Algebra has seen many applications in statistics, but it is only rather recently that computational algebraic geometry and related techniques in algebra and combinatorics have been used to study statistical models and inference problems. The main idea is that polynomials and ratios of polynomials appear in statistics and probability under various guises, in model representations as well as in inferential procedures. This links to some basic concepts in algebraic geometry.
This use of computational algebraic geometry was initiated in work on exact tests for models for contingency tables Diaconis and Sturmfels  (see below). Another line of work was initiated by the group of researchers working at the University of Warwick: Wilfrid Kendall, Giovanni Pistone, Eva Riccomagno, Raffaella Settimi, Jim Q. Smith and Henry Wynn. Their research mainly focused on experimental design (see e.g. Pistone and Wynn ) and other applications of computer algebra in statistics (see Kendall , Settimi and Smith ). This finally led to the monograph Pistone et al.  where the name “algebraic statistics” was used for the ﬁrst time. From this point the ﬁeld largely expanded…
WOGAS3 Workshop on Geometric and Algebraic Statistics 3: 5-7 April 2011 at Warwick. Read more.
Books on algebraic statistics:
Interesting links :
People in Algebraic/Geometric Statistics (to be updated):
past activities (since October 2007):
December 15, 2008 to December 18, 2008
Serkan Hosten (SFSU), Lior Pachter (UCB), Bernd Sturmfels (UCB)
Professor Huzihiro Araki (Mathematical Physics) Professor Araki is famous for his contribution to noncommutative operator theory and quantum field theory.