John Wermer Memorial Symposium | Department of Mathematics

11/18/23 - 11/19/23

Foxboro Auditorium
151 Thayer Street
Providence, RI 02912

Symposium Poster

Symposium Schedule/Shuttle Schedule

Campus Parking

Photos of John

Math Geneology Project

A paper by John Wermer "Function Algebras in the Fifties and Sixties"

Registration: Please complete this form to register for the symposium.

John Anderson, College of the Holy Cross
James Brennan, University of Kentucky
Brian Cole, Brown University
Ted Gamelin, University of California, LA
John Garnett, University of California, LA
Bruno Harris, Brown University
Dmitry Khavinson, University of South Florida
Norm Levenberg, Indiana University, Bloomington
Keith Lewis, New York University
John McCarthy, Washington University in St. Louis
Marshall Whittlesey, California State University, San Marcos

John Wermer (1927-2022) Memorial Minute - Written by Walter Strauss, Professor Emeritus at Brown University

John Wermer died in Providence on August 29, 2022. He was born in Vienna, Austria in 1927. He escaped with his family in 1939 and settled in New York City. After a year in the Navy, he received his BA in 1947 and his PhD in 1951, both from Harvard, followed by a postdoctoral position at Yale. John came to Brown in 1954, became a full professor in the Department of Mathematics in 1961 and was awarded the L. Herbert Ballou University Professorship in 1992. He retired in 1994 but continued to be active at Brown for many years thereafter. His last published paper appeared in 2020.

John made fundamental contributions to a key domain of mathematics called complex function theory, which is fundamental to many aspects of engineering and physics as well as other branches of mathematics. He authored some of the ground- breaking theoretical papers in this subject, especially at the interface between com- plex function theory and functional analysis, and an area known as approximation theory of complex analytic functions. He found definitive conditions under which all continuous complex functions can be approximated uniformly by analytic functions. In later years he expanded his work to functions of many complex variables.

John was invited to the International Congress of Mathematicians in 1962, re- ceived a Sloan Fellowship, was selected as a Fellow of the American Academy of Arts and Sciences, and was honored as a Foreign Member of the Kungliga Vetenskaps- Societeten (Sweden). He held visiting positions at E. T. H. Zurich, the Universit ́e de Paris Orsay, the Mittag-Leffler Institute in Sweden, the Institute for Advanced Study in Princeton, and the University of Illinois at Chicago.

Over his decades at Brown, John had a tremendous influence on the development of the Department of Mathematics. He was an inspiring teacher and supervised 14 Ph.D. students. In particular, he organized and became the soul of the weekly Analysis Seminar. He and his wife Christine, who raised two sons in Providence, opened up their home to their “mathematics family”, hosting many math parties at their house over the years. He personified complex analysis at Brown over these many decades.

In 2015 John recorded a moving personal oral history that focused on his early years and his heritage:

https://www.yiddishbookcenter.org/collections/oral-histories/interviews/woh-fi- 0000727/john-wermer-2015

John had a warm personality and a wry sense of humor. He was a true gentleman, a person of great humility and generosity. We will all miss him greatly.

