Geometry/Physics Seminar

Title: Homotopy algebra and probability theory
Speaker: Gabriel C. Drummond-Cole
Speaker Info: Northwestern University
Brief Description:
Special Note:

I'm going to describe a surprising relationship between operadic algebra and so-called cumulant functions in probability theory, which keep track of independence. One way to think of probability theory is as studying the expectation, which is a map from an algebra of random variables to C which does not respect the product structures. We consider both the algebra of variables and C as trivial infinity-algebras equipped with an extra coderivation (the product). We can describe both cumulants and expectation value as morphisms between these trivial infinity-algebras. This is a purely formal procedure with no mathematical content. The surprising result is that these two morphisms are related by a functorial automorphism of infinity algebras equipped with a coderivation. There are versions for boolean, classical, and free cumulants. There some evidence that this relationship can be developed into a meaningful link between these two fields.
Date: Tuesday, April 09, 2013
Time: 4:00pm
Where: Lunt 107
Contact Person: Philsang Yoo
Contact email: philsang@math.northwestern.edu
Contact Phone:
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