bio | website | vmm.math.uci.edu |
---|---|---|
location | Univ. of California at Irvine | |
age | 84 | |
visits | member for | 5 years |
seen | May 14 at 20:21 | |
stats | profile views | 7,169 |
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 .
Jul 5 |
awarded | Good Answer |
Jul 4 |
awarded | Yearling |
May 12 |
awarded | Nice Question |
May 11 |
comment |
What sort of models did Bolyai and Lobachevsky use to demonstrate the consistency of their models of non-Euclidean Geometry?
>... but neither Bolyai nor Lobachevsky proved that their geometry was internally consistent... That's what I was beginning to suspect, Igor, but is that something that is "As far as I know...", or do you have some strong reason to believe this---say perhaps a well-researched historical reference. |
May 11 |
asked | What sort of models did Bolyai and Lobachevsky use to demonstrate the consistency of their models of non-Euclidean Geometry? |
Apr 30 |
awarded | Nice Answer |
Apr 19 |
awarded | Great Answer |
Jan 11 |
answered | Characterization of the exterior derivative |
Sep 30 |
awarded | Explainer |
Sep 29 |
awarded | Nice Answer |
Jul 4 |
awarded | Yearling |
Jul 2 |
awarded | Curious |
May 24 |
awarded | Enlightened |
May 24 |
awarded | Nice Answer |
Feb 3 |
awarded | Nice Question |
Nov 18 |
awarded | Good Answer |
Nov 2 |
awarded | Popular Question |
Sep 30 |
comment |
About Palais' remark that an isometry of Riemannian manifolds does not induce an isometry of the Hilbert manifolds of curves
The problem lies in the line above defining $g_\sigma(λ,μ)$. This is the metric for $H_0$, NOT the metric for $H_1$. The correct definition of the metric for $H_1$ uses $⟨λ'(t),μ'(t)⟩$ rather than $⟨λ(t),μ(t)⟩$ (see page 222 of my article where both metrics are defined), and with this change it is fairly obvious why my remark in the cited paper is in fact correct. |
Aug 23 |
comment |
Algorithm for finding inverse images of a local diffeomorphism
Yes! Newton's Method is clearly the way to go. For $k=1$, the algorithm I wrote in fact did use Newton's Method, (rather than bisection) since it is much faster. But I guess I forgot that Newton's Method works in higher dimensions too. Thanks Ryan. |
Aug 23 |
accepted | Algorithm for finding inverse images of a local diffeomorphism |