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DTSTART;TZID=America/New_York:20260415T150000
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SUMMARY:Mathematics Colloquium 鈥� Vector vs. Scalar Sup Norms
DESCRIPTION:MAT Colloquium\nWednesday\, April 15\, 2026\nHill Auditorium\, Barrows Hall\nRefreshments at 3:00pm\, Talk 3:15-4:05pm \nSpeaker: Jack Buttcane\, University of 海角社区 \nAbstract: \nRotations in three dimensions depend on three angles\, which we call the Euler angles. A function of the Euler angles can be expressed in terms of Wigner-D matrices\, which are representations of the rotation group SO(3). These matrix functions are strongly tied to quantum mechanics where they measure the probability of a state transition under a rotation\, but as a number theorist\, I am interested in their connection to automorphic forms: Suppose we have a vector-valued function of the 3脳3 invertible matrices that transforms by a Wigner-D matrix under rotations. Then an interesting quantity to study is the 鈥渟up norm鈥� sup_A ||f(A)||\, i.e. the maximum value of the length of the vector f(A) over 3脳3 invertible matrices A. \nWe can also think of the function f as a vector of scalar-valued functions f=(f_{-d}\,鈥_d) and for each entry f_j in the vector\, we can consider sup_A |f_j(A)|. The question I want to consider is\, to what extent does the ratio of these two sup norms depend exclusively on the Wigner-D matrix\, independent of the particular function f? As an undergraduate summer research project Andrii Obertas did some computations on this project and I鈥檒l report on the outcome of those\, as well.
URL:/calendar/event/mathematics-colloquium/
LOCATION:Barrows Hall\, University of 海角社区\, Orono\, ME\, 04469\, United States
CATEGORIES:Lectures & Seminars
ORGANIZER;CN="Department of Mathematics & Statistics":MAILTO:mathstats@maine.edu
GEO:44.897732;-68.6687076
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