Mikhail Katz
Encyclopedia
Mikhail Katz is an Israeli mathematician
, a professor of mathematics at Bar Ilan University. His main interests are differential geometry and geometric topology
; he is the author of a book about systolic geometry.
Katz earned a bachelor's degree in 1980 from Harvard University
. He did his graduate studies at Columbia University
, receiving his Ph.D. in 1984 under the joint supervision of Troels Jørgensen
and Mikhael Gromov. He moved to Bar-Ilan University in 1999, after previously holding positions at the University of Maryland, College Park
, Stony Brook University, Indiana University Bloomington
, the Institut des Hautes Études Scientifiques
, the University of Rennes 1
, Henri Poincaré University
, and Tel Aviv University
.
Katz has performed research in systolic geometry in collaboration with Luigi Ambrosio
, Victor Bangert
, Mikhail Gromov, Steve Shnider
, Shmuel Weinberger
, and others. He has authored research publications appearing in leading journals including Communications on Pure and Applied Mathematics
, Duke Mathematical Journal
, Geometric and Functional Analysis, and Journal of Differential Geometry
. Along with these papers, Katz was a contributor to the book "Metric Structures for Riemannian and Non-Riemannian Spaces
". Marcel Berger
in his article "What is... a Systole?" lists the book (Katz, 2007) as one of two books he cites in systolic geometry.
More recently Katz also contributed to the study of mathematics education
including work that provides an alternative interpretation of the number 0.999...
.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, a professor of mathematics at Bar Ilan University. His main interests are differential geometry and geometric topology
Geometric topology
In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another.- Topics :...
; he is the author of a book about systolic geometry.
Katz earned a bachelor's degree in 1980 from Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
. He did his graduate studies at Columbia University
Columbia University
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
, receiving his Ph.D. in 1984 under the joint supervision of Troels Jørgensen
Troels Jørgensen
Troels Jørgensen is a mathematician at Columbia university working on hyperbolic geometry and complex analysis, who proved Jørgensen's inequality. He wrote his thesis at the University of Copenhagen under Werner Fenchel and Bent Fuglede.-External resources:...
and Mikhael Gromov. He moved to Bar-Ilan University in 1999, after previously holding positions at the University of Maryland, College Park
University of Maryland, College Park
The University of Maryland, College Park is a top-ranked public research university located in the city of College Park in Prince George's County, Maryland, just outside Washington, D.C...
, Stony Brook University, Indiana University Bloomington
Indiana University Bloomington
Indiana University Bloomington is a public research university located in Bloomington, Indiana, in the United States. IU Bloomington is the flagship campus of the Indiana University system. Being the flagship campus, IU Bloomington is often referred to simply as IU or Indiana...
, the Institut des Hautes Études Scientifiques
Institut des Hautes Études Scientifiques
The Institut des Hautes Études Scientifiques is a French institute supporting advanced research in mathematics and theoretical physics...
, the University of Rennes 1
University of Rennes 1
The University of Rennes 1 is one of the two main universities in the city of Rennes, France. It is under the Academy of Rennes. It specializes in science, technology, law, economy, management and philosophy. The University of Rennes 1 has been in existence since 1969, but its heritage stems back...
, Henri Poincaré University
Henri Poincaré University
The Henri Poincaré University is a public research university located in Nancy, France. UHP is a member of the Nancy-Université federation, belonging to the french Nancy-Metz Academy.- History :...
, and Tel Aviv University
Tel Aviv University
Tel Aviv University is a public university located in Ramat Aviv, Tel Aviv, Israel. With nearly 30,000 students, TAU is Israel's largest university.-History:...
.
Katz has performed research in systolic geometry in collaboration with Luigi Ambrosio
Luigi Ambrosio
Luigi Ambrosio is a professor at Scuola Normale Superiore in Pisa, Italy.His main fields of research are the calculus of variations and geometric measure theory....
, Victor Bangert
Victor Bangert
Victor Bangert is Professor of Mathematics at the Mathematisches Institut in Freiburg, Germany. His main interests are differential geometry and dynamical systems theory.-Publications:...
, Mikhail Gromov, Steve Shnider
Steve Shnider
Steve Shnider is professor of mathematics at Bar Ilan University.He received a PhD in Mathematics from Harvard University in 1972, under Shlomo Sternberg....
, Shmuel Weinberger
Shmuel Weinberger
The mathematician Shmuel Aaron Weinberger is an American topologist. He completed a PhD in mathematics in 1982 at New York University under the direction of Sylvain Cappell. Weinberger was from 1994 to 1996 the Thomas A...
, and others. He has authored research publications appearing in leading journals including Communications on Pure and Applied Mathematics
Communications on Pure and Applied Mathematics
Communications on Pure and Applied Mathematics is a scientific journal which is associated with the Courant Institute of Mathematical Sciences. It publishes original research originating from or solicited by the institute, typically in the fields of applied mathematics, mathematical analysis, or...
, Duke Mathematical Journal
Duke Mathematical Journal
Duke Mathematical Journal is a peer-reviewed mathematics journal published by Duke University Press. It was established in 1935. The founding editors-in-chief were David Widder, Arthur Coble, and Joseph Miller Thomas. The first issue included a paper by Solomon Lefschetz...
, Geometric and Functional Analysis, and Journal of Differential Geometry
Journal of Differential Geometry
The Journal of Differential Geometry is a peer-reviewed mathematical journal published by the Lehigh University. The journal publishes nine issues per year and is distributed by International Press. Surveys in Differential Geometry] It also publishes an annual supplement in book form called...
. Along with these papers, Katz was a contributor to the book "Metric Structures for Riemannian and Non-Riemannian Spaces
Metric Structures for Riemannian and Non-Riemannian Spaces
Metric Structures for Riemannian and Non-Riemannian Spaces is a book in geometry by Mikhail Gromov. It was originally published in French in 1981 under the title Structures métriques pour les variétés riemanniennes, by CEDIC . The 1981 edition was edited by Jacques Lafontaine and Pierre Pansu...
". Marcel Berger
Marcel Berger
Marcel Berger is a French mathematician, doyen of French differential geometry, and a former director of the Institut des Hautes Études Scientifiques , France...
in his article "What is... a Systole?" lists the book (Katz, 2007) as one of two books he cites in systolic geometry.
More recently Katz also contributed to the study of mathematics education
Mathematics education
In contemporary education, mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research....
including work that provides an alternative interpretation of the number 0.999...
0.999...
In mathematics, the repeating decimal 0.999... denotes a real number that can be shown to be the number one. In other words, the symbols 0.999... and 1 represent the same number...
.