Vitali Kapovitch's Home Page
Department of Mathematics,
University of Toronto,
Toronto, Ontario, Canada M5S 2E4
Office:
HU
1023
Telephone: (416)-978-6786
Fax:
(416)
978-4107
E-mail: vtk@math.toronto.edu
"God put me on Earth to
accomplish a certain number of things. Right now I am so far behind I
will never die."
--Bill
Watterson
Teaching:
- Winter 2012: MAT247
Algebra II
- Winter 2012: MAT246
Concepts in Abstract Mathematics
Research
Interests: I'm interested in global Riemannian geometry. More
specifically, I'm interested in convergence with lower sectional and
Ricci curvature bounds.
Here are the notes from my lectures
at SMS
2011
Summer
School
on
“Metric
Measure
Spaces:
Geometric
and Analytic Aspects”.
I'm currently working on a book on spaces with curvature bounded below
and above together with Stephganie Alexander and Anton Petrunin.
Here is a section on definitions of
Alexandrov spaces and the proof of the globalization theorem from
this book.
Workshop on Curvature and Global Shape.
Publications/Preprints
(which can also be downloaded here)
- Manifolds without conjugate points and
their fundamental groups, (with S. Ivanov), 2012
- On fibrations with formal elliptic fibers,
(with
M. Amann), 2011
- Structure of fundamental
groups of manifolds with Ricci curvature bounded below, (with B.
Wilking), submitted to Publications Mathématiques de
l'IHÉS, 2011.
- Alexandrov meets Kirzbraun,
(with
S. Alexander and A. Petrunin) , Proceedings of the 17th
Gökova Gemometry and Topology Conference, 2010
- An optimal lower curvature bound for convex
hypersurfaces in Riemannian manifolds, (with S. Alexander,
and A. Petrunin) , Illinois Journal of Mathematics, vol. 52, (2009), No
3, pp 1031-1033
- Perelman's Stability Theorem, Surveys in Differential
geometry, Metric and Comparison geometry, vol XI , International press,
(2007), 103-136
- Nilpotency,
almost
nonnegative curvature and the gradient push, (with A.
Petrunin and W. Tuschmann), Annals of Mathematics, Vol. 171 (2010), No.
1, 343-373
- Nonnegative pinching, moduli spaces and
bundles with infinitely many souls,(with A. Petrunin and W.
Tuschmann), Journal of Diff.
Geometry, 71, (2005), no. 3,
pp. 365-383.
- Pinching
estimates for negatively curved manifolds with nilpotent fundamental
groups,(with
I. Belegradek), Geom. Funct. Anal. 15, (2005), no. 5, 929--938.
- Curvature bounds via Ricci smoothing, Illinois Journal of Mathematics, 49, (2005) no. 1, pp.259-263,
- (with I. Belegradek)
Classification of negatively pinched manifolds with amenable
fundamental groups , Acta Math. 196 (2006), no. 2, 229–260
- Biquotients
with
singly
generated
rational cohomology, (with W. Ziller), Geometriae Dedicata,
104 (1): 149--160, 2004
- Restrictions
on
collapsing with a lower sectional curvature bound, Mathematische
Zeitschrift, 249,
(2005),no.3, pp. 519 - 539
- A note on
rational homotopy of biquotients, preprint
- Regularity
of
limits of noncollapsing sequences of manifolds, Geom. Funct. Anal. 12
(2002), no. 1, 121--137.
- (with
I.Belegradek) Obstructions to nonnegative curvature and rational
homotopy theory, Journal of AMS, 16 (2003), 259-284.
- (with I.Belegradek)
Finiteness theorems for nonnegatively curved vector bundles, Duke
Mathematical Journal, 108 (2001), no. 1, pp. 109--134.
- (with
I.Belegradek)
Topological
obstructions to nonnegative curvature, Math. Ann. 320 (2001),
no.
1, 167--190.
- (with L. Guijarro)
Restrictions on the geometry at infinity of nonnegatively curved
manifolds, Duke Math. J. 78 (1995), no. 2, 257--276.
Here are some geometry links:
This home page is always
under construction 
