Program
Related links
Past SWiM

SWiM 2018 Lectures

Colleen Robles
June 20 (Wednesday)
The GaussBonnet Theorem
The GaussBonnet Theorem is the "crown jewel" of surface geometry. I will explain this beautiful result, what makes it so remarkable, and
how one can prove/verify it using calculus.


Rick Durrett
June 21 (Thursday)
Truth is stranger than fiction: A look at some improbabilities
Probability is full of surprises and paradoxes, most of which result from doing the calculation
incorrectly. We will illustrate this using some familiar old stories and new ones: the Monty Hall problem, cognitive dissonance in Monkeys, the birthday problem, lottery coincidences, the sad story of Sally Clark, the 2016 election, and gerrymandering in North Carolina.
Some of these topics can be found in my blog or in previous versions of this talk, which can be reached by
links on my web page.


Irina Kogan
June 22 (Friday)
A story of two postulates
“I have traversed this bottomless night, which extinguished all light
and joy of my life. I entreat you, leave the science of parallel
alone”, wrote a Hungarian mathematician Farkas Bolyai to his son
János, horrified at the thought that his son is attracted by the
problem of parallels. János was not deterred, however, and discovered,
simultaneously with Lobachevski, a consistent geometry in which the
Euclidean parallel postulate does not hold. We will zoom through the
path of mathematical thought that took over 2000 years, noticing which
results from a high school geometry textbook do not rely on the
parallel postulate, and which are altered completely in hyperbolic
geometry.


Jayce R. Getz
June 25 (Monday)
An invitation to modern number theory via elliptic curves
We will define elliptic curves and use them as a touchstone to introduce a key idea in modern number theory relating analysis and algebra.


Katie Newhall
June 26 (Tuesday)
Applied Stochastic Dynamics
As an applied mathematician, I look to mathematics to help understand the physical world around
us and how it behaves. A pingpong ball dropped follows a mathematical function for the distance traveled.
But imagine a strong wind randomly swirling around, knocking the pingpong ball back and forth as it falls.
Where will it end up? What’s the most likely place it will end up? A combination of probability and calculus
can answer these questions! I will discuss not a pingpong ball, but a magnetic model of spins and
“active matter” as a simplified collection of microorganisms. These are all example systems that exhibit
Stochastic dynamics.


Alexander Kiselev
June 27 (Wednesday)
How fluids move
Attempts to understand the nature of fluid motion have occupied minds of researchers for many
centuries. Fluids are all around us, and we can witness complexity and subtleness of their behavior
in every day life, in ubiquitous technology, and in dramatic phenomena such as tornado or hurricane.
I will discuss derivation of the fundamental equations describing fluid motion, and talk about
some of the modern challenges in mathematical fluid mechanics.


Tom Witelski
June 28 (Thursday)
Complex systems from simple dynamics
Complicated and dramatic systemwide behaviors can be sparked by simple
individual events. Examples include avalanches on mountains and
messages "going viral" in social networks. Intricate behaviors like
pattern formation, synchronization, and chaos will be shown to occur
from problems as simple as the dynamics of a bouncing ball.

