THE CATHOLIC UNIVERSITY OF AMERICA
Washington, DC 20064
SEMINAR IN FUNCTIONAL ANALYSIS
AND RELATED AREAS
Wednesday, March 25, 2026
5:15 p.m. - 6:15 p.m. 

 SPEAKER : Michael Somos
                  The Catholic University of America

TITLE: Multivariate Quadratic Equation Solutions

ABSTRACT: The solutions of a quadratic equation of one variable using the quadratic formula is well known. Less well known is the case of more than one variable quadratic equations. In my research I have found several examples of such equations with interesting applications including elliptic curves, elliptic functions, Somos sequences, spherical triangles, and special Diophantine equations. I will give several numerical examples of solutions to these equations. One special Diophantine problem is the integer solutions of the equation x^2 + y^2 + z^2 = 3 x y z. These integers are known as the "Markov Numbers". Another is the rational solutions of the equation x + y + z = 1/x + 1/y + 1/z.
I have found one instance of "Special Algebraic Identities" derived from the general symmetric two variable quadratic equation. Solutions to such an equation determine a (2,2) correspondence which is involved in "Poncelet's Porism". It is a special case of symmetric correspondences studied by Euphemia Lofton Hayes in her 1943 PhD dissertation at CUA.

 PLACE:  Aquinas Hall, Room 108. The talk will also be held on Zoom from 5:15 p.m. to 6:15 p.m. (ET). See the information about the corresponding link below.

ORGANIZERS: V. Bogdan (The Catholic University of America), P. Kainen (Georgetown University), R. Kalpathy (The Catholic University of America), and A. Levin (The Catholic University of America).

Tel: 202-319-5221  E-mail:levin@cua.edu

Web page:  https://mathematics.catholic.edu/faculty-and-research/mathematics-seminar/index.html

The talk will be on Zoom as well (from 5:15 p.m. to 6:15 p.m. ET).   The following is the information about the corresponding link.