Emerging field of phylogenomics integrates two major disciplines: genomics (the study of the structure and function of genes and genomes) and phylogenetics (the study of the hierarchical evolutionary relationships among organisms and their genomes). The goal of phylogenomics is to identify the common ancestry of organisms and understand their evolution through analysis of genomes.
This presentation has three parts: we will begin by reviewing the hypothesis testing ( chi-square test). Second part offers definitions of the relevant biological terminology. In Part three we describe a simple example of a statistical model for inferring information about the genetic code.

Numerical algebraic geometry is a growing area of applied algebra that involves describing solutions of polynomial systems of equations. This area has already had an impact in kinematics, statistics, PDE's, and pure math. In this talk we focus on using numerical algebraic geometry for maximum likelihood estimation in algebraic statistics.
In the first half, we will introduce a concrete example and develop background information. In the second half, we present computational results consisting of Maximum Likelihood degrees for matrices with rank constraints and present the surprising theoretical result of maximum likelihood duality.

The goal of this talk is to explore the polynomial method and relate this topic to the course material in Math 535. Broadly speaking, we will study how to encode combinatorial optimization problems in terms of systems of polynomial equations, how a famous result in algebraic geometry guarantees the existence of a certificate of infeasibility if a given problem is infeasible, and how this allows us to appeal to the well-understand theory of semi-definite programming to solve our given combinatorial optimization problem. We will also discuss results concerning the computational complexity of the certificate of infeasibility.
Main reference: arXiv:0706.0578.

This talk will cover descriptions of probabilistic conditional independence (CI) models and learning graphical models which has applications in biology (epistasis, gene regulatory networks, protein signaling, systems biology), Markov random processes, probabilistic reasoning, artificial intelligence and more. Given observed data, the goal is to find the CI structure which best explains the data. I will motivate the problem with some interesting biological applications. Next, I will quickly overview graphical approaches to the description of CI structures. Then, I will describe an algebraic description of CI structures introduced by Studeny et al. which has many elegant properties, suitable for applications of linear programming methods. The remainder of the talk will be devoted to linear optimization approaches to learning Bayesian networks, which are special graphical models.

Speaker bio: David Haws is currently a Postdoctoral Researcher at IBM T.J. Watson Research Center in the Computational Genomics group. David recieved his Ph.D. in Mathematics from U.C. Davis working in the area of combinatorial optimaztion and polyhedral geometry. David's current interests includes, machine learning, genomic selection, graphical models, computational genomics & biology, phylogenetics, polyhedral geometry, and topological data analysis. In general his research lies in the intersection of applications, algorithms, and theory and binding these topics together is a deep knowledge of data analysis and computation.