Michael Kapovich

Misha Kapovich, Oberwolfach 2015

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

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]

in 2006 in Madrid he was an Invited Speaker at the International Congress of Mathematicians with talk Generalized triangle inequalities and their applications.^[3]

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

Hyperbolic manifolds and discrete groups. 2001. Reprint of the 2001 edition. Modern Birkhäuser Classics. Birkhäuser Boston, Inc., Boston, MA, 2009. ISBN 978-0-8176-4912-8^[4]
with B. Leeb, J. J. Millson: The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra. Memoirs of the AMS, Volume 192, Number 896. American Mathematical Society. 2008. ISBN 978-0-8218-4054-2.
with Cornelia Druţu: Geometric group theory. AMS Colloquium Publications, vol. 63. American Mathematical Society. 2018.

References

↑ Michael Kapovich at the Mathematics Genealogy Project
↑ "Michael Kapovich". UC Davis Mathematics.
↑ Kapovich, Michael (2006). "Generalized triangle inequalities and their applications" (PDF). In: Proceedings of the International Congress of Mathematicians—Madrid. vol. 2. pp. 719–742.
↑ Taylor, Scott (14 January 2011). "Review of Hyperbolic Manifolds and Discrete Groups by Michael Kapovich". MAA Reviews, Mathematical Association of America.

External links

online preprints by Kapovich. ucdavis.edu.
"M. Kapovich: Introduction to geometric universality". YouTube. 15 November 2013.
"M. Kapovich: Universality for character schemes for 3 manifold groups". YouTube. 12 November 2013.
"Topology of complex projective varieties and 3-dimensional hyperbolic geometry (Misha Kapovich)". YouTube. 10 January 2017.
lectures at Geometry, Groups and Dynamics (GGD) - 2017, International Centre for Theoretical Sciences, Tata Institute
- "Discrete Isometry Group of Higher Rank Symmetric Spaces (Lecture - 01) by Misha Kapovich". YouTube. 16 November 2017.
- "Discrete Isometry Group of Higher Rank Symmetric Spaces (Lecture - 02) by Misha Kapovich". YouTube. 16 November 2017.
- "Discrete Isometry Group of Higher Rank Symmetric Spaces (Lecture - 03) by Misha Kapovich". YouTube. 21 November 2017.
- "Discrete Isometry Group of Higher Rank Symmetric Spaces (Lecture - 04) by Misha Kapovich". YouTube. 21 November 2017.

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[1] Michael Kapovich at the Mathematics Genealogy Project

[2] "Michael Kapovich". UC Davis Mathematics.

[3] Kapovich, Michael (2006). "Generalized triangle inequalities and their applications" (PDF). In: Proceedings of the International Congress of Mathematicians—Madrid. vol. 2. pp. 719–742.

[4] Taylor, Scott (14 January 2011). "Review of Hyperbolic Manifolds and Discrete Groups by Michael Kapovich". MAA Reviews, Mathematical Association of America.