Michael Kapovich

File:Kapovich misha.jpg

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).{{MathGenealogy|id = 40826}} 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, {{ill|spaces of nonpositive curvature|de|CAT(0)-Raum}}, and configuration spaces of arrangements and mechanical linkages.{{cite web|title=Michael Kapovich|website=UC Davis Mathematics|url=https://www.math.ucdavis.edu/research/profiles/?fac_id=kapovich}}{{Citation |last1=Kapovich |first1=Michael |title=Moduli Spaces of Linkages and Arrangements |date=1999 |url=https://doi.org/10.1007/978-1-4612-1770-1_11 |work=Advances in Geometry |pages=237–270 |editor-last=Brylinski |editor-first=Jean-Luc |access-date=2023-04-17 |place=Boston, MA |publisher=Birkhäuser |language=en |doi=10.1007/978-1-4612-1770-1_11 |isbn=978-1-4612-1770-1 |last2=Millson |first2=John J. |editor2-last=Brylinski |editor2-first=Ranee |editor3-last=Nistor |editor3-first=Victor |editor4-last=Tsygan |editor4-first=Boris}}

in 2006 in Madrid he was an Invited Speaker at the International Congress of Mathematicians with talk Generalized triangle inequalities and their applications.{{cite book|author=Kapovich, Michael|chapter=Generalized triangle inequalities and their applications|title=In: Proceedings of the International Congress of Mathematicians—Madrid|volume=2|pages=719–742|year=2006|chapter-url=http://www.icm2006.org/proceedings/Vol_II/contents/ICM_Vol_2_35.pdf}}

He is married to mathematician Jennifer Schultens.{{cite web|url=https://blogs.ams.org/bookends/2017/03/09/author-interview-jennifer-schultens/|title=Author Interview: Jennifer Schultens|publisher=American Mathematical Society|date=March 9, 2017|work=Book Ends: Conversations about math books|first=Eriko|last=Hironaka}} 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.{{Cite web|last=Kapovich|first=Ilya|title=Faculty website of Ilya Kapovich|url=http://math.hunter.cuny.edu/ilyakapo/|access-date=March 2, 2021}}{{Cite web|title=Vitali Kapovitch's homepage|url=http://www.math.utoronto.ca/~vtk/|access-date=2021-03-02|website=www.math.utoronto.ca}}

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: [http://www.math.utah.edu/~kapovich/EPR/plane.pdf 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: [http://emis.de/journals/Annals/151_2/marden.pdf The monodromy groups of Schwarzian equations on closed Riemann surfaces.] Ann. of Math. (2) 151 (2000), no. 2, 625–704.
with B. Kleiner: [http://www.numdam.org/article/ASENS_2000_4_33_5_647_0.pdf 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 =

{{cite book|url=https://books.google.com/books?id=YmphheDo18kC|title=Hyperbolic manifolds and discrete groups|year=2001|isbn=978-0-8176-3904-4|last1=Kapovich|first1=Michael|last2=Kapovich|first2=Mikhail|publisher=Springer }} Reprint of the 2001 edition. Modern Birkhäuser Classics. Birkhäuser Boston, Inc., Boston, MA, 2009. {{ISBN|978-0-8176-4912-8}}{{cite web|author=Taylor, Scott|title=Review of Hyperbolic Manifolds and Discrete Groups by Michael Kapovich|date=14 January 2011|website=MAA Reviews, Mathematical Association of America|url=https://www.maa.org/press/maa-reviews/hyperbolic-manifolds-and-discrete-groups}}
with B. Leeb, J. J. Millson: {{cite book|title=The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra|publisher=American Mathematical Society|year=2008|series=Memoirs of the AMS, Volume 192, Number 896|url=https://books.google.com/books?id=CVzVCQAAQBAJ|isbn=978-0-8218-4054-2}}
with Cornelia Druţu: {{cite book|url=https://books.google.com/books?id=9WXZnQAACAAJ|title=Geometric group theory|year=2018|series=AMS Colloquium Publications, vol. 63|publisher=American Mathematical Society|isbn=978-1-4704-1104-6}}

References

External links

{{cite web|title=Online preprints by Kapovich|website=ucdavis.edu|url=https://www.math.ucdavis.edu/%7Ekapovich/eprints.html}}
{{cite web|url=https://www.youtube.com/watch?v=D_0CsmX_zB0|title=M. Kapovich: Introduction to geometric universality|date=15 November 2013|website=YouTube}}
{{cite web|url=https://www.youtube.com/watch?v=UgQHilGjtZw|title=M. Kapovich: Universality for character schemes for 3 manifold groups|date=12 November 2013|website=YouTube}}
{{cite web|url=https://www.youtube.com/watch?v=8ar7iLp8MvQ|title=Topology of complex projective varieties and 3-dimensional hyperbolic geometry (Misha Kapovich)|date=10 January 2017|website=YouTube}}
lectures at Geometry, Groups and Dynamics (GGD) – 2017, International Centre for Theoretical Sciences, Tata Institute
{{cite web|title=Discrete Isometry Group of Higher Rank Symmetric Spaces (Lecture – 01) by Misha Kapovich|date=16 November 2017|website=YouTube|url=https://www.youtube.com/watch?v=z9hS4Q297jw}}
{{cite web|title=Discrete Isometry Group of Higher Rank Symmetric Spaces (Lecture – 02) by Misha Kapovich|date=16 November 2017|website=YouTube|url=https://www.youtube.com/watch?v=itUtWaOl5WM}}
{{cite web|title=Discrete Isometry Group of Higher Rank Symmetric Spaces (Lecture – 03) by Misha Kapovich|date=21 November 2017|website=YouTube|url=https://www.youtube.com/watch?v=pcrvW8byyn8}}
{{cite web|title=Discrete Isometry Group of Higher Rank Symmetric Spaces (Lecture – 04) by Misha Kapovich|date=21 November 2017|website=YouTube|url=https://www.youtube.com/watch?v=dJqGeF2w8d4}}

Category:20th-century Russian mathematicians

Category:21st-century Russian mathematicians

Category:20th-century American mathematicians

Category:21st-century American mathematicians

Category:University of California, Davis faculty

Category:1963 births

Category:Living people