Program
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Past SWiM

SWiM 2017 Lectures

Ingrid Daubechies
June 21 (Wednesday)
Mathematicians helping Art Historians and Art Conservators
In recent years, mathematical algorithms have helped art historians and art conservators putting together the thousands of
fragments into which an unfortunate WWII bombing destroyed world famous frescos by Mantegna, decide that certain paintings by masters
were "roll mates" (their canvases were cut from the same bolt), virtually remove artifacts in preparation for a restoration campaign, get more insight
into paintings hidden underneath a visible one. The presentation will review these applications, and give a glimpse into the mathematical aspects that
make this possible.


Radmila Sazdanovic
June 22 (Thursday)
Catalan numbers, Chebyshev polynomials, and categorifications
What does it mean to "compute with diagrams"? We will construct a "diagrammatic algebra" based on properties of Catalan
numbers and use
it to recover some wellknown facts about the Chebyshev polynomials. This novel approach, called categorification, provides insight into more complicated
algebraic structures as well as inspiration for visual artists.


Ezra Miller
June 23 (Friday)
Topology for statistical analysis of brain artery images
Statistics looks for trends in data. Topology quantifies
geometric features that don't change when shapes are squished,
stretched, or bent continuously. What does one have to do with
the other? When data objects are already geometric, such as
magnetic resonance images of branching arteries, topology can
isolate information of statistical relevance. This talk
explains what we have learned about the geometry of blood
vessels in aging human brains using topological methods in
statistics. The main results are joint with Paul Bendich,
Steve Marron, Alex Pieloch, and Sean Skwerer (at the time, a
Math postdoc, Stat faculty, Math undergrad, and Operations
Research grad student).


Hubert Bray
June 26 (Monday)
Gravity and the Curvature of Spacetime
Einstein's Theory of General Relativity explains gravity more accurately than any other theory by modeling the universe
as a four dimensional curved spacetime manifold. We'll discuss the mathematics behind this amazing picture of the universe.


Nancy RodriguezBunn
June 27 (Tuesday)
What calculus can tell us about life
In this talk I will discuss how we can use calculus to gain insight
into complex social, ecological, and biological phenomena. We will focus on modeling urban crime and explore various important mathematical
questions from the point of view of their applications.


Robert Bryant
June 28 (Wednesday)
The Idea of Holonomy
The notion of `holonomy' in mechanical systems has been around for more than a century and gives insight into daily operations as mundane as
steering and parallel parking and in understanding the behavior of balls (or more general objects) rolling on a surface with friction. A sample question is this:
What is the best way to roll a ball over a flat surface, without twisting or slipping, so that it arrives at at given point with a given orientation? In geometry and physics, holonomy has turned up in many surprising ways and continues to be explored as a fundamental property of geometric structures.
In this talk, I will illustrate the fundamental ideas in the theory of holonomy using familiar physical objects and explain how it is also related to group
theory and symmetries of basic geometric objects.


Colleen Robles
June 29 (Thursday)
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.

