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)
- On
fibrations with formal elliptic
fibers,
(with
M. Amann), preprint, 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 
