The Brown Bag
Seminar is an informal seminar whose purpose is to give
mid- to upper-division undergraduate math majors a
general survey of mathematics research in different
areas. Instead of focusing on results, speakers
(a) present big ideas within their research area, or (b)
highlight accessible open problems. In any case,
the effect of the seminar is to present material that a
student would otherwise not be exposed to in the
undergraduate curriculum.
The seminar meets every other Thursday at 11:30 a.m. in Math 402. The
Fall 2013 schedule follows. To see abstracts from
previous semesters, click here.
Sep 26
Scott
Kaschner, Department of Mathematics,
University of Arizona
An Introduction
to Dynamics in One Complex Variable
Dynamical systems are physical or mathematical
systems that change over time. Many questions in
the field are rooted in finding patterns and
structure and unpacking the chaos that arises
through repeated processes (for example, the
repeated application of a function). This
talk will introduce some main tools, concepts, and
open problems in the dynamics of one complex
variable. The goal is to provide an
intuition for the distinction between "normal" and
"chaotic" dynamical behavior in the complex
setting.
To get the most out of this talk, familiarity with
complex numbers (and maybe the concept of
compactness) would be helpful, but neither are
necessary.
Oct 10
Joceline
Lega, Department of Mathematics, University
of Arizona
The Mathematics of Complex Systems
This talk will start with a brief introduction to
complex systems. I will present a few examples,
discuss the main challenges, and highlight where
mathematics can help. At the same time, I will
explain how concepts learned in our undergraduate
courses may be extended to understand such
systems, and how the study of complex systems
helps build bridges between mathematics and other
disciplines. I will then turn to some research
questions I am interested in, on the topic of
systems of interacting particles.
The first part of the talk will be accessible to a
general audience of undergraduates interested in
the mathematical sciences. The second part will
involve ideas from physics, nonlinear dynamics,
and random systems.
Oct 24
Josh
Lioi, Department of Mathematics,
University of Arizona
When Zombies
Attack: A Mathematical Approach
The impending zombie apocalypse has been well
documented in film, television, books, and video
games. If we are to survive, we will need to be
prepared. How better to prepare ourselves than
with mathematics? By describing a real world
situation as a system of equations, we can use
our skills from differential equations and
linear algebra to find out what will happen.
This kind of approach is common in applied
mathematics and we will use it to study
population dynamics, including the spread of
disease in a population. This might be our best
hope for determining a strategy for dealing with
this undead threat.
Much of this talk will incorporate both linear
algebra and differential equations. However, the
talk can still be appreciated without this
knowledge.
A capillary surface is the free interface formed
between two adjacent non-mixing fluids, and their
study has attracted the attention of many
scientific luminaries such as Gauss, Laplace and
da Vinci. In fact, observations about their
behavior can be traced back to the times of
antiquity, when measurements of the rise of
liquids in a narrow tube were recorded. While this
focus has resulted in a long, rich history, the
study of capillary surfaces has recently found a
renewed interest due to applications in small
scale technologies. In this talk, we will review
the history of these free interfaces, discuss the
involvement of mathematics and preview what the
future holds.
Nov 14*
Kenny
Salau,
Department of Mathematics, University of Arizona
Agent-based Modeling in
the Life and Social Sciences
Agent
based modeling can be described as the use of
artificial, autonomous agents to understand
complex social and biological systems through
repeated simulation and scenario testing. There
exists a variety of software for implementing
agent-based models (ABMs), I will introduce
Netlogo, a program with intuitive commands and
the ABM software of choice among many
interdisciplinary scientists—such as myself. I
will present and discuss three ABMs stemming
from my own research, these include (1) the
evolution of soccer teams and soccer transfer
markets, (2) the co-existence of predator-prey
metapopulations, and (3) specialized predation
by Galapagos sharks.
Nov 21
Jennifer
Beichman, Department of Mathematics,
University of Wisconsin at Madison
The Hilbert transform: From Complex Analysis to
Fluid Mechanics
By taking a certain limit of the Cauchy
integral formula, a mapping from a holomorphic
function to its value on the boundary of a domain
appears. This operator is called the Hilbert
transform, and it appears all over mathematics. In
this talk, we will make connections between the
Hilbert transform, fluid mechanics, and harmonic
analysis.
Familiarity with holomorphic functions will be
helpful, but not necessary, for this talk.
If you are an undergraduate who is interested in the
prospect of doing research in math (or if you are simply
curious!), we encouraged you to attend the Brown Bag
Seminar!
If you are a graduate student or faculty member who is
interested in giving a future talk in the Brown Bag
Seminar, please contact me
with information about your proposed topic and your
availability!