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Henry Cohn

Henry Cohn I'm a principal researcher (and one of three founding members) at Microsoft Research New England in Cambridge, Massachusetts and an adjunct professor in the MIT Department of Mathematics. Previously I was head of the cryptography group at Microsoft Research Redmond, and before that, I was a senior researcher in the theory group.

If you're interested in the future of mathematical publishing, you should read the article that Douglas Arnold and I wrote about the Elsevier boycott for the Notices of the American Mathematical Society.


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 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 (or more familiar but still remarkable relatives, such as the regular icosahedron). 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, especially those arising in science and technology, and I'm particularly happy when abstract mathematics turns out to be useful. 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 arXiv (in order by when they were last updated).

Contact Information

Microsoft Research New England       Phone: (857) 453-6311
One Memorial Drive       Fax: (425) 93MSFAX
Cambridge, MA 02142       E-mail: cohn -at- microsoft -dot- com

If you send me a FAX, be sure to specify my name on the cover sheet.

My office is on the 12th floor, but the receptionist is on the 1st floor, so you should check in there before proceeding to the 12th floor.


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.


I've got a web page on which I keep some informal notes, thoughts, and links.