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| Benjamin Weiss | |
|---|---|
| Name | Benjamin Weiss |
| Birth date | 1941 |
| Birth place | New York City |
| Fields | Mathematics |
| Workplaces | State University of New York at Binghamton, University of Chicago, Hebrew University of Jerusalem |
| Alma mater | Columbia University, Stanford University |
| Doctoral advisor | Donald Samuel Ornstein |
| Known for | Ergodic theory, dynamical systems, entropy, measure-preserving transformations |
Benjamin Weiss
Benjamin Weiss is an American mathematician noted for his work in ergodic theory, dynamical systems, and measure theory. His research on entropy, invariant measures, and topological dynamics influenced developments in the theory of dynamical systems during the late 20th century, with connections to the work of colleagues at Columbia University, Stanford University, and institutions in Israel. Weiss has held faculty positions at major universities and contributed foundational results that link measurable dynamics to topological and symbolic models.
Weiss was born in New York City in 1941 and pursued undergraduate studies at Columbia University during a period when the department included prominent figures such as Paul Halmos and André Weil. He completed graduate work at Stanford University, where his doctoral advisor was Donald Ornstein (often published as Donald S. Ornstein), a central figure in the classification of Bernoulli shifts and isomorphism problems for measure-preserving transformations. Weiss's thesis work built on techniques from ergodic theory and measurable dynamics developed in the 1950s and 1960s by researchers including John von Neumann, Kolmogorov (A. N. Kolmogorov), and Anatole Katok.
After receiving his doctorate, Weiss held academic appointments that included visiting and permanent positions at the University of Chicago, the Hebrew University of Jerusalem, and the State University of New York at Binghamton. During his tenure at these institutions he collaborated with researchers associated with the Institute for Advanced Study and participated in seminars with members of the American Mathematical Society and the Mathematical Reviews community. Weiss supervised graduate students who later took faculty positions at universities such as Tel Aviv University and University of California, Berkeley. He was an invited speaker at conferences organized by societies including the International Congress of Mathematicians and the European Mathematical Society.
Weiss made major contributions to the structure theory of measure-preserving transformations and the interplay between measurable and topological dynamics. He worked on classification problems related to entropy invariants introduced by Andrey Kolmogorov and refined by Donald Ornstein, establishing connections between measure-theoretic entropy and topological conjugacy for classes of systems. His research explored symbolic models for smooth and measurable systems, linking shifts of finite type, subshifts, and odometers to transformations studied by John Milnor and Mikhail Lyubich.
Weiss produced influential results on expansive behavior, almost periodic points, and minimal sets, often employing techniques from combinatorics on words and symbolic coding introduced by Shannon-inspired approaches and later by researchers such as Michael Keane and Roy Adler. He addressed the realization problem for entropy values and constructed examples illustrating subtle distinctions between topological entropy and measure-theoretic entropy, drawing on methods similar to those used by Rudolph (Daniel J. Rudolph), Edward A. Robinson Jr., and David Ruelle.
Another strand of Weiss’s work concerned orbit equivalence and the classification of amenable group actions, connecting to the orbit equivalence theory advanced by Hillel Furstenberg, Giordano, Putnam, and Skau, and Ornstein and Weiss (note: Ornstein and Weiss collaborated on amenable group actions). Weiss also investigated entropy pairs, measure-theoretic mixing properties, and the relationships among recurrence, rigidity, and spectral phenomena in dynamical systems, overlapping with results from William Parry and Ilya Piatetski-Shapiro-style spectral theory influences.
- Contributions to the theory of entropy and isomorphism for measure-preserving transformations, with examples and counterexamples that clarified classification schemes developed by Donald Ornstein and Andrey Kolmogorov. - Papers on symbolic dynamics, including construction of symbolic extensions and codings related to systems considered by Rufus Bowen and Morse and Hedlund-type symbolic frameworks. - Articles on orbit equivalence and amenable group actions, situating his results alongside work by Furstenberg and Giordano, Putnam, and Skau. - Studies on topological dynamics, minimal sets, and expansive homeomorphisms, connecting to the literature of Roy Adler and Rufus Bowen.
(Representative titles are often cited in surveys of ergodic theory and symbolic dynamics, and appear in proceedings of the International Congress of Mathematicians and journals affiliated with the American Mathematical Society and the London Mathematical Society.)
Weiss received recognition from mathematical societies for his contributions to dynamics, including invited lectures at the International Congress of Mathematicians and fellowships or visiting appointments at research centers such as the Institute for Advanced Study and the Mathematical Sciences Research Institute. His work has been cited in award citations and surveys produced by the American Mathematical Society and in collective volumes honoring major figures in ergodic theory such as Donald Ornstein and Hillel Furstenberg.
Weiss has maintained academic ties in the United States and Israel, collaborating with colleagues at institutions including the Hebrew University of Jerusalem and attending long-term seminars at centers like the Mathematical Sciences Research Institute and the Courant Institute of Mathematical Sciences. Outside mathematics he has been associated with cultural and academic communities in New York City and Jerusalem and has contributed to programs supporting young researchers at venues such as the Institute for Advanced Study and regional mathematics schools.
Category:American mathematicians Category:Ergodic theorists Category:Living people