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] [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
- Kapovich, Michael; Kapocivh, Mikhail (2001). Hyperbolic manifolds and discrete groups. Springer. ISBN 978-0-8176-3904-4. Reprint of the 2001 edition. Modern Birkhäuser Classics. Birkhäuser Boston, Inc., Boston, MA, 2009. ISBN 978-0-8176-4912-8 [8]
- 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. ISBN 978-1-4704-1104-6.
References
- ^ Michael Kapovich at the Mathematics Genealogy Project
- ^ a b "Michael Kapovich". UC Davis Mathematics.
- ^ 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
- ^ Kapovich, Michael (2006). "Generalized triangle inequalities and their applications" (PDF). In: Proceedings of the International Congress of Mathematicians—Madrid. Vol. 2. pp. 719–742.
- ^ Hironaka, Eriko (March 9, 2017). "Author Interview: Jennifer Schultens". Book Ends: Conversations about math books. American Mathematical Society.
- ^ Kapovich, Ilya. "Faculty website of Ilya Kapovich". Retrieved March 2, 2021.
- ^ "Vitali Kapovitch's homepage". www.math.utoronto.ca. Retrieved 2021-03-02.
- ^ 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.
| International | |
|---|---|
| National | |
| Academics | |
| Other | |
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] [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
- Kapovich, Michael; Kapocivh, Mikhail (2001). Hyperbolic manifolds and discrete groups. Springer. ISBN 978-0-8176-3904-4. Reprint of the 2001 edition. Modern Birkhäuser Classics. Birkhäuser Boston, Inc., Boston, MA, 2009. ISBN 978-0-8176-4912-8 [8]
- 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. ISBN 978-1-4704-1104-6.
References
- ^ Michael Kapovich at the Mathematics Genealogy Project
- ^ a b "Michael Kapovich". UC Davis Mathematics.
- ^ 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
- ^ Kapovich, Michael (2006). "Generalized triangle inequalities and their applications" (PDF). In: Proceedings of the International Congress of Mathematicians—Madrid. Vol. 2. pp. 719–742.
- ^ Hironaka, Eriko (March 9, 2017). "Author Interview: Jennifer Schultens". Book Ends: Conversations about math books. American Mathematical Society.
- ^ Kapovich, Ilya. "Faculty website of Ilya Kapovich". Retrieved March 2, 2021.
- ^ "Vitali Kapovitch's homepage". www.math.utoronto.ca. Retrieved 2021-03-02.
- ^ 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.
| International | |
|---|---|
| National | |
| Academics | |
| Other | |