Iowa State University |

Department of Mathematics Colloquium Fall 2019 |

Tuesdays 4:10pm in Carver 268 Tea and cookies starting at 3:45pm in Carver 404 |

The ISU Department of Mathematics Colloquium is organized by Pablo Raúl Stinga (stinga@iastate.edu) |

Upcoming in Spring 2020 Michelle Manes (NSF -
University of Hawaii at Manoa)February 25Title: Abstract: Selenne Bañuelos (California
State University Channel Islands)March 24 Title: Abstract: April 28 Armin Schikorra (University of Pittsburgh) Title: Abstract: |

Past Fall
2019September 10Jason McCullough (Iowa State University)Title: On the degrees of complexity of algebraic
varietiesAbstract: Given a system of polynomial equations in
several variables, there are several natural questions
regarding its associated solution set (algebraic variety):
What is its dimension? Is it smooth or are there
singularities? How is it embedded in affine/projective
space? Free resolutions encode answers to all of these
questions and are computable with modern computer algebra
programs. This begs the question: can one bound the
computational complexity of a variety in terms of readily
available data? I will discuss two recently solved
conjectures of Stillman and Eisenbud-Goto, how they relate
to each other, and what they say about the complexity of
algebraic varieties.Steve Butler (Iowa State University)September 17Title: On the mathematics of jugglingAbstract: The mathematics of juggling focuses on
the exploration of constrained periodic patterns,
including enumeration and transitions between patterns. We
will look at the mathematics of juggling with an emphasis
on some of the more recent results that have emerged in
this area. A few "practical" applications will also be
demonstrated.Alicia Carriquiry (Iowa State University)September 24Title: Statistics, mathematics and the fair
administration of justiceAbstract: In criminal proceedings, we often wish
to know whether the suspect was the source of the
evidence at the crime scene. The prosecutor and the
defense propose competing hypothesis: the defendant is
the source of the evidence or someone else is the source
of the evidence. The task of the forensic scientist is
to determine whether the evidence favors the
prosecutor's or the defense's propositions. We focus on
pattern evidence (latent prints, tool marks, etc) and
discuss approaches to quantify the similarity between
two images. If two items are similar, does that indicate
same source? We use firearms examination for
illustration.October 1James Dibble (University of Iowa) Title: Riemannian manifolds with no
conjugate pointsAbstract: Riemannian manifolds with no
conjugate points or no focal points are natural
generalizations of those with nonpositive sectional
curvature, but they are defined using synthetic
conditions about geodesics rather than strict
curvature bounds. In this talk, it will be shown
that the foundational theorems of Eells-Sampson and
Hartman about maps from manifolds with nonnegative
Ricci curvature into those with nonpositive
sectional curvature, initially proved using the heat
flow and the Bochner identity for harmonic maps,
generalize to targets with no focal points by an
essentially geometric, rather than analytical,
argument. The extent to which other classical
splitting theorems generalize to manifolds with no
conjugate points will also be discussed, along with
recent results about their fundamental groups and
applications to other questions to Riemannian
geometry.October 8David Herzog (Iowa State University) Title: On the large-time behavior of
singular stochastic Hamiltonian systemsAbstract: We discuss the problem of
convergence to equilibrium in two stochastic
differential equations used in statistical
sampling algorithms. In each system, the
equilibrium probability distribution has an
explicit density which is known up to a
normalization constant. Moreover, each density is
of the Boltzmann-Gibbs form. In the context of the
algorithm, this form is exploited in order to take
samples from a wide array of probability
distributions by running the stochastic dynamics
"long enough" started from conveniently chosen
prior distributions. However, outside of a
particular class of target distributions, very
little is known about how fast the stochastic
dynamics converges to this equilibrium. This talk
will cover joint work with my collaborators to
bridge this gap, ultimately resolving a challenge
posed by Denis Talay at an AIM conference in 2007
about convergence to equilibrium for the singular,
Lennard-Jones potential.October 15Genetha Gray (Intel) Title: Mathematics of the WorkforceAbstract: Advances in technology are
challenging traditional concepts of the when,
where, and how of work. Employees no longer
spend their entire career at one job. The Bureau
of Labor Statistics reports that the average
tenure of current workers is 4.6 years and that
this number decreases with employee age. In
2018, Gallup reported that 43% of US workers are
remote at least sometimes. Moreover, as measured
by FlexJobs in 2018, the math and economics job
category had the highest growth in remote job
opportunities. Finally, it should be noted that
the fourth industrial revolution has created a
high demand and a shortage of some critical
skills and highlighted the need for employers to
have the ability to respond to transformation by
employing people with a wide range of skills
that can be readily adapted to the new areas. To
respond to these new realities, companies have
turned to the practice of people analytics, a
data-driven approach to managing the workforce.
In this talk, we will describe how people
analytics has matured and give some examples of
problems and studies in this space. We will
focus on the data-driven nature of the work and
the mathematical tools required to find
insights.October
24 (Thursday - Carver 0018)Bill Johnson (Texas A&M University) Title: Some 20+ year old problems about
Banach spaces and operators on them.Abstract: The title is
self-explanatory; no abstract needed!No colloquiumOctober
29November 5Ryan Martin (Iowa State University) Title: Extremal functions and
symmetrizationAbstract: In this talk we will
discuss the connections between
symmetrization and extremal functions of
graphs that exclude both a triangle and some
fixed bipartite graph. In some cases the
extremal number can be determined
asymptotically. The techniques arise from
the study of the edit distance problem. This
preliminary work is joint with Zhana
Berikkyzy and Felix Lazebnik.November
12Talea Mayo (University of Central Florida) Title: Statistical data
assimilation for hurricane storm surge
modeling applicationsAbstract: Coastal ocean models are
used for a variety of applications,
including the simulation of tides and
hurricane storm surges. As is true for
many numerical models, coastal ocean
models are plagued with uncertainty, due
to factors including but not limited to
the numerical discretization of continuous
processes, uncertainties in specified
boundary and initial conditions, and the
approximation of meteorological conditions
and hydrodynamics. Quantifying and
reducing these uncertainties is essential
for developing reliable and robust storm
surge models. Statistical data
assimilation methods are often used to
estimate uncertain model states (e.g.
storm surge heights) by combining model
output with uncertain observations. We
have used these methods in storm surge
modeling applications to reduce
uncertainties resulting from coarse
spatial resolution. While state estimation
is beneficial for accurately simulating
the surge resulting from a single,
observed storm, larger contributions can
be made with the estimation of uncertain
model parameters. In this talk, I will
discuss applications of statistical data
assimilation methods for both state and
parameter estimation in coastal ocean
modeling. |