41,591 reputation
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bio website math.uga.edu/~pete
location Athens, GA
age 38
visits member for 5 years, 3 months
seen 10 hours ago
assistant associate prof of math @ University of Georgia.

Primary research interests: number theory, arithmetic geometry, Galois cohomology

Secondary research interests: field theory, commutative algebra, general topology, model theory, and various combinations thereof

I also have an enduring interest in mathematical exposition.

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Jan
5
comment Companion to theoretical physics for working mathematicians
@Allen: Yes, but no Princeton Comprehensive Companion to Mathematics. (Perhaps I am taking that one word too seriously...)
Dec
28
comment Companion to theoretical physics for working mathematicians
The idea that one book could be a comprehensive companion to any well-established academic field strikes me as a bit far-fetched.
Dec
28
comment Splitting varieties of two Galois cohomology symbols
Maybe I didn't understand what you meant by a splitting variety for both symbols. I took that to mean a variety $X$ which for $L/k$ has an $L$-rational point iff both cohomology classes become trivial upon restriction to $L$. If so, $(X_{\alpha} \times X_{\beta})(L) \neq \varnothing \iff X_{\alpha}(L) \neq \varnothing$ and $X_{\beta}(L) \neq \varnothing$. There's no more to my answer than that.
Dec
28
answered Splitting varieties of two Galois cohomology symbols
Dec
17
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Dec
14
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Dec
12
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Dec
10
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Nov
30
comment Elliptic curves with maximal order in an imaginary field
Just a note for the OP: the keyword for the final sentence is "Deuring's criterion".
Nov
30
comment How can we join two points with a small ruler?
@Bogdan: You might have mentioned sooner that the question had already been posted on math.SE.
Nov
30
comment How can we join two points with a small ruler?
I have never seen any treatment of Euclidean constructions that uses $\epsilon$ approximations (but I am no expert on this). It is pretty clear though that you don't need to express things that way. For instance, you should regard a line as "given" if you have two points on that line. A circle is "given" by its center and one point. To bisect an angle, you have to be given the angle, say by an ordered triple of non-colinear points. Then the usual bisection construction uses no flexibility or "almost": it's all about constructing certain points as the intersection of circles and lines.
Nov
30
comment How can we join two points with a small ruler?
@Lennart: Thanks. After reflection I think it is meant to be implicit that we can really start with a polygonal path from $A$ to $B$ and our task is to straighten it. I suppose I have been rather obtuse about this (but I still wish it had been made more explicit; why not?).
Nov
30
comment How can we join two points with a small ruler?
@Daniel: Sorry, I still don't get it. In classical Euclidean constructions, we begin by saying exactly what we can do: given any two distinct points, we can construct the line they determine. Given distinct points P and Q, we can draw the circle centered at P and with radius $|P-Q|$. That's it. In this situation, in what manner are we allowed to "put other points on the plane"?
Nov
30
comment How can we join two points with a small ruler?
@Reimundo: Well, I still don't get it. Which line segments through $A$ of length at most $\ell$ are we allowed to draw? If we are allowed to draw all of them then obviously we can solve the problem. If we are only allowed to draw segments when we already have both of the endpoints, then obviously we cannot solve the problem. So it must be somewhere in between...?
Nov
30
comment How can we join two points with a small ruler?
Maybe the rules need to be made a little more clear. My interpretation is that whenever we have two points in the plane of distance at most $\ell$, we are allowed to draw the line segment between them, and that's it. But this means that if we are given precisely two points with distance greater than $\ell$, then we are not allowed to do anything, so the construction is not only impossible but clearly impossible. Obviously others are not interpreting the question this way...so I wonder what they have in mind.
Nov
23
revised Intersection of nonzero prime ideals is zero — does it have a name?
added 7 characters in body
Nov
23
revised Intersection of nonzero prime ideals is zero — does it have a name?
added 11 characters in body
Nov
23
answered Intersection of nonzero prime ideals is zero — does it have a name?