# Implementing algebraic geometry algorithms

This web page contains material for the workshop
Implementing algebraic geometry algorithms.

Contributions from the workshop participants are available in
dvi,
postscript or
pdf.

## Useful references

*General:*

"Lectures on Algebraic Statistics" by Drton, Sturmfels, Sullivant
(Birkhauser 2009, Oberwolfach Seminar Series)
*Equivariant Buchberger Algorithm:*

Equivariant Grobner bases and the Gaussian
two-factor model by Brouwer and Draisma

*Background on Markov bases:*

Markov Bases of Binary Graph Models by Develin and Sullivant,

A Finiteness Theorem for Markov Bases of
Hierarchical Models by Hosten and Sullivant,

Minimal and minimal invariant Markov bases of
decomposable models for contingency tables by Hara, Aoki, and Takemura,

Indispensable monomials of toric ideals and
Markov bases by Aoki, Takemura and Yoshida

*Markov subbases* (more precisely, the set of connecting moves for contingency table
with assumption of positive margins):

Markov bases and subbases for bounded contingency
tables by Rapallo and Yoshida,

Markov Chains, Quotient Ideals, and Connectivity
with Positive Margins edited by Chen, Dinwoodie, and Yoshida

*Identifiability problems:*

The Identifiability of Covarion Models in
Phylogenetics, by Allman and Rhodes

Estimating Trees from Filtered Data: Identifiability of
Models for Morphological Phylogenetics by Allman, Holder, and Rhodes

Identifiability of 2-tree mixtures for group-based
models by Allman, Petrovic, Rhodes, and Sullivant

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A list of registered participants is available.

Questions or comments to *workshops@aimath.org*