MSRI-UP 2013: Algebraic Combinatorics
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Prof. Gibor Basri, University of California, Berkeley
NASA's Search for Earth-sized PlanetsFour years ago a dedicated space telescope (“Kepler”) was launched to search for terrestrial planets around other stars, and even possibly discover a planet that might be like the Earth. The main purpose of the mission is to find out how common smaller planets are. I explain how the mission works, and highlight some of its most amazing discoveries. Nearly 3000 potential planets have been found, including many in multiple planet systems. The most common planet may be something that we don’t have in our own Solar System: “super-Earths” which are 1.5-3 times as big as our planet. Some of these may be rocky, some may be “water worlds”, and some may be more like warm Neptunes. The Kepler mission is rapidly leading us to the conclusion that most stars have planets going around them, and the number of earth-sized planets in our Galaxy could easily be in the billions.
Prof. Herbert Medina, Loyola Marymount University
Computing Pi Via New Polynomial Approximations to Arctangent: a new contribution to (arguably) the oldest approximation problem
Prof. Talitha Washington, Howard University
A Glimpse of Dynamical Modeling in the BioscienesIn mathematics, a differential equation is a tool which may be used to describe a quantity that changes with
respect to time. This talk explores how differential equations describe the spread of infectious diseases, hormone secretions of a cell, and calcium homeostasis.
Prof. Alissa S. Crans, Loyola Marymount University & MSRI
A Surreptitious Sequence: the Catalan NumbersWe are all familiar with Fibonacci’s famous sequence that begins 1, 1, 2, 3, 5, 8, … as well as other popular sequences such as the perfect squares 1, 4, 9, 16, 25, … or the triangular numbers 1, 3, 6, 10, 15, … But what about the sequence 1, 1, 2, 5, 14, …? These are the Catalan numbers, named after the Belgian mathematician Eugène Catalan (1814 – 1894), despite having been described by Leonhard Euler 100 years earlier. It turns out these numbers take a variety of different guises as they provide the solution to numerous combinatorial problems! After introducing this sequence, we will explore some of the many ways in which the Catalan numbers are hidden throughout mathematics.
Prof. Mariel Vazquez, San Francisco State University
Random knots, viruses and DNADNA presents high levels of condensation in all organisms. We are interested in the problem of DNA packing
inside bacteriophage capsids. Bacteriophages are viruses that infect bacteria, and DNA extracted from bacteriophage P4 capsids is highly knotted. These knots can shed information on the packing reaction and DNA architecture inside the capsid. I here will overview a few research questions stemming from the DNA packing problem.
"Zero Forcing and its Applications,"
Michael Young, Iowa State University
Zero forcing (also called graph infection) on a simple, undirected
\[ G \] is based on the
color-change rule: If each vertex of \[ G \]is colored either white or
and vertex \[ v \] is a blue vertex with only one white neighbor $w$, then
change the color of \[ w \] to blue. A minimum zero forcing set is a set
blue vertices of minimum cardinality that can color the entire graph
using the color change rule. In this talk will discuss the role of
forcing in systems control, electrical engineer, and linear algebra.
though various scientist have been using zero forcing, it wasn't until
recently that it was realized they were all doing the same type of
propagation. Zero forcing gets its name from the linear algebraists,
were using the propagation to force entries of a vector to be zero.
"Compactifications in Algebraic Geometry,"
Pablo Solis, University of California at Berkeley
In this talk I'll give a basic introduction to the field of algebraic
geometry and discuss the problem of
compactification which has become a very active area of research
I'll define what it means for something to be compact and show how
and non compact things appear in algebraic geometry. I'll describe one
problem algebraic geometry in detail which can be phrased as follows:
many degree 2 plane curves are tangent to 5 given given plane curves?
was a question posed by a mathematician named Steiner in 1846. The
solution, which took almost 20 years to be found, is one of the
instances of how compactification can be used.
"A (very) brief introduction to graphical models,"
April Harry, Purdue University
Probabilistic Graphical Models is a framework used in statistics and
machine learning to represent
complex dependencies between random variables. By combining concepts
graph theory and probability, graphical models allow us to leverage
efficient algorithms from computer science for statistical decision
and inference. We explore one class of graphical models, Bayesian
through an example with three random variables. Also, we discuss some
practical applications of graphical models in bioinformatics, speech
language processing, and atmospheric sciences.
by Ivelisse Rubio, University of Puerto Rico
- 2013 MSRI-UP Latex Handout.pdf
2013 MSRI-UP Latex Handout.tex
MSRI-UP Report Template.tex
"GRE Math Subject Test,"
by Herbert Medina, Loyola Marymount University
"Oral and Poster Presentations,"
by Ivelisse Rubio, University of Puerto Rico
- Ideas for Presentations.pdf
- Using Beamer2.pdf
- Poster Presentations.pdf
- MSRI-UP Presentation Template.tex
- Using Beamer2.tex