**Contents:** Timetable | Books | Papers | Links

## Timetable

This is tentative and subject to what people are interested in discussing, volunteers, etc.

Wk |
Date |
Topic |
Presenter |
Reading |

1 |
24th Nov 2009 | Introduction Ideals and Varieties (slides here) |
Robin Evans | IVA - Chapter 1; Drton, Sturmfels and Sullivant (2007) |

2 |
1st Dec | Groebner Bases | Charles Doss | IVA - Chapter 2 |

3 |
8th Dec | Algebraic Inference for Contingency Tables | Anna Klimova | Diaconis and Sturmfels (1998) |

Christmas Break |
||||

4 |
13th Jan | Implicitization, Nullstellensatz (?) | Alex Volfovsky | IVA - Chapters 3, 4 |

5 |
20th Jan | Rational Functions on Varieties | collaborative | IVA - Chapter 5 |

6 |
27th Jan | Likelihood Inference - Discrete and Gaussian Models | collaborative | LAS - Chapter 2.1 |

7 |
3rd Feb | Markov Bases | collaborative | LAS - Chapter 1.1-1.2 |

8 |
10th Feb | Likelihood Inference | collaborative | LAS - Chapter 2.2-2.3 |

9 |
17th Feb | |||

10 |
24th Feb | A geometric Buchberger algorithm for integer programming | Rekha Thomas | Thomas (1995) |

11 |
3rd Mar | |||

12 |
10th Mar | |||

Spring Break |

Meetings at 3:30pm on Tuesdays in Padelford C-301. This will change to Wednesdays, 3:30pm after Christmas.

## Books

*Algebraic Statistics* (AS) - Pistone, Riccomagno & Wynn

*Ideals, Varieties and Algorithms*, Third Edition (IVA) - Cox, Little & O'Shea

*Lectures on Algebraic Statistics* (LAS) - Drton, Sturmfels & Sullivant

## Papers

Cavender, J.A. and Felsenstein, J. (1987) - InvariantsĀ of phylogenies in a simple case with discrete states

Thomas, R.R. (1995) - A geometric Buchberger algorithm for integer programming

Diaconis, P. and Sturmfels, S. (1998) - Algebraic algorithms for sampling from conditional distributions

Drton, M. (2006) - Algebraic techniques for Gaussian models, *Prague Stochastics*

Allman, E.S. and Rhodes, J.A. (2006) - Phylogenetic invariants for stationary base composition

Drton, M. and Sullivant, S. (2007) - Algebraic statistical models

Drton, M., Sturmfels and Sullivant, S. (2007) - Algebraic factor analysis: tetrads, pentads and beyond

Allman, E.S. and Rhodes, J.A. (2008) - Phylogenetic ideals and varieties for the general Markov model

Drton, M. (2009) - Likelihood Ratio Tests and Singularities

Zwiernik, P. and Smith, J.Q. (2009) - The Geometry of Independence Tree Models with Hidden Variables

## Links

**SINGULAR** - Software for automatic algebraic computations.

**Laboratory for Mathematical and Computational Biology**, UC Berkeley