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location University of California, Berkeley
age 67
visits member for 4 years
seen Mar 24 at 1:18

Nov
15
awarded  Nice Answer
Oct
10
awarded  Yearling
Sep
30
awarded  Nice Answer
Jun
25
awarded  Excavator
Jan
11
revised Examples of common false beliefs in mathematics.
it's -> its
Jan
11
comment Are there smooth bodies of constant width?
I took a look at the Fillmore paper, and just before his Corollary to Theorem 2 -- which reads "Corollary. There exists an analytic hypersurface of constant width in E^n having the same group of symmetries as a regular n-simplex." -- he writes "If we imitate the construction of a Reuleux triangle . . .. Thus:" This seems to imply that he is assuming that [the intersection of four balls in 3-space, centered at the vertices of a regular tetrahedron and each with radius = the side-length of the tetrahedron] is a body of constant width. But this is known to be false.
Dec
24
comment $SU(2)$ and the three sphere
It's not so much that you also need det(x) = 1, as that this is exactly the same as saying |a|<sup>2</sup> + |b|<sup>2</sup> = 1.
Sep
14
comment Riemann zeta at even integers
In the functional equation for ζ(s), the term Γ(s) should be Γ(s/2), and the term Γ(1-s) should be Γ((1-s)/2).
Aug
13
comment Irreducible homology 3-spheres that bound smooth contractible manifolds
The usual contractible 2-complex discovered by Bing is called a "House With Two Rooms", and this is not what is depicted in the image above this answer. The 2-complex depicted is not contractible (since a loop around either inner cylinder is a nontrivial 1-cycle, as is easily verified). To obtain the House With Two Rooms, one needs to add two disjoint rectangles IxI to the image, each one intersecting one inner cylinder in an interval, the outer cylinder in an interval, and the 2-complex depicted in its entire (rectangular) boundary circle.
Mar
28
awarded  Yearling
Mar
29
awarded  Yearling
Feb
25
awarded  Nice Answer
Jan
12
awarded  Nice Answer
Oct
25
awarded  Nice Answer
Aug
25
revised Infinite-dimensional complex polynomial or rational Lie algebras and their pseudogroups
changed title
Aug
25
revised Infinite-dimensional complex polynomial or rational Lie algebras and their pseudogroups
Added note about the ease of computing formulas for the flows
Aug
25
revised Infinite-dimensional complex polynomial or rational Lie algebras and their pseudogroups
probably -> surely
Aug
25
asked Infinite-dimensional complex polynomial or rational Lie algebras and their pseudogroups
Aug
16
comment How well can we localize the “exoticness” in exotic R^4?
Removing a standard $D^4$ from a potentially-exotic smooth $S^4$ yields a potentially-exotic $\mathbb{R}^4$ that's standard at infinity. So if it were known that the latter must be globally standard, then replacing the $D^4$ would imply the original $S^4$ is standard, and hence the 4-dimensional smooth Poincaré conjecture. And there's essentially only one way to replace the $D^4$, since Gamma_4 = 0 (Cerf) implies oriented diffeos of $S^3$ are smoothly isotopic.
Aug
15
comment Measure on real Grassmannians
For one application, an explicit curve {C(t) : t in [0,oo)}, dense in a Grassmannian of 2-planes in n-space, is the basis for the animation technique in statistical computer graphics known as the Grand Tour. It's important to ensure that as t -> oo, the curve C spends time in any open set U proportional to the invariant measure* of U. * Though the invariant measure on a Grassmannian is unique up to a scalar multiple, the invariant metric is not in the sole case of 2-planes in 4-space. This oriented Grassmannian's metric is the product of two round 2-spheres whose radii may be in any ratio.