# William H. Barker

Bowdoin College

Brunswick, Maine

*Books: **Continuous Symmetry: From Euclid to Klein* (AMA, 2007)

_______ Harmonic Analysis on Reductive Groups

###### (NOTE: A conference on Harmonic Analysis on Reductive Groups was held at Bowdoin College in Brunswick, Maine from July 31 to August 11, 1989. The stated goal of the conference was to explore recent advances in harmonic analysis on both real and p-adic groups. It was the first conference since the AMS Summer Symposium on Harmonic Analysis on Homogeneous Spaces, held at Williamstown, Massachusetts in 1972, to cover local harmonic analysis on reductive groups in such detail and to such an extent. While the Williamstown conference was longer (three weeks) and somewhat broader (nilpotent groups, solvable groups, as well as semisimple and reductive groups), the structure and timeliness of the two meetings was remarkably similar. The program of the Bowdoin Conference consisted of two parts. First, there were six major lecture series, each consisting of several talks addressing those topics in harmonic analysis on real and p-adic groups which were the focus of intensive research during the previous decade. These lectures began at an introductory level and advanced to the current state of research. Second, there was a series of single lectures in which the speakers presented an overview of their latest research.

_____ Lp harmonic analysis on SL(2,R)

First email: Friday, 7 February 2020

Dear Prof. Dr. William H. Barker:

My work in 1972 focused on continuity, symmetry, and harmony. I was attempting to define what I thought would entail “a moment of perfection” within our quantum universe. By 1980, after working with an array of distinguished scholars in Boston, Cambridge (USA), and Paris, I went back to work within a business that I had started in 1971. From a little service bureau, we soon had a software business with well over 100 employees. My first opportunity to attempt to dig back into it all back was in 2011. I was helping a nephew with his high school geometry classes when we went inside the tetrahedron — https://81018.com/tot/ — and then its octahedron, step-by-step, deeper and deeper by dividing all the edges by 2 and connecting those new vertices. Within 45 steps we were within particle physics. In 67 additional steps, we were within the Planck scale. By multiplying those classroom objects by 2, in 90 steps we were out to the approximate age and size of the universe. Instead of base-10 like Kees Boeke (1957), we used base-2, we had an inherent geometry, and we went from the Planck units to the current time.

It was an unusual, albeit, rather idiosyncratic chart of 202 notations: https://81018.com/chart/

*Prima facie, do you see any merit to such a chart? *

I will continue my readings of your work, *Continuous Symmetry: From Euclid to Klein* (AMA, 2007) and Harmonic Analysis on Reductive Groups in hopes that you might have some guiding thoughts for this rather idiosyncratic chart of the universe. Thank you.

Most sincerely,

Bruce

PS. In 1746 our family settled in Bremen, Maine. Bowdoin had always been on my list of schools to consider, but in 1965 the call for voter registration in the South won the day. I always think of you all on my way out of Freeport and as we go through Brunswick. -BEC