Status:: confirmed (TJ)
Misc::
Dinner:: personnel committee
Abstract:: Outlier detection is well known in the single-sample and
regression setting but not in the recurrent event setting where the observed
inter-event times are not normally distributed and contains dependent
components. In this talk, we consider the problem of detecting whether a
specific inter-event time within a subject or whether the subject itself is
an outlier. We limit this talk to a situation where the stochastic process
governing event occurrences for each subject or unit is a homogeneous
Poisson process (HPP), and the mathematical framework utilized to develop
the outlier detection procedures is similar to that of Neyman's smooth
embedding in the general case. Through this framework, we are able to derive
jackknife-based procedures. We discuss several conditioning schemes for the
sampling distributions of the test statistics, in particular, we discuss the
relevance of the Conditionality Principle in this problem. Results of
simulation studies regarding power comparisons of the different conditioning
schemes will be presented, and the procedures will be illustrated by applying
to Proschan's air-conditioning data set. Finally, we describe how
the procedures are extended the results to the general recurrent event setting.
===
Date:: February 6, 2007 (Tuesday)
Title:: Diffusion Flame Stability
Speaker:: Amy Moore
Email:: [e-mail]
From:: Alma College
Time:: 4:00 pm
Location:: NH 276
Status:: confirmed (TJ)
Misc::
Dinner:: personnel committee
Abstract:: We will discuss the solutions of a boundary value problem
arising from a one-dimensional diffusion flame. The effect of parameter
values on the steady state, or time-independent, solutions will be
addressed. We will also discuss the stability of the steady state
solutions by analyzing the eigenvalues of the linearized system. Lastly,
we will identify the parameter values at which periodic solutions exist
and classify the periodic solutions as stable or unstable.
===
Date:: February 8, 2007
Title:: Formalizing and analyzing (and even breaking part of) the Kerberos
authentication protocol
Speaker:: Aaron Jaggard
Email:: [e-mail]
From:: Tulane University
Time:: 3:40 pm
Location:: NH 276
Status:: confirmed (TJ)
Misc::
Dinner:: personnel committee
Abstract:: We survey an ongoing project to formalize and analyze the
Kerberos 5 protocol suite. This has provided a real-world application for
various formal mathematical methods of protocol analysis and has
involved the development of new proof techniques for the MSR framework
and the discovery of a design-level flaw in the public-key extension
(PKINIT) to the basic Kerberos protocol. We also discuss positive
results — proofs of authentication and confidentiality at various
levels of detail — including formal verification of the fix of PKINIT
that was adopted in response to the flaw we discovered.<br>
&nbsp;<br>
After reviewing the Kerberos 5 protocol, we discuss our abstract-level
(Dolev-Yao style) results for the basic, cross-realm, and public-key
versions of the protocol. We then outline our recent work using the
Backes-Pfitzmann-Waidner computational library as well as future
directions for this research.<br>
&nbsp;<br>
This work is joint with Iliano Cervesato and Andre Scedrov; various
parts of it are also joint with Fred Butler, Chris Walstad, Joe-Kai
Tsay, and Michael Backes.
===
Date:: February 12, 2007 (Monday)
Title:: Applying Spectral Theory to the Study of Bose-Einstein Condensates
Speaker:: Todd Kapitula
Email:: [e-mail]
From:: University of New Mexico
Time:: 3:30 pm
Location:: NH 276
Status:: confirmed (TJ)
Misc::
Dinner:: personnel committee
Abstract:: Especially since the Nobel Prize experimental work conducted in
the mid-90's, there has been a great deal of mathematical study of the
governing equations for the dynamics of matter waves for Bose-Einstein
condensates (BECs). The purpose of this talk is two-fold. First, I will
give a brief description as to how an experimentalist can create a BEC, as
well as some of the interesting dynamics and structures (e.g., vortices,
multi-poles, and rings) associated with the condensate. Afterwards, I will
discuss an interesting mathematical problem which comes up in the stability
study of these structures; in particular, the problem of determining the
manner in which the eigenvalues of a symmetric matrix H correspond to the
eigenvalues of <i>JH</i>, where <i>J</i> is a skew-symmetric matrix.
