Mikhail Katz

Mikhail Katz (born 1958)^[1] 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.^[1] He did his graduate studies at Columbia University, receiving his Ph.D. in 1984 under the joint supervision of Troels Jørgensen and Mikhael Gromov.^[2] 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.^[1]

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".^[3] Marcel Berger in his article "What is... a Systole?"^[4] 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^[5] including work that provides an alternative interpretation of the number 0.999....^[6]

Selected publications

• Borovik, Alexandre; Katz, Mikhail G. (2011), "Who gave you the Cauchy--Weierstrass tale? The dual history of rigorous calculus", Foundations of Science (4), doi:10.1007/s10699-011-9235-x .

• Katz, Karin Usadi; Katz, Mikhail G. (2011), "Cauchy's continuum", Perspectives on Science 19 (4): 426–452, doi:10.1162/POSC_a_00047 .
• Katz, Karin Usadi; Katz, Mikhail G.; Sabourau, Stéphane; Shnider, Steven; Weinberger, Shmuel (2011), "Relative systoles of relative-essential 2-complexes", Algebraic and Geometric Topology 11 (1): 197–217, doi:10.2140/agt.2011.11.197, MR2764040 .
• Katz, Karin Usadi; Katz, Mikhail G. (2011), "Stevin numbers and reality", Foundations of Science, doi:10.1007/s10699-011-9228-9 .
• Katz, Karin Usadi; Katz, Mikhail G. (2011), "A Burgessian critique of nominalistic tendencies in contemporary mathematics and its historiography", Foundations of Science, arXiv:1104.0375, doi:10.1007/s10699-011-9223-1 .
• Katz, Mikhail G. (2007), Systolic geometry and topology, Mathematical Surveys and Monographs, 137, Providence, RI: American Mathematical Society, ISBN 978-0-8218-4177-8, MR2292367 . With an appendix by J. Solomon.
• Katz, Karin Usadi; Katz, Mikhail G. (2010), "When is .999... less than 1?", The Montana Mathematics Enthusiast 7 (1): 3–30, http://www.math.umt.edu/TMME/vol7no1/ .
• Katz, Karin Usadi; Katz, Mikhail G. (2010), "Zooming in on infinitesimal 1–.9.. in a post-triumvirate era", Educational Studies in Mathematics 74 (3): 259–273, arXiv:1003.1501, doi:10.1007/s10649-010-9239-4 .
• Bangert, Victor; Katz, Mikhail G. (2003), "Stable systolic inequalities and cohomology products", Communications on Pure and Applied Mathematics 56 (7): 979–997, doi:10.1002/cpa.10082, MR1990484 .
• Katz, Mikhail G.; Rudyak, Yuli B. (2006), "Lusternik–Schnirelmann category and systolic category of low-dimensional manifolds", Communications on Pure and Applied Mathematics 59 (10): 1433–1456, doi:10.1002/cpa.20146, MR2248895 .
• Bangert, Victor; Katz, Mikhail G.; Shnider, Steven; Weinberger, Shmuel (2009), "E₇, Wirtinger inequalities, Cayley 4-form, and homotopy", Duke Mathematical Journal 146 (1): 35–70, arXiv:math.DG/0608006, doi:10.1215/00127094-2008-061, MR2475399 .
• Croke, Christopher B.; Katz, Mikhail G. (2003), "Universal volume bounds in Riemannian manifolds", in Yau, S. T., Surveys in Differential Geometry VIII, Lectures on Geometry and Topology held in honor of Calabi, Lawson, Siu, and Uhlenbeck at Harvard University, May 3–5, 2002, Int. Press, Somerville, MA, pp. 109–137, arXiv:math.DG/0302248, MR2039987 .
• Katz, Mikhail G. (1983), "The filling radius of two-point homogeneous spaces", Journal of Differential Geometry 18 (3): 505–511, MR723814, http://projecteuclid.org/getRecord?id=euclid.jdg/1214437785 .

References

1. ^ ^{a b c} Curriculum vitae, retrieved 2011-05-23.
2. ^ Mikhail Katz at the Mathematics Genealogy Project.
3. ^ Gromov, Misha: Metric structures for Riemannian and non-Riemannian spaces. Based on the 1981 French original. With appendices by M. Katz, P. Pansu and S. Semmes. Translated from the French by Sean Michael Bates. Progress in Mathematics, 152. Birkhäuser Boston, Inc., Boston, MA, 1999. xx+585 pp. ISBN 0-8176-3898-9
4. ^ Berger, M.: What is... a Systole? Notices of the AMS 55 (2008), no. 3, 374–376.
5. ^ Katz & Katz (2010).
6. ^ Stewart, I. (2009) Professor Stewart's Hoard of Mathematical Treasures, Profile Books, p. 174.

External links

• Mikhail Katz's home page

Persondata
Name	Katz, Mikhail
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Date of birth	1958
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