## EVENT DETAILS AND ABSTRACT

**Geometry/Physics Seminar**
**Title:** Homotopy algebra and probability theory

**Speaker:** Gabriel C. Drummond-Cole

**Speaker Info:** Northwestern University

**Brief Description:**

**Special Note**:

**Abstract:**

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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