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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

Series: Research Horizons Seminar

In Fall 2017 I will teach `Random Discrete Structures', which is an advanced course in discrete probability and probabilistic combinatorics. The goal of this informal lecture is to give a brief outline of the topics we intend to cover in this course. Buzz-words include Algorithmic Local Locasz Lemma, Concentration Inequalities, Differential Equation Method, Interpolation method and Advanced Second Moment Method.

Series: Research Horizons Seminar

Defined in the early 2000's by Ozsvath and Szabo,
Heegaard Floer homology is a package of invariants for three-manifolds,
as well as knots inside of them. In this talk, we will describe how work
from Poul Heegaard's 1898 PhD thesis,
namely the idea of a Heegaard splitting, relates to the definition of
this invariant. We will also provide examples of the kinds of questions
that Heegaard Floer homology can answer. These ideas will be the subject
of the topics course that I am teaching in
Fall 2017.

Series: Research Horizons Seminar

I
will continue the discussion on the group actions of the graph Jacobian
on the set of spanning trees. After reviewing the basic definitions, I
will explain how polyhedral geometry leads to a new family of such
actions.
These actions can be described combinatorially, but proving that they
are simply transitive uses geometry in an essential way. If time
permits, I will also explain the following surprising connection: the
canonical group action for a plane graph (via rotor-routing
or Bernardi process) is related to the canonical tropical geometric
structure of its dual graph. This is joint work with Spencer Backman and
Matt Baker.

Series: Research Horizons Seminar

Every graph G has canonically associated to a finite abelian group called the Jacobian group. The cardinality of this group is the number of spanning trees in G. If G is planar, the Jacobian group admits a natural simply transitive action on the set of spanning trees. More generally, for any graph G one can define a whole family of (non-canonical) simply transitive group actions. The analysis of such group actions involves ideas from tropical geometry. Part of this talk is based on joint work with Yao Wang, and part is based on joint work with Spencer Backman and Chi Ho Yuen.

Series: Research Horizons Seminar

In this talk, we will have an overview of: the Gaming Industry, specifically on the Video Slot Machine segment; the top manufactures in the world; the game design studio Gimmie Games, who we are, what we do; what is the process of making a video slot game; what is the basic structure of the math model of a slot game; current strong math models in the market; what is the roll of a game designer in the game development process; the skill set needed to be a successful Game Designer. Only basic probability knowledge is required for this talk.

Series: Research Horizons Seminar

On the two-dimensional square grid, remove each
nearest-neighbor edge independently with probability 1/2 and consider
the graph induced by the remaining edges. What is the structure of its
connected components? It is a famous theorem of Kesten that 1/2 is the
``critical value.'' In other words, if we remove edges with probability
p \in [0,1], then for p < 1/2, there is an infinite component remaining,
and for p > 1/2, there is no infinite component remaining. We will
describe some of the differences in these phases in terms of crossings
of large boxes: for p < 1/2, there are relatively straight crossings of
large boxes, for p = 1/2, there are crossings, but they are very
circuitous, and for p > 1/2, there are no crossings.

Series: Research Horizons Seminar

I will start with a brief presentation of the Probability activities in SOM. I will continue by presenting results obtained in SOM, over the past ten years, answering long standing questions insequences comparison.

Series: Research Horizons Seminar

A matroid is a combinatorial abstraction of an independence structure, such as linear independence among vectors and cycle-free-ness among edges of a graph. An algebraic variety is a solution set of a system of polynomial equations, and it has a polyhedral shadow called a tropical variety. An irreducible algebraic variety gives rise to a matroid via algebraic independence in its coordinate ring. In this talk I will show that the tropical variety is compatible with the algebraic matroid structure. I will also discuss some open problems on algebraic matroids and how they behave under operations on tropical varieties.