Before I arrived to MSU I was a Whyburn Instructor at UVA.
There, I collaborated with
Ira Herbst
and
John Imbrie.
I earned my Ph.D. in Mathematics at
UC, Irvine under my dissertation advisor:
Svetlana Jitomirskaya.
Prior to that, I earned a Master of Science in Applied Mathematics at
Rennselaer Polytechnic under the advisement of
Chjan Lim.

See my CV.

## Research

Most of my research to date focuses
on phases of matter in quantum systems in and out of equilibrium.
Lately, I have been working on several problems in Anderson Localization,
a phenomena occurring in systems with disordered environments which leads to
states of the system being localized in space, so that the system is blocked from thermalization.

In another vein, I worked on a problem studying quasistable states (resonances).
Stable states under a small perturbation tend to continuously deform to other stable states or quasistable states.
However, we show that the analogy is not true for resonances, where small perturbations
`erase and replace' the resonances.

Recently I have begun a project in random graphs.
A natural application of graphs are representations of social networks.
I am interested in the shape of social networks
where instances of cliques in the networks are rewarded or penalized.

See my page on the arXiv.

Please see my research page for a more thorough discussion of my research.

## Teaching

### Philosophy

I enjoy making mathematics meaningful to my students
by appealing to their personal interests and ambitions, scholastic or professional.
Therefore, it is important to me to have an open dialogue with my students
in and out of the classroom.
I do this partly by
frequently asking questions to my class, some relatively simple designed to spark
a discussion - or at least lead to a sequence of related questions I can ask the class.
Other questions are designed to get them to think about the material more deeply.
I also have `narrative sessions' every class, usually at the beginning
as I fit the material we are currently studying in to broader context of the course,
and at times how it relates to practical issues in other sciences or topics of popular interest.

I have often tried to engage with students in various ways.
At UCI I participated in the UCI math circle, an outreach project to local high school students.
While I was part of the circle we ran series on preparations for mathematics competitions
and an enjoyable series on `proofs by pictures' - mathematical proofs achieved by pictures.
Later, at UVA I organized the Putnam exam preparation seminar.
During weekly seminars we would discuss exam strategies and problem solving techniques.
At UVA I also gave a lecture on Benford's law,
I discussed its real world implications as well as its theoretical basis
to undergraduates with knowledge of calculus being the only prerequisite.
I am always looking to engage with students in creative ways and I am open to
participating in new projects.