SCHEDULE
SATURDAY, 11/18/23
9:30-10:00am	Coffee/Refreshments
10:00-10:45am	Dmitry Khavinson, University of South Florida	Title: Approximation Theory and Some Free Boundary Problems Abstract: I shall try to outline the program started 4 decades ago (at Brown, in fact) that focuses on approximating particular “badly approximable” functions that leads to unexpectedly exciting problems in mathematical physics. So called free boundary problems. For example studying the approximation of z* by analytic functions leads to the isoperimetric inequality, J. Serrin’s problem in hydrodynamics, equilibrium shape of electrified droplets, St. Venant’s inequality for torsional rigidity, etc. Many simply stated open questions, that still remain open in spite of the recent progress in the last decades, will be mentioned. The talk should be accessible to everyone.
11:00-11:45am	John McCarthy, Washington University in St. Louis	Title: Isometric extensions of holomorphic functions Abstract: Suppose V is a subvariety of an open set U in $C^n$. When does the pair (V,U) have the property that every holomorphic function from V to the unit disk extends to a holomorphic function from U to the unit disk? If U is very nice (eg a ball) then V has to be a retract. But without convexity assumptions, almost anything can happen. We will talk about what is known, and why convexity plays a role.
11:45am-1:15pm	Lunch break
1:15-2:00pm	Norman Levenberg, Indiana University, Bloomington	Title: Weighted holomorphic polynomial approximation Abstract: Which continuous functions on [0,1] can be uniformly approximated by a sequence of "incomplete" polynomials {p_n}, deg(p_n)=n, i.e., p_n is a linear combination of monomials x^k with k bigger than a for some 0<a<1? The answer comes from weighted potential theory. We discuss this background as motivation for more recent results on weighted holomorphic polynomial approximation in the complex plane and some observations in the several complex variable setting. This is joint work with S. Charpentier and F. Wielonsky (Université Aix-Marseille).
2:15-3:00pm	James Brennan, University of Kentucky	Title: The Property of Unique Continuation in Certain Spaces Spanned by Rational Functions on Compact Nowhere Dense Sets Abstract: It has been known for over a century that certain large classes of functions defined on a compact nowhere dense subset X of the complex plane, and obtained as limits of analytic functions in various metrics, can sometimes inherit the property of unique continuation characteristic of the approximating family. I shall discuss the subject from an historical point of view beginning with E ́mile Borel’s confrontation with Poincar ́e at his thesis defense in 1892, adding along the way some new results on the existence of boundary values for certain L2-spaces defined on sets without interior points together with a more direct approach to finely holomorphic functions.
3:00-3:45pm	Coffee break
3:45-4:30pm	John Garnett, University of California, LA	Title: H¹ − BMO Duality Revisited Abstract: Among the domains in R^d+1 satisfying a corkscrew condition and a boundary capacity density condition we study those for which an H¹ − BMO duality theorem holds for harmonic functions, in two different formulations.
6:00-9:00pm	Banquet Dinner	Brown Faculty Club (Invitation Only)
SUNDAY, 11/19/23
9:30-10:00am	Coffee/Refreshments
10:00-10:45am	Marshall Whittlesey, California State University, San Marcos	Title: Fibered polynomial hulls: work of Wermer and work of others that followe
11:00-11:45am	Brian Cole, Brown University	Title: Interpolation by bounded analytic functions and positive harmonic functions Abstract: In 1916 Pick characterized those values that can be interpolated by a bounded analytic function at n points on the unit disk D. The set K of those values is called the associated interpolation body. We generalize these problems and reformulate all concepts in terms of uniform algebras. Next, consider all non-negative harmonic functions defined on an open subset of Euclidean space. The set Λ of all values that can be interpolated by such functions is analogous to K. In some cases, we show that Λ is a semialgebraic set. Some of these results derive from joint work with John Wermer and Keith Lewis.
11:45am-1:15pm	Lunch break
1:15-1:45pm	Keith Lewis, New York University	Title: Efficient Portfolios Abstract: Given two random realized returns on an investment, which is to be preferred? This is a fundamental problem in finance that has no definitive solution except in the case one investment always returns more than the other. In 1952 Markowitz and Roy introduced the following criterion for risk vs. return in portfolio selection: if two portfolios have the same expected realized return then prefer the one with smaller variance. An efficient portfolio has the least variance among all portfolios having the same expected realized return. The primary contribution of this short note is the observation that the CAPM formula holds for realized returns as random variables, not just their expectations. This follows directly from writing down a mathematical model for one period investments.
1:55-2:25pm	Bruno Harris, Brown University	Title: “John Wermer at Yale” Abstract: John Wermer’s first academic appointment was as Instructor at Yale (1951),where he helped write the Dunford- Schwartz 3-volume book on Linear Operators and taught the Complex Analysis Graduate course. This speaker was a student in this course, and will describe the Mathematical atmosphere at Yale and the many links created by John between Yale and Brown.
2:35-3:05pm	Ted Gamelin, University of California, LA	Title: Recollections of John Wermer and the Early Years of Function Algebras.
3:15-3:45pm	Coffee Break

Sponsored by: Department of Mathematics

Organizers: Brian Cole, Lori Nascimento and Sharon Brennan