Marty
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Registered User
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Associate Professor of Mathematics, UC Santa Cruz
Research interests: Automorphic representations and representations of p-adic groups, especially exceptional groups and "metaplectic" groups lately. Theta correspondences (exceptional ones). Geometric methods in representation theory. Periods and Hodge theory. Model theory applied to number theory and geometry.
Book blog: Illustrated Theory of Numbers
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May 16 |
asked | Could the Jacobian conjecture be undecidable? |
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May 8 |
comment |
examples of “exotic” moduli problems for elliptic curves? But such a cool-looking paper! |
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May 8 |
comment |
examples of “exotic” moduli problems for elliptic curves? Either that's a bizarre TeX error, or else I have a new entry for the question mathoverflow.net/questions/18593/… |
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May 7 |
comment |
quasi-minuscule representations en.wikipedia.org/wiki/Minuscule_representation |
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Apr 29 |
comment |
Criterion for nilradical of a maximal parabolic subalgebra to be abelian? The reference of (my) choice is Richardson, Rohrle, Steinberg, "Parabolic subgroups with abelian unipotent radical," in Inventiones v.110, no. 3 (1992), p. 649-671. |
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Apr 23 |
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Can I use both of setbuilder notations in one article? I like using "such that" (i.e., \text{such that}) whenever there's room for it. And with semicolons, it might seem like the paper is sadly winking ); |
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Apr 19 |
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Great mathematics books by pre-modern authors Way too broad a question for my taste. It's good the OP realized that older math books could be worthwhile, but asking for a list is kind of like asking for "the greatest books of all time". There are just too many. But criticism aside, I found my horizons broadened by "The Mathematics of Egypt, Mesopotamia, China, India, and Islam," edited by V. Katz. That's where I first realized that I could read and enjoy much older math texts, especially those from outside the Eurocentric canon. You could start with Katz's book as a source for excerpts, and look up full books when interested. |
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Apr 1 |
awarded | ● Nice Answer |
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Apr 1 |
comment |
The octonions on a bad day @Mariano: Not really. I guess my point is that matrix algebras are in general endomorphism rings of vector spaces -- the 2x2 case is just one example of the infinite family of examples of type $A_n$. But the octonions are really connected to $G_2$ -- no way around it, no easy shortcuts. I would still say that Zorn's split octonions are simpler than the non-split octonions. For example, identifying a maximal order in the non-split octonions is difficult (due to Coxeter after earlier mistakes), but the maximal order in the split octonions is the obvious choice. |
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Mar 31 |
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The octonions on a bad day @Mariano, I think the issue you're describing is that most mathematicians are happy to live without the octonions and exceptional groups. Matrix algebras and $GL_n$ (and classical groups) are sufficient for most people's work. The octonions and $G_2$ are not so universally studied, and maybe people think they are more difficult than they really are. I don't think Zorn's model of the split octonions (over $Z$) is too bad at all -- just 2x2 matrices with vectors in $Z^3$ off the diagonal. Hard to get much simpler than Zorn, I think. |
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Mar 31 |
revised |
The octonions on a bad day spelling mistake corrected. |
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Mar 31 |
answered | The octonions on a bad day |
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Feb 6 |
comment |
Rep Theory Consequences of Bott--Weil--Borel First, I don't think that representations are coming from nowhere. When a group $G$ acts on a space $X$, and you have a $G$-equivariant bundle on the space $X$, then you get a representation of $G$ on the sections (and higher cohomology) of the bundle. Maybe the most impressive results beyond the theorem itself are how useful it is for generalizations. The generalization that comes first to my mind is Schmid's "L²-cohomology and the discrete series" (Annals, 1976) which proved a conjecture of Langlands by using a geometric realization in the spirit of Borel-Weil-Bott. |
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Jan 26 |
awarded | ● Yearling |
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Jan 20 |
accepted | The simplest even Artin representations of degree 2 and the corresponding Maaß forms |
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Jan 5 |
asked | Asymptotics of arithmetic Fuchsian groups and Shimura curves. |
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Jan 4 |
revised |
Triality of Spin(8) Fixed typo |
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Jan 3 |
revised |
Triality of Spin(8) Fix / clarification for triality action on Spin(8). |
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Dec 21 |
comment |
Center of mass from the abstract point of view, or could the ancient Greeks invent modern analysis? "I assume that the ancient Greeks had an idea of a complete normed space (${\mathbb R}$ and ${\mathbb R}^2$ would be enough for our purposes for quite a while), a set, a linear transformation, and the center of mass." Really? Really??! |
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Dec 18 |
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Triality of Spin(8) I'm not sure if continuing questions are supposed to be given as answers... but here are a few comments. First, I don't know what you would mean by conjugating $g_1$, $g_2$, and $g_3$. They are real matrices. The fixed points of the triality automorphism on $Spin(8)$ form the subgroup $G_2$. Changing the lift should just conjugate the $G_2$ within the $Spin(8). |
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Dec 18 |
awarded | ● Nice Answer |
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Dec 18 |
revised |
Triality of Spin(8) Put mathbb on R, and reference update. |
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Dec 18 |
comment |
Triality of Spin(8) Since kreck brought it up, it works over Z too, using Coxeter's maximal order in the octonions. Thanks also to Figueroa-O'Farrill for fixing the Tex! |
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Dec 18 |
revised |
Triality of Spin(8) More consistent notation. |
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Dec 18 |
answered | Triality of Spin(8) |