===
Date:: February 15, 2007
Title:: Dropping Quiz Scores and Other Matters
Speaker:: Thomas Scofield
From:: Calvin College
Time:: 3:40 pm
Location:: NH 276
Abstract:: You may have encountered the following problem in some guise:
Given <i>n</i> quiz scores not all of equal value with <i>r</i> of them to
be omitted from the calculation of a grade, how do you determine which
<i>r</i> to remove so that the percentage on the remaining quizzes is
maximized? The obvious approaches do not usually yield the optimal percentage
which, to those who have taken statistics, is a familiar result known as
Simpson's paradox. A recent paper of Kane and Kane from the June, 2006
issue of Mathematics Magazine (Vol. 79, No. 3) gives an efficient algorithm
for solving this problem. We will look at this algorithm and why it works.<br>
&nbsp;<br>
A seemingly unrelated problem is that of constructing a Voronoi diagram.
When one has <i>n</i> nodes (perhaps cell phone towers) distributed through
a planar region, a Voronoi diagram shows a partitioning of that region into
sets of points closest to the various nodes. Kane and Kane's method for the
above problem bears a resemblance to Fortune's algorithm for producing
Voronoi diagrams, which we will describe.
===
Date:: February 21, 2007
Title:: Kummer's Conjecture
Speaker:: Marilyn Myers
Email:: [e-mail]
From:: Queen's University
Time:: 3:30 pm
Location:: NH 276
Status:: confirmed (TJ)
Misc::
Dinner:: personnel committee
Abstract:: In 1851 Kummer predicted a formula for the asymptotic growth of
ratios of class numbers of cyclotomic fields. We will discuss what
Kummer's conjecture means, what is known about it, and how it may be
generalised.
===
Date:: February 22, 2007
Title:: Circle Packings and Tensegrity Frameworks
Speaker:: William Dickinson
Email:: [e-mail]
From:: Grand Valley State University
Time:: 3:40 pm
Location:: NH 276
Status:: confirmed (TS)
Misc::
Dinner::
Abstract:: Dense packings of <i>n</i> equal circles in a unit square have
been studied for over thirty years. The globally densest packings have
been determined for all values of <i>n</i> up to about 27 and there are
candidate best arrangements for many larger values of <i>n</i>. While there
are many techniques for finding dense packings (in 1970 Goldberg apparently
used actual coins!), this talk will focus on a little utilized connection
between locally maximally dense arrangements and the rigidity of certain
kinds of tensegrity frameworks. Using this connection it turns out that
merely counting the contacts in a packing can tell you about the local
density of that packing. The basics of tensegrity frameworks will be
explained and generalizations to packings on tori (which will be a topic
for undergraduate research in an REU in the summer of 2007) will be briefly
discussed. This talk will be illustrated with many examples and should be
accessible to any student with knowledge of some proof techniques,
calculus, and linear algebra. <br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
<IMG SRC="http://www.calvin.edu/~scofield/courses/m391/S07/dickinsonAbstractPicture.jpg" HEIGHT=400 WIDTH=676>
===
Date:: March 1, 2007
Title:: An Examination of the 'Class Number Problem
Speaker:: John Stoughton
From:: Hope College
Time:: 3:40 pm
Location:: NH 276
Status:: (TS)
Misc:: confirmed
Dinner::
Abstract:: In 1801, Gauss first posed what has become known as the &#147;class
number problem&#148; which he was never able to solve. In fact, it remained
unsolved until 1983. But exactly what IS the class number problem and what
was unusual about its proof? What is special about the integer 163? More
philosophically, what is a number? We will ponder these and other
interesting questions.
