Stephen

D.

Miller

Newer preprints:

Gimme a date! John Conway's shortcuts to cracking the calendar, expository article on computing days of the week of the secular and Hebrew calendars.

Nonunitarity outside the fundamental parallelepiped

Stochastic global optimization of continuous functions via random walks on Grassmannians, with Kartik Gupta, Pradeep Ravikumar, Ramarathnam Venkatesan.

The D⁶R⁴ interaction as a Poincare series, and a related shifted convolution sum, with Kim Klinger-Logan and Danylo Radchenko.

Selected older publications

Sphere packing and energy minimization:

• Universal optimality of the E₈ and Leech lattices and interpolation formulas, with Henry Cohn, Abhinav Kumar, Danylo Radchenko, and Maryna Viazovska
• The sphere packing problem in dimension 24, with Henry Cohn, Abhinav Kumar, Danylo Radchenko, and Maryna Viazovska
• Some properties of optimal functions for sphere packing in dimensions 8 and 24, with Henry Cohn.
  • A comment on OpenAI's reuse of Section 5 of the above paper: Does the inability to perform simple literature/web searches really reflect "superhuman intelligence"?

Unitary representations:

• On Arthur's unitarity conjecture for split groups, with Joseph Hundley
• Residual automorphic forms and spherical unitary representations of exceptional groups
• Small representations, string instantons, and Fourier modes of Eisenstein series, with Michael Green and Pierre Vanhove; includes appendix "Special Unipotent Representations" by Dan Ciubotaru and Peter E. Trapa.

Automorphic forms:

• The archimedean theory of the Exterior Square L-functions over Q, with Wilfried Schmid
• Automorphic Distributions, L-functions, and Voronoi Summation for GL(3), with Wilfried Schmid