RAP "SPACES OF NON-POSITIVE CURVATURE"
Based on the book "Metric Spaces of non-positive curvature"
by M.Bridson and A.Hefliger.
Organizers in the Spring of 2001 are:
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Ilya Kapovich kapovich@math.uiuc.edu
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Stephanie Alexander sba@math.uiuc.edu
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Paul Scupp schupp@math.uiuc.edu
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Richard Bishop bishop@math.uiuc.edu
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Peter Brinkmann brinkman@math.uiuc.edu
Time and Place: Tuesdays, 2pm, Altgeld Hall 345
This term I hold "official" RAP office hours:
Mondays 2-4pm,
Illini Hall, Room 328
Appointments at other times are possible!! Call or
e-mail me to set an appointment.
Office phone number: (217)265-0633
E-mail: kapovich@math.uiuc.edu
WWW: http://www.math.uiuc.edu/~kapovich
Schedule of talks:
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Feb 6, Dick Bishop, Introduction to spaces of curvature
bounded above
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Feb 13, Dick Bishop, Introduction to spaces of curvature
bounded above (continued)
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Feb 20, Elizabeth Denne, Basic definitions and propetries
of CAT(k) geometries
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Feb 27, Brad Edge, The CAT(k) 4-point condition
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March 6, Ilya Kapovich, Asymptotic cones and CAT(k) geometry
Abstract:
The notion of an asyptotic cone of a metric space with
respect to a
non-principal ultrafilter was introduced by
Van den Dries and Wilkie to study limits of metric spaces
which do not
converge in the Gromov-Hausdorff sense. We will discuss
asyptotic cones of
CAT(k) spaces and their properties.
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March 20, Craig Davis, Convexity of the metric and rigidity
of flat shapes in CAT(0)-spaces
Abstract:
We will discuss the convexity of the distance function
on CAT(0)-spaces and geometric centers of bounded sets.
We will also show that a geodesic triangle in a CAT(0)-space,
which is ``no thinner" than the corresponding comparison triangle, is itself
Euclidean or ``flat".
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March 27, Misha Gavrilovich, UIUC; Cones, spherical
joins and the space of directions in CAT(0)-spaces
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April 3, Misha Gavrilovich and Noah Salvaterra, UIUC,
Berestovsky's theorem and the space of directions
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April 10, Professor Peter Brinkman, UIUC; Cartan-Hadamard
Theorem
Abstract: I will present the Cartan-Hadamard
Theorem for complete connected metric spaces. This theorem strongly resembles
the Cartan-Hadamard Theorem of
Riemannian geometry because it uses local curvature conditions
to draw powerful conclusions about the global geometry and topology of
a space.
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April 17, Professor Peter Brinkman, UIUC; Cartan-Hadamard
Theorem (continued)
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April 24, Bogdan Petrenko, UIUC; Cartan-Hadamard
Theorem and Alexandrov patchwork
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May 1, Bogdan Petrenko, UIUC; Alexandrov patchwork
(continued)
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