Algebraic Geometry in Algebraic
Statistics and Geometric Modeling

Texas Advanced Research Program

    This project is a collaboration between faculty and students at Sam Houston State University and Texas A&M University to investigate some common algebraic geometric structures in algebraic statistics, geometric modeling, and algebraic geometry. For example, the animation at left illustrates the how, under a toric degeneration (a concept in algebraic geometry), a cubic Bézier triangle degenerates to its control polyhedron (concepts from geometric modeling).
    This is primarily funded by the Texas Advanced Research Program, with additional support from the National Science Foundation. It will support students at both institutions for the duration of the grant (May 2008 through May 2010, as well as travel to relevant scientific meetings and necessary computer equipment.
    For more information, please see the proposal.

  Poster, "Algebraic Methods for Phylogenetic Inference", by Diaz and Howard was a prize winner at the MAA Undergraduate Student Poster Session on January 7.

  Sam Houston State University
Principal Investigator:   Luis David Garcia-Puente
Students:   Alexander Diaz
Andy Howard
Sarah Spielvogel
Texas A&M University
Principal Investigator:  Frank Sottile
Graduate Student:   Corey Irving
Graduate Student:   Weronika Buczynska

  Products and Presentations

Updates and expansion of the small phylogenetic trees website. Work of Andy Howard.
Linear precision for toric surface patches Work of Frank Sottile, H.-C. Graf von Bothmer, and K. Ranestad.
Linear precision for parametric patches, Talk by Sottile at MMCS 08, 26 June 2008. text.
Linear Precision for Toric Surface Patches, Talk by Sottile at Special session on Applications of Algebraic Geometry, AMS Sectional Meeting in Vancouver, BC 4-5 October 2008. Abstract.
Generalized Barycentric Coordinates, Talk by Irving at Graduate student seminar, 30 October 2008. Abstract.
Some geometrical aspects of control points for toric patches Work of G. Craciun, Luis David Garcia-Puente, and Frank Sottile.
Algebraic Methods for Phylogenetic Inference, poster by Alex Diaz and Andy Howard in the MAA Undergraduate Student Poster Session on January 7 in Washington, DC. One of the prize winners.
Geometrical aspects of control points for toric patches talk by Luis D. Garcia-Puente in the AMS Special Session on Computational Algebra and Convexity at the AMS meeting in Washington, DC, 7 January 2009.

  Research Supported by the Texas Advanced Research Program Grant 010366-0054-2007 and NSF grant DMS-0701050