43,164 reputation
9145293
bio website math.uga.edu/~pete
location Athens, GA
age 39
visits member for 5 years, 10 months
seen 1 hour 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.

NOTE: In Spring 2015 my department adjusted the mechanics of its webpage, which broke a lot of my links. For now, if you see a broken link like http://www.math.uga.edu/~pete/inversemw.pdf, try changing it to http://math.uga.edu/~pete/inversemw.pdf. It should fix the problem.


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Aug
30
revised Integrability of derivatives
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28
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21
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Aug
14
revised Is Monsky's theorem depending on axiom of choice ?
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Jul
7
comment uncountable algebraically closed field other than C ?
@potentially dense: See $\S$12.2 of math.uga.edu/~pete/FieldTheory.pdf. Alternately, as the comments describe, from a model theoretic perspective this is a consequence of the model completeness of the theory of algebraically closed fields, itself a corollary of quantifier elimination in such fields. For that perspective, see $\S$5.4 of math.uga.edu/~pete/modeltheory2010FULL.pdf. (Or better, see any introductory model theory text whatsoever...)
Jul
7
comment A quasicompact space with a net that contains no convergent strict subnet
In other words...compact does not imply sequentially compact.
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revised Is there an introduction to probability theory from a structuralist/categorical perspective?
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May
30
comment Naturally occuring groups with cardinality greater than the reals.
@few__reps: Certainly; this kind of cardinality construction is pursued in more generality in math.uga.edu/~pete/settheorypart4.pdf. The point is that it trivially works for all infinite cardinals, so it is precisely what I mean to exclude when I asked (not so precisely) for a "natural example".
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May
27
comment What are the most misleading alternate definitions in taught mathematics?
@Alexey: Yes, you are using that $a \mapsto \overline{a}$ is a group homomorphism and that addition in $\mathbb{Z}$ is associative.
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