Research Interests

Some of my interests, listed in chronological order.

Automorphic Forms, Trace Formulae, Algebraic Geometry

I will be studying endoscopy and trace formulae for my PhD. More coming soon!

Homological Algebra

Homological algebra is not really a real research interest for me but it's an important technical tool and I find it pretty interesting that one can calculate isomorphism classes without explicit computation.

Residually Finite Groups

A residually finite group is a group in which every nontrivial element survives in some finite quotient. My masters thesis, which I will submit this semester (Winter 2011) shows that some specific groups are residually finite. I am also preparing a paper with my supervisor on this topic.

Large Groups

Largeness is a simple condition to state: a group G is large if it has a finite index subgroup H with a surjection from H to the free group on two generators. Even though this condition is easy to state, it is not always easy to determine whether a group is large. Groups with deficiency greater than one are large, which was proven by Baumslag and Pride in 1978 in a really slick paper consisting of two pages using elementary ideas from combinatorial group theory.

I started studying large groups in the Fall 2010 although later I switched topics to residually finite groups.