Date

Presenter

Title

Time/Location

12/4/15

Dr. Bryce Weaver

Ergodic
theory and dynamical systems
From its
birth in celestial mechanics and particle physics, to
its recent applications to number theory (see, for
example, the celebrated GreenTao or
EinsiedlerKatokLindenstrauss theorems), ergodic
theory has shown itself to be a powerful tool in the
modern mathematical toolbox. In these first two talks,
we will explore some of the basics of this field at
the intersection of dynamical systems, measure theory,
and functional analysis. We will introduce
definitions, motivation, and some first results,
including: Poincare recurrence and the Birkhoff and
Von Neumann ergodic theorems. Although these talks are
``stand alone", they are envisioned as the first two
in a series of at least four lectures on ergodic
theory that culminate in ergodic decomposition. No
background in dynamical systems will be assumed.
However, a certain comfort with the terminology of
measure theory, topology, and functional analysis will
be assumed. Significant results and techniques in
these fields will be recalled as needed.

2:303:30pm/Roop 349

1/11/15 
Dr. Bryce Weaver 
Poincare recurrence and the law of large
numbers

2:304:30pm/Roop G110

1/29/15

Dr. Bryce Weaver

Birkhoff's
ergodic theorem
We will
discuss the Birkhoff Ergodic theorem and the
definition of ergodicity. The theorem will be
presented as one of the key ingredients for the
Ergodic Decomposition theorem, the objective of this
series of talks. Time permitting, we will begin
discussing one of the other key ingredients: Riesz
Representation Theorem or the theory of measurable
partitions.

3:305:00pm/Roop 105

2/12/16

Dr. Rebecca Field

Why do we
care about complex cobordism?
Groups have
topology: for example GLn is a twisted product of odd
spheres. How can we measure the twisting? Ordinary
cohomology doesn’t see this twisting in any obvious
way which is one reason we construct exotic cohomology
theories. We’ll discuss the connection between complex
oriented cohomology theories and formal group laws and
why we care about a particular one called complex
cobordism!

3:305:00pm/Roop 105

2/26/16

Dr. Rebecca Field

Line
bundles and complex cobordism
Last time we
described how groups are twisted products of
topological spaces. For this talk, we will further
describe how to detect and measure twisting in the
specific case of a (complex) line bundle (which is a
twisted version of the cross product
$X\backslash times$
). We will describe how to classify line bundles
according to how twisted they are (construction of the
first Chern class) via classifying spaces. We will end
with a description of where and how generalized
cohomology theories (like complex cobordism) show up
in terms of line bundles. We will not assume that
anyone is familiar with the material from the first
talk and will not assume that the audience knows
cohomology.

3:305:00pm/Roop 105 
3/4/16

Dr. Rebecca Field

Line
bundles and complex cobordism II (with donuts)
This will be a
continuation of the talk from last week when we got as
far as defining a line bundle and giving some
examples. This week, we will complete last week's plan
by showing how a homotopy between two spaces produces
an identification of isomorphism classes of line
bundles and introducing both the Chern class and the
classifying space of complex line bundles. We hope to
eventually discuss complex cobordism. We will be happy
to review definitions for anyone who wasn't able to
attend part 1, and yes, there will be donuts, real
ones, from Strite's.

3:305:00pm/Roop 105

3/18/16

Dr. Hasan Hamdan

Statistical
Paradoxes, Concepts and Misconceptions in Elementary
Courses*
Paradoxes and
misconceptions abound in probability and statistics.
Dr. Hamdan will discuss some crucial concepts and
cases, including the Monty Hall Problem, the
Prisoner’s Paradox, and Simpson’s Paradox. The uses
and abuses of other statistical concepts such as
statistical significance and pvalues, averages, the
false positive paradox, and Bedford’s Law will be
highlighted.

3:304:30pm/Wilson 107

3/25/16


Math Department Meeting


4/1/16


Is
String Theory Scientific?**

2:005:30pm
MadisonUnion 256 
4/8/16

Dr. Dominic Lanphier Western
Kentucky University

Subgroups of
cyclic groups and values of the Riemann zeta function
If we select an
element at random from a large cyclic group, what
should we expect the order to be? More generally, if
we select k elements at random, what should be the
order of the subgroup generated by those k elements?

3:305:00pm/Roop 105

4/15/16

Genesis Alberto JMU/Howard
University

The
division polynomials for the Holm curve and their
properties
Let p be a
prime number and K = Fp be the finite field with p
elements, and λ ∈ K such that
$\backslash lambda\backslash neq0,\backslash pm1$.
In this work we will study the division polynomials of
the Holm elliptic curve in its original form, and a
remodeled form,
$H\_\lambda \; :\; y^3\; \; y\; =\; \lambda (x^3\; \; x)$
and a remodeled form,$H\_\lambda \text{'}\; :(u\lambda )v^2=u^3\lambda $.
We will explicitly state their group structures
together with the birational correspondence to their
Weierstrass models. Using these mappings, we will
derive the multivariable division polynomials and the
single variable division polynomials, then investigate
their properties.

3:305:00pm/Roop 105

4/22/16




4/29/16


Math Department Meeting


8/2/16

Dr. Anda Degeratu University of Freiburg

The mathematics of gravitational waves

3:004:00pm/Roop 105




