# Henry Cohn

Adjunct Professor, MIT Department of Mathematics

Senior Principal Researcher, Microsoft Research New England

### Contact information

**Email:** cohn at mit.edu or microsoft.com**Phone:** +1 (857) 453-6311**Mail:** Microsoft Research New England, One Memorial Drive, Cambridge, MA 02142, USA**MIT office:** 2-341B**Microsoft Research office:** 12200 [you'll need to check in with the Microsoft receptionist on floor M]

### Research in discrete mathematics

My principal research projects are currently on sphere packing and conformal field theory, potential energy minimization and ground states, 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. I am interested in both pure and applied mathematics, with a particular interest in their intersection: pure mathematics inspired by applications, and opportunities to apply mathematics in unexpected ways.

One conceptual issue that fascinates me is the role of symmetry in mathematics and physics, particularly for exceptional structures such as E_{8} (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 far more going on here than we currently understand.

I've always been interested in understanding simple, idealized 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?

For example, when should we expect a material's ground state to be crystalline, as opposed to intrinsically disordered? Essentially the same problem arises in information theory: when should we expect an optimal code to be highly symmetrical, as opposed to pseudorandom?

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 publications 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).

### Teaching

I regularly teach, supervise graduate students, and work with research interns.

### 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 Redmond from 2000 to 2007: I came as a postdoc and became a long-term member of the group a year later. I was head of the cryptography group from 2007 to 2008, was one of three founding members of Microsoft Research New England in 2008, and became an adjunct professor at MIT in 2010.

### Other

I've got a web page on which I keep some informal notes.