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Series: Research Horizons Seminar

A motivating problem in number theory and algebraic geometry is to find
all integer-valued solutions of a polynomial equation. For example,
Fermat's Last Theorem asks for all integer solutions to x^n + y^n = z^n,
for n >= 3. This kind of problem is easy
to state, but notoriously difficult to solve. I'll explain a p-adic
method for attacking Diophantine equations, namely, p-adic integration
and the Chabauty--Coleman method. Then I'll talk about some recent
joint work on the topic.

Series: Research Horizons Seminar

Series: Research Horizons Seminar

The talk will include a crash course on infinite dimensional
topology, with applications to various topological properties of the
space of congruence classes of convex bodies in the Euclidean space.

Series: Research Horizons Seminar

This
talk will cover some recent and preliminary results in the area of
non-smooth dynamics, with connections to applications that have been
overlooked.
Much of the talk will present open questions for research projects related to this area.

Series: Research Horizons Seminar

Series: Research Horizons Seminar

Taffy pullers are machines designed to stretch taffy. They can modeled
by surface homeomorphisms, therefore they can be studied by geometry and
topology. I will talk about how efficiency of taffy pullers can be
defined mathematically and what
some of the open questions are. I will also talk about Macaw, a computer
program I am working on, which does related computations and which will
hopefully help answer some of the open questions.

Series: Research Horizons Seminar

Series: Research Horizons Seminar

An academic webpage allows you to better communicate your work and help you become more recognizable in your research community. We'll talk about the very basics of how to set one up and what you should put on it----no prior experience necessary! Please bring a laptop if you can---as usual, refreshments will be provided.

Series: Research Horizons Seminar

Antibiotics have greatly reduced morbidity and mortality from
infectious diseases. Although antibiotic resistance is not a new
problem, it breadth now constitutes asignificant threat to human health.
One strategy to help combat resistance is to find novel
ways of using obsolete antibiotics. For strains of E. coli and P.
aeruginosa, pairs of antibiotics have been found where evolution of
resistance to one increases, sometimes significantly, sensitivity to the
other. These researchers
have proposed cycling such
pairs to treat infections. Similar strategies are being investigated to
treat cancer. Using systems of ODEs, we model several possible treatment
protocols using pairs and triples of such antibiotics, and investigate
the speed of ascent of multiply resistant
mutants. Rapid ascent would doom this strategy. This is joint work with
Klas Udekwu (Stockholm University).

Series: Research Horizons Seminar

SPORT
is a 12-week *PAID* summer internship offered by the National Security
Agency (NSA) that provides 8 U.S. Citizen graduate students the
opportunity to apply their technical skills to current, real-world
operations research problems at the NSA. SPORT
looks for strong students in operations research, applied math,
computer science, data science, industrial and systems engineering, and
other related fields.
Program Highlights:
-- Paid internship (12 weeks, late May to mid-August 2018)
-- Applications accepted September 1 - October 31, 2017
-- Opportunity to apply operations research, mathematics, statistics, computer science, and/or engineering skills
-- Real NSA mission problems
-- Paid annual and sick leave, housing available, most travel costs covered
-- Flexible work schedule
-- Opportunity to network with other Intelligence Agencies