Stochastics Seminar

Speaker: Dr. Jerzy Szulga

Title: Signed multiplicative systems, part III

Review and abstract:

Part I (Sep 9):

Algebra and Calculus of operators acting on Gaussian, then on Rademacher chaos (i.e., the algebra spanned by random signs), motivated by application in quantum physics.

Part II (Oct 7):

Just two operators, called "rotation" and "symmetry," span a universal signed multiplicative system (all elements either commute or anticommute, squares are either 1 or -1). At the first glance this is a simple system, but its simplicity is tricky if not deceiving. Some tools of finite fields of characteristic 2 were discussed as well as matrix or double-sequence representations.

Part III (Nov 4):

1. Brief review of notation, terms, and tools.

2. Replacements of generators, classification, counts.

3. Pattern generating algorithms.

4. Open problems.

Technically, this is algebra intertwined with set theory and combinatorics, but with a strong probabilistic flavor because of the aforementioned origins.