Colloquium Schedule of Mathematics
Department
Central Michigan University
Spring 2016 and Fall
2015
Schedule (Last updated:
04/28/2016, 04:13 PM EST)
Note 1: because there might be a time
delay for the updates on this webpage, please always first
check with the Colloquium Speaker Committee for the available
dates.
Note 2: Typically the colloquium talk
would occur from 4-5pm in PE227, but there may be exceptions.
Please check the following table for more accurate
information.
Speaker: Hengguang Li
Time/Room: Thursday, 9/10/2015, 4-5pm, PE 227
Title: Finite Element Approximations of Singularities
Abstract:
First, we review the finite element formulation in a general
mathematical setting. Then, we discuss recent advances in the
development of effective finite element algorithms approximating
a class of singular solutions, including corner singularities
with different boundary conditions and singularities from the
non-smooth points on the interface in transmission problems. We
establish a-priori estimates (well-posedness, regularity, and
the Fredholm property) for the singular solution in weighted
Sobolev spaces. Then, based on these theoretical results, we
propose a simple and explicit construction of the finite element
space to recover the optimal convergence rate of the numerical
solution. We also mention applications in physics and
engineering.
Speaker: Emil
Straube
Time/Room: Thursday, 10/1/2015, 4-5pm, PE 227
Title: $\overline{\partial}$-Methods in Complex
Analysis
Abstract: We will first discuss the inhomogeneous $\overline
{\partial}$-equation in one complex variable and show how it can
be used to give a simple proof of the classical Mittag-Leffler
Theorem on prescribing poles (including principal parts) of a
meromorphic function. In the second part, we show how to solve
$\overline{\partial}$ in $\mathbb{C}^{2}$ ( for a compactly
supported right hand side). This solution then gives a short
proof of the Hartogs Extension Theorem , one of the striking new
phenomena that arise in several complex variables, clearly
distinguishing the higher dimensional theory from the one
dimensional case.
Speaker: Mandi
A. Schaeffer Fry
Time/Room: Thursday, 10/08/2015, 4-5pm, PE 227
Title: On the Action of Galois Automorphisms on Characters
of Groups of Lie Type
Abstract:
Given a finite group with size n, the Galois group
Gal(Q(\omega)/Q), where \omega is an nth root of unity, acts
naturally on the irreducible characters of G. We discuss
some parametrizations for characters of groups of Lie type and
the problem (and its motivation) of describing this Galois
action in terms of these parametrizations.
Speaker: Michael
Pokojovy
Time/Room: Thursday, 10/15/2015, 4-5pm, PE 227
Title: A Multistep, Cluster-Based Multivariate Chart for
Retrospective Monitoring of Individuals
Abstract: The presence of several outliers in an individuals
retrospective multivariate control chart distorts both the
sample mean vector and covariance matrix, making the classical
Hotelling's T2 approach unreliable for outlier detection. To
overcome the distortion or masking, we propose a
computer-intensive multistep cluster-based method. Compared with
classical and robust estimation procedures, simulation studies
show that our method is usually better and sometimes much
better at detecting randomly occurring outliers as well as
outliers arising from shifts in the process location. Additional
comparisons based on real data are given. This is joint work
with J. Marcus Jobe (Miami University, Oxford, OH).
Speaker: Stephen
Yau
Time/Room: Friday, 10/30/2015, 3:00-3:50pm, PE223
Title: Distinguishing Proteins From Arbitrary Amino Acid
Sequences
What kinds of amino acid sequences could possibly be protein
sequences? From all existing databases that we can find, known
proteins are only a small fraction of all possible combinations
of amino acids. Beginning with Sanger's first detailed
determination of a protein sequence in 1952, previous studies
have focused on describing the structure of existing protein
sequences in order to construct the protein universe. No one,
however, has developed a criteria for determining whether an
arbitrary amino acid sequence can be a protein. Here we show
that when the collection of arbitrary amino acid sequences is
viewed in an appropriate geometric context, the protein
sequences cluster together. This leads to a new computational
test, described here, that has proved to be remarkably accurate
at determining whether an arbitrary amino acid sequence can be a
protein. Even more, if the results of this test indicate that
the sequence can be a protein, and it is indeed a protein
sequence, then its identity as a protein sequence is uniquely
defined. We anticipate our computational test will be useful for
those who are attempting to complete the job of discovering all
proteins, or constructing the protein universe.
