Mikhail Katz
Mikhail "Mischa" Gershevich Katz (born 1958, in Chișinău)[1] is an Israeli mathematician, a professor of mathematics at Bar-Ilan University. His main interests are differential geometry, geometric topology and mathematics education; he is the author of the book Systolic Geometry and Topology, which is mainly about systolic geometry. The Katz–Sabourau inequality is named after him and Stéphane Sabourau.[2][3]
Mikhail Katz | |
|---|---|
| Born | 1958 |
| Nationality | Israeli |
| Education | Harvard University Columbia University |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Bar-Ilan University |
| Thesis | Jung's Theorem in Complex Projective Geometry |
| Doctoral advisor | Troels Jørgensen Mikhail Gromov |
| Website | http://u.cs.biu.ac.il/~katzmik/ |
Biography
Mikhail Katz was born in Chișinău in 1958. His mother was Clara Katz (née Landman). In 1976, he moved with his mother to the United States.[4][5]
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.[6] His thesis title is Jung's Theorem in Complex Projective Geometry.
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]
Work
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 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".[7] Marcel Berger in his article "What is... a Systole?"[8] 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[9] including work that provides an alternative interpretation of the number 0.999....[10]
Selected publications
- Bair, Jacques; Błaszczyk, Piotr; Ely, Robert; Henry, Valérie; Kanovei, Vladimir; Katz, Karin; Katz, Mikhail; Kutateladze, Semen; McGaffey, Thomas; Schaps, David; Sherry, David; Shnider, Steve (2013), "Is mathematical history written by the victors?" (PDF), Notices of the American Mathematical Society, 60 (7): 886–904, arXiv:1306.5973, doi:10.1090/noti1001.
- Katz, Mikhail G.; Sherry, David (2012), "Leibniz's laws of continuity and homogeneity", Notices of the American Mathematical Society, 59 (11): 1550–1558, arXiv:1211.7188, Bibcode:2012arXiv1211.7188K, doi:10.1090/noti921, S2CID 42631313.
- Katz, Mikhail G.; Schaps, David; Shnider, Steve (2013), "Almost Equal: The Method of Adequality from Diophantus to Fermat and Beyond", Perspectives on Science, 21 (3): 283–324, arXiv:1210.7750, Bibcode:2012arXiv1210.7750K, doi:10.1162/POSC_a_00101, S2CID 57569974.
- Borovik, Alexandre; Jin, Renling; Katz, Mikhail G. (2012), "An Integer Construction of Infinitesimals: Toward a Theory of Eudoxus Hyperreals", Notre Dame Journal of Formal Logic, 53 (4): 557–570, arXiv:1210.7475, Bibcode:2012arXiv1210.7475B, doi:10.1215/00294527-1722755, S2CID 14850847.
- Kanovei, Vladimir; Katz, Mikhail G.; Mormann, Thomas (2013), "Tools, Objects, and Chimeras: Connes on the Role of Hyperreals in Mathematics", Foundations of Science, 18 (2): 259–296, arXiv:1211.0244, doi:10.1007/s10699-012-9316-5, S2CID 7631073.
- Katz, Mikhail; Tall, David (2012), "A Cauchy-Dirac delta function", Foundations of Science, 18: 107–123, arXiv:1206.0119, Bibcode:2012arXiv1206.0119K, doi:10.1007/s10699-012-9289-4, S2CID 119167714.
- Katz, Mikhail; Sherry, David (2012), "Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, and Their Foes from Berkeley to Russell and Beyond", Erkenntnis, 78 (3): 571–625, arXiv:1205.0174, Bibcode:2012arXiv1205.0174K, doi:10.1007/s10670-012-9370-y, S2CID 119329569.
- Błaszczyk, Piotr; Katz, Mikhail; Sherry, David (2012), "Ten misconceptions from the history of analysis and their debunking", Foundations of Science, 18: 43–74, arXiv:1202.4153, Bibcode:2012arXiv1202.4153B, doi:10.1007/s10699-012-9285-8, S2CID 119134151.
- Katz, Mikhail; Tall, David (2012), Tension between Intuitive Infinitesimals and Formal Mathematical Analysis, Bharath Sriraman, Editor. Crossroads in the History of Mathematics and Mathematics Education. The Montana Mathematics Enthusiast Monographs in Mathematics Education 12, Information Age Publishing, Inc., Charlotte, NC, pp. 71–89, arXiv:1110.5747, Bibcode:2011arXiv1110.5747K.
