Schedule 
Monday, January 30
Davis 201, 3:45

Diana Davis
Williams College
Three Flavors of Billiards
Abstract:
The mathematical study of billiards extends well beyond the popular table
game. I’ll tell you about three different types of billiards (inner
billiards, outer billiards and tiling billiards), and I’ll explain
some of the research I’ve done in two of these areas.

Wednesday, February 1
Davis 201, 3:45

William R. Green
RoseHulman Institute of Technology
Time Decay for Schrödinger and Dirac Equations
Abstract:
Differential
equations are ubiquitous in the sciences due to their ability to model real
world phenomena. Unfortunately, many physically relevant differential
equations are very difficult or impossible to solve in terms of elementary
functions. The Schrödinger equation is a partial differential equation
that models the behavior of subatomic particles. Despite the inherent
difficulties in both solving this equation, and interpreting the meaning of
these solutions, many advances have been made using quantum theory that
arises from the Schrödinger equation. In this talk, we will
survey some mathematical ideas needed to study the behavior of subatomic
particles. In particular, we will investigate what we can say about
solutions to the underlying partial differential equations without solving
them. We will also discuss what happens to and how to model a subatomic
particle as it moves at relativistic speeds.

Friday, February 3
Davis 201, 3:45

Evan Randles
University of California Los Angeles
Convolution Powers of ComplexValued Functions
Abstract:
Central to random walk
theory is the study of iterative convolution powers of probability
distributions on the square lattice. When such distributions are allowed
to be complexvalued, their convolution powers exhibit surprising and
disparate behaviors not seen in the probabilistic setting. In this talk, I
will describe recent work on this topic, briefly discuss its connections
to statistics and partial differential equations, and outline directions
for future research. This is joint work with Laurent SaloffCoste.

Monday, February 6
Davis 201, 3:45

Ekaterina Shemyakova
SUNY New Paltz
Differential Operators on the Superline, Berezinians and Darboux
Transformations
Abstract:
Supermathematics is a standard tool for Quantum Physics that allows us to
describe both fermions and bosons. The name comes from
“supersymmetry.” Darboux transformations are a tool in
integrable systems theory, which seeks exact solutions of nonlinear and
linear partial and ordinary differential equations. In this talk I shall
present my results on developing Darboux transformations in
supergeometry. I shall touch on my results about superdeterminants, such as
a nontrivial analogue of row (column) expansion. Overall I aim to
introduce the audience to the world of supermathematics, show analogues of
familiar concepts and give some idea of my work. I shall not be assuming
any prior knowledge besides Linear Algebra and Calculus.

Thursday
February 16
3:30 PM

Wes Viles
Dartmouth College
Network Data Analysis: Inference and Characterization
Abstract:
The analysis of network data is
widespread across scientific disciplines. In applied network analysis, a
common approach is to gather basic measurements on the interactions among
elements in the system, construct a networkbased representation of the
system, and numerically summarize the structure of the resulting network
graph. We address the empirically relevant problem that errors made in
assigning links between nodes accumulate in the reporting of motif count
statistics in characterizing the network as a whole. We demonstrate the
utility of network characterization in two clinically relevant
applications: (i) the highorder interactions among microbes constituting
the ecological network of the human gut microbiome and (ii) the rate of
percolation in the human brain network at the onset of an epileptic
seizure.

February 27

Jan Holly
Colby College
Dizzy Patients and a Mathematical Playground of Probabilities on
Spheres
Abstract:
Interesting
mathematical topics often arise in reallife problems. This talk will
begin with a description of research on vestibular patients at Baylor
College of Medicine and a comparison with previously published data on eye
movements, and then will dive into mathematical questions—and even
some answers—that arose. Above all, this talk will point out some
intriguing questions about probabilities on spheres that lead to a whole
playground of mathematical (and statistical) questions.

March 13

Scott Taylor
Colby College
Constrained Flexibility: Some Surprising Connections between Geometry
and Topology
Abstract:
Length, area, curvature are geometric properties. An object’s
topological properties, on the other hand, are those which don’t
change when the object is stretched, twisted, or bent. Curves in the plane
or in 3dimensional space exhibit an interesting variety of both geometric
and topological properties. I’ll survey they ways these properties
are related to each other, tracing a line of investigation which begins in
the early 20th century and extends to very recent results concerning how
twisted knots can be. (Image by Conan Wu)

March 27

Michael Barany
Dartmouth College
Inclusion, Exclusion, and the Theory and Practice of “Truly
International” Mathematics
Abstract:
Group photo at the 1950
ICM In theory, just about anyone can be a
mathematician. Theorems and proofs, for the most part, don’t
discriminate based on race, class, gender, disability, national origin, or
anything else, at least in princniple. Historically, however, the field
and profession has been open to very few. Mathematicians have grappled in
many different ways with this gap between an ideal of openness and and a
reality of exclusion and even outright discrimination. I will show how
American mathematicians took leadership of the international mathematics
community over the period between 1920, when they first proposed to host
an International Congress of Mathematicians, and 1950, when they finally
brought one to fruition. American mathematicians tried to reshape
mathematics as a more interconnected and inclusive discipline, succeeding
in some ways and failing in others. In particular, they tried to create
what they called a “truly international” discipline. I
will explain how this ambiguous and shifting phrase helped them navigate a
wide range of political, financial, and other obstacles, while covering
over persistent problems and blindspots.

April 3

Thomas Pietraho
Bowdoin College
Fast Matrix Multiplication: An Adventure in Machine Learning
Abstract:
Neural nets have been used to attack a
variety of problems, including image classification, speech recognition,
and autonomous driving. After detailing how neural nets can be used in
settings of this sort, we will use them to solve a problem in algebra
instead.

April 10

Tom Hulse
Colby College
Square Pegs in a Round Circle Problem
Abstract:
In this talk we’ll introduce Gauss’s Circle
Problem, the centuriesold conjecture concerning estimates of the number
of integercoordinate points inside a circle as we vary the
radius. We’ll also discuss variants on this problem in higher
dimensions, and how we can get information from the Fourier coefficients
of a particular theta function with interesting analytic properties. Some
joint work with Chan Ieong Kuan, David LowryDuda, and Alexander Walker
may also be presented.

April 17

Malia Kawamura ’14, Anne Crumlish ’98, Ben Hauptman ’09,
Tom Hulse ’07
Mathematics and Statistics Alumni Panel
Abstract:
TBA

May 1

David Krumm
Colby College
Japanese Temple Geometry
Abstract:
During the
period of Japanese history known as the Edo period, Japan followed a
strict isolationist foreign policy in which travel outside the country was
forbidden and cultural exchange with European nations was effectively cut
off. Coupled with the peace and economic prosperity enjoyed during the Edo
period, this “closed country” policy led to a flourishing of
uniquely Japanese arts and culture. One of the curious practices that
developed during this time was a tradition of hanging wooden tablets
inscribed with geometry problems in Buddhist temples and Shinto
shrines. In this talk we will discuss the Japanese mathematics of the Edo
period generally and the sangaku tablets in particular, including the one
problem from these tablets that remains unsolved.
