Authors: Marcelo Aguiar ¹; Carlos André ^2,3; Carolina Benedetti ⁴; Nantel Bergeron ⁴; Zhi Chen ⁴; Persi Diaconis ⁵; Anders Hendrickson ⁶; Samuel Hsiao ⁷; I. Martin Isaacs ⁸; Andrea Jedwab ⁹; Kenneth Johnson ¹⁰; Gizem Karaali ¹¹; Aaron Lauve ¹²; Tung Le ¹³; Stephen Lewis ¹⁴; Huilan Li ¹⁵; Kay Magaard ¹⁶; Eric Marberg ¹⁷; Jean-Christophe Novelli ¹⁸; Amy Pang ¹⁹; Franco Saliola ²⁰; Lenny Tevlin ²¹; Jean-Yves Thibon ¹⁸; Nathaniel Thiem ²²; Vidya Venkateswaran ²³; C. Ryan Vinroot ²⁴; Ning Yan ²⁵; Mike Zabrocki ⁴

• 1 Department of Mathematics and Statistics [Texas Tech]
• 2 Université de Lisbonne
• 3 Universidade de Lisboa = University of Lisbon = Université de Lisbonne
• 4 Department of Mathematics and Statistics [Toronto]
• 5 Department of Statistics [Stanford]
• 6 Concordia College [MN]
• 7 Bard College
• 8 University of Wisconsin-Madison
• 9 University of Southern California
• 10 Pennsylvania State University [Penn State]
• 11 Pomona College
• 12 Loyola University [Chicago]
• 13 University of Aberdeen
• 14 University of Washington [Seattle]
• 15 Computer Science Department [Drexel]
• 16 University of Birmingham [Birmingham]
• 17 MIT Laboratory for Computer Science
• 18 Laboratoire d'Informatique Gaspard-Monge
• 19 Stanford University
• 20 Laboratoire de combinatoire et d'informatique mathématique [Montréal]
• 21 New York University [New York]
• 22 Department of Mathematics, University of Colorado
• 23 California Institute of Technology
• 24 College of William and Mary [Williamsburg]
• 25 Unknown

We identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite field, and the ring of symmetric functions in noncommuting variables. Each is a Hopf algebra and the two are isomorphic as such. This allows developments in each to be transferred. The identification suggests a rich class of examples for the emerging field of combinatorial Hopf algebras.