About Me

I am a mathematician and a Ph.D. candidate in the Department of Electrical Engineering and Computer Science at MIT (Ph.D. expected: summer 2012). My advisor is Todd Kemp. I am spending the 2011-2012 academic year as a Chateaubriand Fellow at the Université Paris-Est, working with Philippe Biane.

I was a 2010-2011 Claude E. Shannon Research Assistant at MIT, an NSERC PGS-D Fellow, and a recipient of a 2008 Ernst A. Guillemin S. M. Thesis Award (2nd place) at MIT.

Research

I deal in non-commutative probability, examples of which include random matrix theory and free probability. My work is principally grounded in operator theory and combinatorics.

My thesis work is concerned with the structures arising from interpolation between two essential relations in quantum physics: the canonical commutation relation (CCR) and canonical anti-commutation relation (CAR), describing the behavior of Bosons and Fermions, respectively.

The Fock space representations of the CCR and CAR algebras have a natural interpretation as algebras of certain non-commutative random variables. And the algebras corresponding to an interpolation between the two relations? Well, they fundamentally give a continuum of non-commutative probability theories with varying commutativity structures.

The meat of what I do is available here:
N. Blitvic, "The (q,t)-Gaussian Process", arXiv:1111.6565v1 [math.OA].

Teaching

In Spring 2009 and Spring 2010, I taught recitations in 6.262 Discrete Stochastic Processes. I learned everything I know about teaching (and then some) from this guy.

For the Spring 2009 issue, I was awarded the departmental Carlton E. Tucker teaching award at MIT. The Spring 2010 recitations were filmed for financial analyst training by the Bank of America.

About Me

Research

Teaching

Natasha Blitvic