UCLA

MATH

PETER PETERSEN

 

Research:

Riemannian Geometry

Spring 2009

 

 

E-mail:

Email

Phone:

(310) 825 4149

Fax:

(310) 206 6673

Office:

Math Sciences: MS 6126

Address:

UCLA Mathematics Department
520 Portola Plaza
Los Angeles, CA 90095-1555

Here are a few handouts that I’ve used when teaching at UCLA:

 

·        A growing essay on manifold theory, de Rham cohomology and more.

·        An attempt to explain various counting methods in combinatorics and handout on max flow min cut

·        A book on linear algebra with a larger and less edited version here.

·        (updated 2/9/09) Errata and now also additional proofs for 2nd edition of Riemannian Geometry, New York: Springer Verlag, GTM 171, 2006.

 

Here are links to some of my research:

 

·        On the Set of Images Modulo Viewpoint and Contrast Changes with Ganesh Sundaramoorthi and Stefano Soatto

·        Classification of Almost Quarter Pinched Manifolds with Terence Tao (to appear in PAMS.)

·        An Exotic Sphere with Positive Sectional Curvature with Fred Wilhelm. (Fred’s beamer presentation)

·        Classification of Gradient Solitons with William Wylie

·        Ricci Solitons with Symmetries with William Wylie (to appear in PAMS.)

·        Rigidity of Ricci Solitons with William Wylie (to appear in Pac. J. math)

·        Generalized Doubling Meets Poincare with Colin Hinde (appeared in J. Geo. Anal.)

·        Published Work (requires access to MatSciNet)

My Ph D students:

·        Joe Borzellino, 1992

·        Liang-Koon Koh, 1992

·        Mark Cassorla, 1994

·        Sam Steingold, 1996

·        Chad Sprouse, 1999

·        Colin Hinde, 2008

Little known historical “facts” (I hope to elaborate on these and add more facts later):

·        Newton proved integrability of monotone functions (Principia: Book I, section I)

·        Lagrange proved the spectral theorem (for bilinear forms using Lagrange multipliers)

·        Bianchi classified the homogeneous geometries in dimension 3 (Google keyword: Bianchi Classification)

·        Lichnerowicz discovered the f-Laplacian and Bakry-Emery tensor and more in this paper for more details you have to checkout Lichnerowicz, André
Variétés kählériennes à première classe de Chern non negative et variétés riemanniennes à courbure de Ricci généralisée non negative.
J. Diff. Geo. 6 (1971/72), 47—94.