10,827 reputation
24875
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
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 .

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awarded  Good Answer
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awarded  Yearling
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awarded  Nice Question
May
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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that is "As far as I know...", or do you have some strong reason to believe this---say perhaps a well-researched historical reference.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?
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awarded  Nice Answer
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awarded  Great Answer
Jan
11
answered Characterization of the exterior derivative
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awarded  Explainer
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awarded  Nice Answer
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awarded  Yearling
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awarded  Curious
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awarded  Enlightened
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awarded  Nice Answer
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awarded  Nice Question
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awarded  Good Answer
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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