Reconstructing a 3-dimensional scene from 2-dimensional images of it is a fundamental problem in computer vision. Real solutions to systems of polynomials play a key role in solving this problem. In this talk I will explain recent work that attempts to bring in tools from algebra and geometry to some of the foundational problems in 3D computer vision with a particular focus on the most basic problem of reconstruction from two images.

Dr. Nicolas Flores Castillo, Rice University

Modeling Cancer Evolution using Quasi-Stationary Distributions in Resurrected Moran Models

In recent years, there have been an increasing interest in modeling the evolution of cancer tumors through different stochastic models. Some of these models assume that there is no interaction among daughter cells with their progenitors (branching processes) and there are some others that indeed consider this interaction: Moran models.

If recurrent mutations are allowed in wild-type cells, they will be eventually replaced by mutants. However, if the time to extinction is suﬃciently long, the conditional distribution of surviving wild-type cells arises. If it is stationary given non-extinction, it is called the quasi-stationary distribution (QSD). In this talk, I will give a brief introduction to the Moran model and some of its variants. I will also show the analytical forms of the QSD for the case of birth and death rates being constant, for the neutral case and for the directionally selective Moran models.

Dr. Candice Price, University of San Diego, (MSRI-UP 2008 & 2009 Graduate Assistant, MSRI-UP 2013 Postdoc)

Applications of Knot Theory: Using Knot Theory to Unravel Biochemistry Mysteries

Although knots have been used since the dawn of humanity, the mathematical study of knots is only a little over 100 years old. Not only has knot theory grown theoretically, the fields of physics, chemistry and molecular biology have provided many applications of mathematical knots. In this talk, I provide an overview of some connections between knot theory and DNA-protein interaction, outlining specifics of the biological mechanisms of DNA replication while providing an overview of related knot invariants.

Dr. Natalie Durgin, Spiceworks, (MSRI-UP 2007)

From GIT to Git and The Titanic Problem

We will trace a personal journey from the study of Geometric Invariant Theory (GIT) to a career in data science which requires daily use of Git, the version control system. Machine learning algorithms for classification also figure prominently in this field. We will briefly survey the most popular algorithms and engage in a relaxed, interactive demo applying these algorithms to classify survivors of the RMS Titanic disaster.

Dr. Illya Hicks, Rice University

Discrete Optimization and Network Analysis

This talk gives a general overview of discrete optimization and its relationship with network analysis. In particular, we will concentrate on the maximum k-plex problem which characterizes some degree of cohesiveness within a network. The maximum k-plex problem was first introduced in the context of social network analysis but can be utilized in other applications like graph-based data mining, wireless networks, and telecommunications.