- Katz, Karin Usadi; Katz, Mikhail G. (2011), "Meaning in Classical Mathematics: Is it at Odds with Intuitionism?", Intellectica, 56 (2): 223–302, arXiv:1110.5456, Bibcode:2011arXiv1110.5456U.
- Borovik, Alexandre; Katz, Mikhail G. (2012), "Who gave you the Cauchy—Weierstrass tale? The dual history of rigorous calculus", Foundations of Science, 17 (3): 245–276, arXiv:1108.2885, doi:10.1007/s10699-011-9235-x, S2CID 119320059.
- Katz, Karin Usadi; Katz, Mikhail G. (2011), "Cauchy's continuum", Perspectives on Science, 19 (4): 426–452, arXiv:1108.4201, doi:10.1162/POSC_a_00047, MR 2884218, S2CID 57565752.
- Katz, Karin Usadi; Katz, Mikhail G.; Sabourau, Stéphane; Shnider, Steven; Weinberger, Shmuel (2011), "Relative systoles of relative-essential 2-complexes", Algebraic & Geometric Topology, 11 (1): 197–217, arXiv:0911.4265, doi:10.2140/agt.2011.11.197, MR 2764040, S2CID 20087785.
- Katz, Karin Usadi; Katz, Mikhail G. (2012), "Stevin numbers and reality", Foundations of Science, 17 (2): 109–123, arXiv:1107.3688, doi:10.1007/s10699-011-9228-9, S2CID 119167692.
- Katz, Karin Usadi; Katz, Mikhail G. (2012), "A Burgessian critique of nominalistic tendencies in contemporary mathematics and its historiography", Foundations of Science, 17 (1): 51–89, arXiv:1104.0375, doi:10.1007/s10699-011-9223-1, MR 2896999, S2CID 119250310.
- Katz, Mikhail G. (2007), Systolic geometry and topology, Mathematical Surveys and Monographs, vol. 137, Providence, RI: American Mathematical Society, ISBN 978-0-8218-4177-8, MR 2292367. 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, arXiv:1007.3018, Bibcode:2010arXiv1007.3018U, doi:10.54870/1551-3440.1381, S2CID 11544878, archived from the original on 2011-07-20.
- 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, Bibcode:2010arXiv1003.1501K, doi:10.1007/s10649-010-9239-4, S2CID 115168622.
- Bangert, Victor; Katz, Mikhail G. (2003), "Stable systolic inequalities and cohomology products", Communications on Pure and Applied Mathematics, 56 (7): 979–997, arXiv:math/0204181, doi:10.1002/cpa.10082, MR 1990484, S2CID 14485627.
- 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, arXiv:dg-ga/9708007, doi:10.1002/cpa.20146, MR 2248895, S2CID 15470409.
- 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, MR 2475399, S2CID 2575584.
- Croke, Christopher B.; Katz, Mikhail G. (2003), "Universal volume bounds in Riemannian manifolds", in Yau, S. T. (ed.), 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, MR 2039987.
- Katz, Mikhail G. (1983), "The filling radius of two-point homogeneous spaces", Journal of Differential Geometry, 18 (3): 505–511, doi:10.4310/jdg/1214437785, MR 0723814.
References
- Curriculum vitae, retrieved 2011-05-23.
- Kalogeropoulos, Nikolaos (2017). "Systolic aspects of black hole entropy". arXiv:1711.09963 [gr-qc].
- Chavel, Isaac (2006-04-10). Riemannian Geometry: A Modern Introduction. Cambridge University Press. ISBN 978-1-139-45257-1.
- "Clara Katz, a Soviet émigré who saved her ailing granddaughter, dies at 85 – The Boston Globe". archive.boston.com. Retrieved 2018-01-10.
- "Grandmother bucked the Soviet system – Obituaries – smh.com.au". www.smh.com.au. 12 October 2006. Retrieved 2018-01-10.
- Mikhail Katz at the Mathematics Genealogy Project
- 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
- Berger, M.: What is... a Systole? Notices of the AMS 55 (2008), no. 3, 374–376.
- Katz & Katz (2010).
- Stewart, I. (2009) Professor Stewart's Hoard of Mathematical Treasures, Profile Books, p. 174.
External links
- Mikhail Katz's home page
- Mikhail Katz publications indexed by Google Scholar