Michael Kapovich

Michael Kapovich (also Misha Kapovich, Михаил Эрикович Капович, transcription Mikhail Erikovich Kapovich, born 1963) is a Russian-American mathematician.

Misha Kapovich, Oberwolfach 2015

Kapovich was awarded a doctorate in 1988 at the Sobolev Institute of Mathematics in Novosibirsk with thesis advisor Samuel Leibovich Krushkal and thesis "Плоские конформные структуры на 3-многообразиях" (Flat conformal structures on 3-manifolds, Russian lang. thesis).[1] Kapovich is now a professor at University of California, Davis, where he has been since 2003.

His research deals with low-dimensional geometry and topology, Kleinian groups, hyperbolic geometry, geometric group theory, geometric representation theory in Lie groups, spaces of nonpositive curvature, and configuration spaces of arrangements and mechanical linkages.[2][3]

in 2006 in Madrid he was an Invited Speaker at the International Congress of Mathematicians with talk Generalized triangle inequalities and their applications.[4]

He is married to mathematician Jennifer Schultens.[5] He has two brothers, both of whom are mathematicians as well: Ilya Kapovich works in group theory and geometric topology at CUNY, and Vitali Kapovich researches global Riemannian geometry at the University of Toronto.[6][7][2]

Selected publications

Articles
  • On monodromy of complex projective structures. Invent. Math. 119 (1995), no. 1, 243–265. doi:10.1007/BF01245182
  • with B. Leeb: On asymptotic cones and quasi-isometric classes of fundamental groups of 3-manifolds. Geom. Funct. Anal. 5 (1995), no. 3, 582–603. doi:10.1007/BF01895833
  • with J. J. Millson: On the moduli space of polygons in the Euclidean plane. J. Differential Geom. 42 (1995), no. 1, 133–164.
  • with J. J. Millson: The symplectic geometry of polygons in Euclidean space. J. Differential Geom. 44 (1996), no. 3, 479–513. doi:10.4310/jdg/1214459218
  • with B. Leeb: Quasi-isometries preserve the geometric decomposition of Haken manifolds. Invent. Math. 128 (1997), no. 2, 393–416. doi:10.1007/s002220050145
  • with J. J. Millson: On representation varieties of Artin groups, projective arrangements and the fundamental groups of smooth complex algebraic varieties. Inst. Hautes Études Sci. Publ. Math. 88 (1998), 5–95 (1999). doi:10.1007/BF02701766
  • with D. Gallo, A. Marden: The monodromy groups of Schwarzian equations on closed Riemann surfaces. Ann. of Math. (2) 151 (2000), no. 2, 625–704.
  • with B. Kleiner: Hyperbolic groups with low-dimensional boundary. Ann. Sci. Ecole Norm. Sup. (4) 33 (2000), no. 5, 647–669.
  • with M. Bestvina, B. Kleiner: Van Kampen's embedding obstruction for discrete groups. Invent. Math. 150 (2002), no. 2, 219–235. doi:10.1007/s00222-002-0246-7
  • Homological dimension and critical exponent of Kleinian groups. Geom. Funct. Anal. 18 (2009), no. 6, 2017–2054. doi:10.1007/s00039-009-0705-z
  • Dirichlet fundamental domains and topology of projective varieties. Invent. Math. 194 (2013), no. 3, 631–672 doi:10.1007/s00222-013-0453-4
  • with J. Kollár: Fundamental groups of links of isolated singularities. J. Amer. Math. Soc. 27 (2014), no. 4, 929–952. doi:10.1090/S0894-0347-2014-00807-9
  • with B. Leeb, J. Porti: Anosov subgroups: Dynamical and geometric characterizations. Eur. J. Math. 3 (2017), 808–898. doi:10.1007/s40879-017-0192-y

Books

References
  1. Michael Kapovich at the Mathematics Genealogy Project
  2. "Michael Kapovich". UC Davis Mathematics.
  3. Kapovich, Michael; Millson, John J. (1999), Brylinski, Jean-Luc; Brylinski, Ranee; Nistor, Victor; Tsygan, Boris (eds.), "Moduli Spaces of Linkages and Arrangements", Advances in Geometry, Boston, MA: Birkhäuser, pp. 237–270, doi:10.1007/978-1-4612-1770-1_11, ISBN 978-1-4612-1770-1, retrieved 2023-04-17
  4. Kapovich, Michael (2006). "Generalized triangle inequalities and their applications" (PDF). In: Proceedings of the International Congress of Mathematicians—Madrid. Vol. 2. pp. 719–742.
  5. Hironaka, Eriko (March 9, 2017). "Author Interview: Jennifer Schultens". Book Ends: Conversations about math books. American Mathematical Society.
  6. Kapovich, Ilya. "Faculty website of Ilya Kapovich". Retrieved March 2, 2021.
  7. "Vitali Kapovitch's homepage". www.math.utoronto.ca. Retrieved 2021-03-02.
  8. Taylor, Scott (14 January 2011). "Review of Hyperbolic Manifolds and Discrete Groups by Michael Kapovich". MAA Reviews, Mathematical Association of America.
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