10,807 reputation
24675
bio website vmm.math.uci.edu
location Univ. of California at Irvine
age 84
visits member for 4 years, 11 months
seen May 14 at 20:21
I'm a Professor at UC Irvine, but spent most of my career at Brandeis. My research areas: Differential Topology, Transformation Groups, and Global Analysis. Recently I developed a math visualization program, 3D-XplorMath, freely available at http://3D-XplorMath.org) and a companion website, the Virtual Math Museum at http://VirtualMathMuseum.org. Last year I co-authored a differential equations text with my son Bob, most of which is downloadable from http://ode-math.com .

Feb
6
awarded  Enlightened
Feb
6
awarded  Nice Answer
Jan
13
comment Lie group action with no slice
@Yves Cormulier I don't think that's so Yves. If it were then even a compact group action wouldn't have a slice at an isolated fixed point p, whereas in fact an invariant neighborhood of p is a slice at p in that case.
Jan
13
revised Lie group action with no slice
added 22 characters in body
Jan
13
comment Lie group action with no slice
After thinking about my answer a bit I realized that an even simpler example is the action of the group Z of integers on the circle generated by rotation through an irrational angle.
Jan
13
answered Lie group action with no slice
Jan
10
awarded  Popular Question
Dec
28
awarded  Good Answer
Dec
28
awarded  Nice Question
Dec
9
awarded  Enlightened
Dec
7
awarded  Nice Answer
Dec
7
comment Notes for Bott's 1963 lectures on Morse theory
I did some more searching with Google and found that Amazon has a reference to: "Lectures on Morse theory: [revised and expanded version of notes of lectures delivered at Professor R. Bott's topology seminar at Harvard in February and March of 1963 [Unknown Binding] Richard S Palais (Author)" with Brandeis Univ, listed as the publisher. I suspect this must have been an early preprint version of "Morse Theory on Hilbert Manifolds"
Dec
7
answered Notes for Bott's 1963 lectures on Morse theory
Nov
7
answered Any good books on numerical methods for ordinary differential equations?
Oct
16
comment Proof synopsis collection
@mathahada Where do you see a geometric series in my proof? (One of the points I had in publishing the above proof was to show that the geometric series argument (used since Banach's original proof) is really not necessary.
Oct
14
comment Can the level set of a critical value be a regular submanifold?
You probably should say amend the statement of the theorem to say that a non-empty level set of a regular value of a smooth function f:M→ℝ on a smooth manifold is a regular submanifold of codimension one. (That takes care of the problem with f identically zero.)
Oct
11
answered Proofs for doubly ruled surfaces
Sep
21
revised Definition of Sobolev spaces as a space of sections of certain type
Added a link to a copy of referenced work; deleted 1 characters in body; added 1 characters in body
Sep
20
answered Definition of Sobolev spaces as a space of sections of certain type
Sep
19
comment Collapsing of Riemannian manifolds with a group action
"...Consider the fixed point set F, it is of course a submanifold of M by the slice theorem". Note that it is really simpler than that; in geodesic coordinates at a point p of F, the fixed point set is locally the linear subspace left fixed by the linearized action at p.