Algebraic statistics advocates the use of algebraic geometry, commutative algebra, and geometric combinatorics as tools for making statistical inferences. The starting point for this connection is the observation that most statistical models for discrete random variables are, in fact, algebraic varieties. While some of the varieties that appear are classical varieties (like Segre varieties and toric varieties), most are new, and there are many challenging open problems about the algebraic structure of these varieties.
Now there is a great program holding at the Mittag-Leffler Institute.
There are several famous professors in this field:
Alicia Dickenstein from Buenos Aires
Bernd Sturmfels from UC Berkeley
Seth Sullivant from North Carolina State University
Sumio Watanabe, Ph.D. from Tokyo Institute of Technology
Caroline Uhler from Berkeley
Here is a short course on Algebraic statistics by Professor Seth Sullivant:
Here is the video lecture by Risi Kondor:
And you can find his thesis on this topic in his homepage.