Speaker: Scott
Kersey
Time/Room: Thursday, 11/05/2015, 4-5pm, PE 227
Title: Polynomial Approximation on Quasi-Uniform Grids
Abstract:
A simple generalization of univariate polynomial interpolation
and approximation to the bivariate setting is by tensor
products. Here, one can easily construct a polynomial
interpolant (in Lagange or Newton form) or quasi-interpolant
(using Bernstein polynomials and dual functionals) over uniform
bivariate grids, and compute the error in approximation based on
the error in univariate polynomial interpolation. In this talk
we focus on interpolation and approximation over certain
``quasi-uniform'' grids. These are grids much sparser than
full tensor product grids. In particular, we will
construct a quasi-interpolant on these grids, and derive an
error of approximation. In particular, we show that for certain
quasi-uniform grids we can achieve the same rate of
approximation as by interpolation on the full tensor product
grid. Hence, we have a class of ``serendipity'' elements
analogous to those in the finite element literature. The
construction involves a technique called discrete blending based
on Boolean sum methods for interpolation and approximation.
We conclude with a brief mention of the construction of a
subdivision scheme on quasi-uniform grids.
Speaker: Suk-Ho
Lee
Time/Room: Thursday, 02/04/2016, 4-5pm, PE 227
Title: Kernel based Deep Learning
Abstract : Nowadays, deep learning
based on neural networks has opened a new era of
revolution in many areas like automatic driving, face
recognition etc. Drived by the results of neural network
based deep learning, people are starting to adapt the idea
of multi-layer learning to support vector machines,
especially to kernel based learning. In this talk, I will
introduce the basic concepts of deep learning and some
recent results of it, and also introduce how people try to
build up a similar learning archtecture in kernel based
learning.
Speaker: Catherine
Lewis
Time/Room: Thursday, 03/17/2016, 4-5pm, PE 227
Title: Lesson Study to
Improve Mathematics Instruction: Recent Research
Abstract:
Lesson study consists of cycles of collaborative,
practice-focused professional learning, centered
around joint observation of live classroom instruction. In
Japan, lesson study has long been credited for the shift to
teaching mathematics through problem-solving and to teaching for
understanding.Recent
research suggests that lesson study can positively impact
teachers’ and students’ mathematical knowledge in the U.S., as
well. Of 643 mathematics professional learning studies reviewed
using What Works
Clearinghouse criteria, only two studies showed impact on
student mathematical proficiency (while meeting scientific
design criteria), and one was lesson study.This presentation will
highlight recent research that points to the role of
high-quality content resources in supporting successful lesson
study in the U.S.
Speaker: Carolyn Gordon
Time/Room: Tuesday, 03/22/2016, 4-5pm, PE 227
Title:
You can't hear the shape of a drum
Abstract:
In spectroscopy, one attempts to recover the chemical
composition of, say, a star from the characteristic frequencies
of emitted light. Analogously, Mark Kac's question "Can one hear
the shape of a drum?" asks whether the shape of a vibrating
membrane (a drumhead) can be determined from its
characteristic frequencies of vibrations (its fundamental tone
and overtones). We will answer this question in the negative by
constructing explicit examples of exotic shaped "sound-alike"
drums, and we will listen to a simulation of their sound,
developed by Dennis DeTurck of the University of
Pennsylvania. Speaker: Nancy Reid
Time/Room: Thursday, 04/07/2016, 4-5pm, PE 227
Title: Statistical inference, learning and
models for Big Data Abstract:
The Canadian Statistical Sciences Institute and
the Fields Institute for Research in the Mathematical Sciences
recently completed a six month thematic research program on
Big Data. I will give an overview of the topics covered with
emphasis on linkages between different areas, common problems,
and common strategies. While the program was only able to
cover a small fraction of the world of Big Data, the breadth
of the material covered by the large number of speakers was
very stimulating.
Speaker: Louis
Nirenberg
Time/Room: Thursday, 04/14/2016, and Friday 4/15/2016, both
from 4-5pm at French Auditorium
Title: The
maximum principle and some applications
Abstract:
The lectures will be devoted to the maximum principle and
various applications. These will be to geometry and to
properties of solutions of elliptic partial differential
equations. Some proofs will be given, and the talks will be
expository.