===
Date:: March 8, 2007
Title:: Fractals and Self-Similarity
Speaker:: Dorette Pronk
From:: Dalhousie University
Email:: [e-mail]
Time:: 3:40 pm
Location:: NH 276
Status:: confirmed (TS)
Misc::
Dinner::
Abstract:: A subset of <i>n</i>-dimensional space
<b>R</b>^<i>n</i> is called <i>self-similar</i> if it can
be described as a union of scaled down copies of itself. Common
examples of such subsets are rectangles and triangles, but in this
talk we will look at a more interesting class of examples,
namely the IFS-fractals.<br>
If an object is self-similar we can define its dimension according to
the way its volume scales when you change its length parameters.
We will see that for fractals this dimension is not necessarily an
integer. We will then discuss and compare a couple of different ways
of defining the notion of dimension; the Hausdorff dimension and the
box counting dimension. Finally, we will consider some other examples
of classes of fractals and the techniques one could use to study them.
===
Date:: March 15, 2007
Title:: Unwinding the clock: the fundamental group and covering spaces
Speaker:: Paul Goerss
Email:: [e-mail]
From:: Northwestern University
Time:: 3:40 pm
Location:: NH 276
Status:: invited (JT)
Status:: confirmed (JT)
Misc::
Dinner::
Abstract:: When the minute hand completes its circuit, it's back where
it started, but we're all an hour older. Or if I take a complicated
walk, maybe a figure eight around two lakes, I'm back where I started
but have covered a lot of interesting ground. Abstracting to
mathematics, in both cases we have a loop and we wish to keep track of
how we got around it. I'll talk about the fundamental group &#151; a
way of organizing loops &#151; and what they tell us about geometry.
Then I'll talk about covering spaces, which give us a way to talk
about loops and how we get around them.
===
Date:: March 22, 2007
Title:: Spring Break
Speaker:: no meeting
===
Date:: March 29, 2007
Title:: The Least-Squares Property of the Lanczos Derivative
Speaker:: Paul Fishback
Email:: [e-mail]
From:: Grand Valley State University
Time:: 3:40 pm
Location:: NH 276
Status:: tentative (TS)
Status:: confirmed (TS)
Misc::
Dinner::
Abstract:: In his text <i>Applied Analysis</i>, Cornelius Lanczos presented
a technique in which it is possible to &#147;differentiate&#148; by means of
integration. On the surface, Lanczos' derivative formula appears quite odd
and bears little resemblance to the usual derivative. However, its
construction is quite elementary and is based upon the simple concept of
least-squares regression. <br>&nbsp;<br>
This talk begins with a derivation of the Lanczos derivative and a discussion
of its basic properties (e.g. do the usual differentiation rules apply?).
From there, the focus becomes one of constructing higher-order versions of
this derivative. This process demonstrates interesting connections between
the areas of probability, vector space projections, and orthogonal polynomials.
===
Date:: April 5, 2007
Title:: Reclassifying data to combat classification errors: a statistical
method applied to genotyping with Single Nucleotide Polymorphisms (SNPs)
Speaker:: Nathan Tintle
Email:: [e-mail]
From:: Hope College
Time:: 3:40 pm
Location:: NH 276
Status:: on Hope's faculty since last year
Status:: research in biostatistics
Status:: wife is due to have baby in mid October
Status:: set to come in spring
Status:: get back with him about specific date in Jan. or Feb.
Status:: confirmed (TS)
Abstract:: When categorical data is collected, we typically assume that
individuals are categorized correctly. However, errors of classification
can occur. Classification errors can significantly bias estimates and
increase type I and type II error rates when hypothesis testing. For some
automated classification mechanisms, we can model the way that
classification errors occur. I will present a general model for
classification errors in SNP data, and demonstrate how duplicate genotyped
(re-classified) data can be included in genetic tests of association (an
asymptotic &chi;² test and a permutation test) to increase
statistical power. No knowledge of genetics will be pre-supposed. This
talk will make use of some concepts from an introductory statistics course.
