Jason DeVito

Email: devito [at] math.upenn.edu .

Office Phone: (215) 898-8200
Office: David Rittenhouse Lab 4N35
 

About Me: I am a fifth year grad student in the Ph.D. program in Mathematics at the University of Pennsylvania. I'm primarily interested in geometry with a secondary interest in logic/set theory. My research is in Riemannian geometry, involving Lie groups. My thesis is on the classification of simply connected compact biquotients of dimension less than or equal to 7.

A biquotient is any manifold obtained as the quotient of a compact homogeneous manifold by an isometric group action. "Classification" up through dimension 6 means up to diffeomorphism, while in dimension 7 I hope to have a full list of cohomology rings and characteristic classes of all biquotients (such invariants are not strong enough to distinguish all manifolds).

I have also recently shown the manifold Sp(3)/Sp(1)xSp(1) has a metric of almost positive curvature - positive curvature on an open dense subset. (Kris Tapp has already shown this space has a metric with quasipositive curvature - nonnegative sectional curvature everywhere and a point with positive sectional curvature on all 2-planes). There are 4 4 distinct free isometric actions of nondiscrete Lie groups on this space - 2 by S¹ and 2 by Sp(1). This implies that the 4 manifolds Sp(3)/Sp(1)x Sp(1) x Sp(1), &Delta Sp(1)\Sp(3)/Sp(1)xSp(1), Sp(3)/Sp(1)xSp(1)xS¹, and &Delta S¹\ Sp(3)/Sp(1)xSp(1) all have metrics with almost positive curvature. Of the 4 manifolds, the space Sp(3)/Sp(1)^3 and %Delta Sp(1)\ Sp(3)/ Sp(1)xSp(1) were already known to admit metrics of almost positive curvature (in fact, the first is known to admit a metric of positive curvature). It is unkown whether this metric on the latter space has any 0 curvature planes.

For a list of papers (most of them written to help me prepare for very informal talks) I've written, please click here:

Papers