Topic #6 --------------- OP-SF NET --------------- September 7, 1995

From: Walter Van Assche
Walter.VanAssche@wis.kuleuven.ac.be

Subject: **Report on conference in honour of Lee Lorch
**

(A slightly longer report by Walter Van Assche will appear in the Newsletter)

In September 1995, Lee Lorch will celebrate his eightieth birthday. For this occasion, a conference was organized at York University (Canada) on June 9 and 10, 1995. Some forty people were present and attended various talks on mathematical topics of interest to Lee Lorch, but also talks related to the societal topics in which Lee always has had active interest.

One of Lee's mathematical interests has been the monotonicity properties of zeros of Bessel functions or functions of a similar nature. A basic method for studying monotonicity properties of zeros of special functions is Sturm's method, for which there is a continuous version (for zeros of the solution of a Sturm-Liouville differential operator) and there is also a discrete version for polynomials which form a Sturm sequence (a three-term recurrence with a particular sign property). Lee Lorch's main contributions can be found in joint papers with Peter Szego and Martin Muldoon. Lee also had an continuing interest in Lebesgue constants and various methods of summability.

On the first day of the conference (June 9, 1995) there were one hour talks by Richard Askey on "Bessel functions and how to use them when considering more general classes of functions" and Cora Sadosky on "Restricted BMO in products spaces". There were also some 30 minute talks by P.G. Rooney, Walter Van Assche, Angelo Mingarelli, A. McD. Mercer, Mark Ashbaugh, Mourad Ismail, James A. Donaldson, and Arpad Elbert dealing with Hankel transforms, zeros of orthogonal polynomials, eigenvalues of matrices and differential operators, Bessel functions and isoperimetric inequalities, integral operators and $q$-Sturm-Liouville problems, and linear shallow water theory.

The morning of the second day of the conference was still devoted to mathematics with one hour talks by Roderick Wong on "Asymptotics and special functions", Jean-Pierre Kahane on "Summability, order and products of Dirichlet series", and 30 minute talks by Dennis Russell and Mark Pinsky on Fourier transforms and Fourier integrals in several variables. In the afternoon there was a nice talk by Donald J. Newman with a beautiful proof of the Morley triangle theorem:

*
Let ABC be an arbitrary triangle with vertices at the points A, B, C.
Construct a new triangle (the Morley triangle) by trisecting the
angles alpha, beta and gamma at respectively A, B and C inside the
triangle ABC and by taking the first intersection points as the
vertices of the new triangle. Then this Morley triangle is always an
equilateral triangle.
*

There was also a 30 minute talk by Amram Meir on random trees, and the rest of the afternoon of June 10 was devoted to Lee's societal contributions for which he has become well-known, with talks by Chandler Davis, Mary Gray, and Johnny Houston pointing out the "Contributions of Lee Lorch to expanding access to mathematics", showing that Lee Lorch is "A mathematician who cares".

Finally, the conference was closed with a dinner during which Lee was awarded the Lifetime Achievement Award of the National Association of Mathematicians by Jack Alexander, president of the Association.

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