In joint work with I. M. Singer, he introduced the notion of analytic (or Ray-Singer) torsion in Riemannian geometry.
In joint work with Ching-Li Chai we prove a conjecture (1995) that predicted the answer to this question.
In joint work with Xin Sun, we prove a strong relationship between these two natural models for random surfaces.
In joint work with Vera Vertesi, we extend the functoriality in Heegaard Floer homology by defining a Heegaard Floer invariant for tangles which satisfies a nice gluing formula.
In joint work with Valentino Tosatti, Collins described the singularity formation of the Ricci flow on Kahler manifolds in terms of algebraic data.
Supporting this hypothesis, in joint work with experimental collaborators, we found that ILCs respond potently to signaling through one such neuropeptide by amplifying allergic airway inflammation.
I will present some recent results obtained on these problems, partly in joint work with Philip Gressman, Sebastian Herr, and Gigliola Staffilani.
Distant collaborators often use meetings, email, chat, and other technology to talk about their work, but during site visits we saw constant, quick discussions, with colleagues asking and answering questions in the moment as they were engrossed in joint work.
In joint work with Arul Shankar and also with Christopher Skinner, Bhargava came to the surprising conclusion that a positive proportion of elliptic curves have only one rational point and a positive proportion have infinitely many.