===
Date:: April 12, 2007
Title:: Six Degrees of Separation: It's a Small World After All
Speaker:: Mike Stob
Email:: [e-mail]
From:: Calvin College
Time:: 3:40 pm
Location:: NH 276
Status:: confirmed
Abstract:: There are over six billion people in the world but we are each
connected to a surprisingly large number of them by a small chain of
acquaintances. The mathematics of this "small world" phenomenon is
explored in this talk.
===
Date:: April 19, 2007
Title:: My Journey Toward a Christian Perspective on Mathematics
Speaker:: Jim Bradley
Email:: [e-mail]
From:: Calvin College
Time:: 3:40 pm
Location:: NH 276
Status:: confirmed
Abstract:: There are many way to look at mathematics from the position of a
person of faith. There are issues of ethics and values in its application;
there are historical and cultural perspectives; and there are philosophical
issues such as ontology, epistemology, and the nature of truth. Furthermore,
great theologians such as Augustine and Aquinas have written extensively about
mathematics. This talk will survey my efforts, over several years, to come to
grips with many of these issues.
===
Date:: April 26, 2007
Title:: Native American Mathematics
Speaker:: Robert Megginson
Email::[e-mail]
From:: University of Michigan
Time:: 3:40 pm
Location:: NH 276
Status:: invited (TS)
Status:: interested, get back with him in late Sept.
Status:: will come, Mar. or Apr. are good times for him
Status:: confirmed (TS)
Abstract:: This talk will be a fast tour of mathematics in the Americas
before European contact. This is mathematically interesting material in its
own right that does not get enough attention in our standard mathematics
curricula, but part of the admitted purpose is to show that great
mathematical sophistication is not alien to the native cultures of the
Americas, as is sometimes asserted and used as a reason to counsel
Native Americans away from mathematics-based careers. Some examples will
assume a small amount of knowledge of number theory, but the bulk of the
talk is aimed at a general audience, particularly undergraduates who
need not be majoring in mathematics.
===
Date:: May 3, 2007
Title:: Awards and Pizza
Time:: 3:30 pm
Location:: NH 276
Status:: confirmed
Abstract:: Come enjoy the comradeship of fellow students and faculty as the
school year comes to a close. Pizza and beverages will be served at 3:30
pm in NH 282. At 3:40, we will have a brief presentation of awards for
submissions to the Problem of the Week over the past year, announcement
of the recipients of next year's Departmental Named Scholarships,
culminating with the announcement of this year's winners of the department's
highest awards for graduating majors, the Rinck and Boonstra Prizes.
===
Date:: TBA
Title::
Speaker:: Tim Pennings
From:: Hope College
Email:: [e-mail]
Time:: 3:40 pm
Location:: NH 276
Status:: has new talk on bifurcations (Elvis, his dog, again featured)
Status:: not invited because already 2 talks from Hope people in spring
Status:: should be personally invited in 2007-08 (not only
Status:: via en masse invitation thru chair)
===
Date:: TBA
Title::
Speaker:: Terrell Hodge
From:: Western Michigan University
Email:: [e-mail]
Phone:: [phone]
Time:: 3:40 pm
Location:: NH 276
Status:: on sabbatical 2006-07
Status:: happy to come in 2007-08
===
Date:: TBA
Title::
Speaker:: Clark Wells
From:: Grand Vallen State University
Email:: [e-mail]
Phone:: [phone]
Time:: 3:40 pm
Location:: NH 276
Status:: would have come in 2006-07 but for so many GVSU speakers
Status:: happy to come in 2007-08
Status:: should be one of first people invited from GVSU next year
===
Date:: TBA
Title::
Speaker:: David Austin
From:: Grand Vallen State University
Email:: [e-mail]
Phone::
Time:: 3:40 pm
Location:: NH 276
Status:: was happy to come in both 2005-06 and 2006-07
Status:: prohibitive circumstances have intervened in both years
Status:: should be one of first people invited from GVSU next year