Henry Cohn

I'm a principal researcher (and one of three founding members) at Microsoft Research New England in Cambridge, Massachusetts. Previously I was head of the cryptography group at Microsoft Research in Redmond, Washington, and before that, I was a senior researcher in the theory group. I am also an affiliate faculty member in the department of mathematics at the University of Washington.

Research

My principal research projects are currently on sphere packing, energy minimization, and fast matrix multiplication. More broadly, my mathematical interests include discrete geometry, coding theory, cryptography, combinatorics, computational and analytic number theory, and theoretical computer science.

One conceptual issue that fascinates me is the role of symmetry in mathematics and physics, particularly for exceptional structures such as E₈. Why do the same beautiful structures occur in so many different contexts? There is clearly far more going on here than we currently understand.

I've always been interested in understanding simple physical systems, ranging from the dimer model to hard spheres and soft-matter systems. Many of the deepest issues deal with order vs. disorder, for example in phase transitions or the study of defects in ground states. Which conditions lead to order and symmetry?

My preference is for a mixture of concrete and abstract mathematics. I love concrete problems (there are so many things we don't yet understand), but I'm always happiest when they turn out to be connected with abstract mathematics. For example, I am interested in the use of harmonic analysis in sphere packing or representation theory in computational algebra.

My research page includes all my research papers. You can also download my research papers directly from the front to the arXiv, which is one of the best resources on the internet for mathematicians.

Contact Information

You can get directions to Microsoft Research New England here.

Teaching

Although I work in industry, I have an active interest in teaching. I've listed my teaching activities on a separate page.

Professional Background

I received my Ph.D. in mathematics in 2000 from Harvard, where my advisor was Noam Elkies. Before that, I was an undergraduate mathematics major at MIT (in the class of 1995). I was in the theory group at Microsoft Research from 2000 to 2007: I came as a postdoc and became a long-term member of the group a year later. I became head of the cryptography group in 2007 and helped found Microsoft Research New England in 2008.

Other

I've got a web page on which I keep various informal notes, thoughts, and links. My non-research publications can be found here.