Trapa currently serves as the dean of the College of Science at the University of Utah.[1] He previously served as the chair of the Department of Mathematics and the chair of the Department of Physics & Astronomy.[1]
Trapa works on unitary representations of Lie groups, and is a member of the Atlas of Lie Groups project.[5] With Jeffrey Adams, Marc van Leuuwen, and David Vogan, he devised an algorithm to compute the unitary dual of a real reductive group. With his collaborators, he developed a Shimura correspondence for split reductive groups and introduced a Dirac operator for p-adic spaces. He was named a Fellow of the American Mathematical Society in 2019.[6]