bio  website  math.umn.edu/~garrett 

location  US  
age  63  
visits  member for  4 years, 1 month 
seen  1 hour ago  
stats  profile views  5,156 
I am interested in the application of modern analysis to the spectral theory of Eisenstein series and other automorphic forms, Lfunctions, and number theory. This includes representation theory of (mostly reductive) Lie groups and padic groups, and harmonic analysis on these groups and their homogeneous spaces. Necessarily Schwartz' distributions, Sobolev spaces, and similar things play important supporting roles. I find that a mildly categorical viewpoint is very helpful in keeping things straight.
1d

comment 
Resolvent estimate of hyperbolic Laplacian
Doesn't such an estimate hold for any nonpositive selfadjoint operator, without using the specifics? 
May 19 
answered  Intertwining Operators Associated to Simple Reflections 
May 17 
comment 
Old books still used
Let's not forget Iwasawa's ICM report on the same topic, at the same time, which might have inhibited Tate from publication... until CasselsFrohlich's 1967. So I myself find "IwasawaTate theory" a more accurate descriptor... 
May 17 
comment 
Old books still used
Apart from the details of its revision, I think historically "navigation" was very much a topic in mathematics: spherical trigonometry and all that! Bowditch was certainly a mathematician by U.S. standards, such as they were! :) 
May 15 
comment 
Equidistribution of Hecke points and $p = (a+bi)(abi) = e^{i\theta}\sqrt{a^2 + b^2}$
@johnmangual, the earlier parts of my notes do aim at an economical setup of enough basics to (supposedly) make the later things reasonably intelligible. But/and, as always, a variety of sources is helpful in getting perspective. 
May 15 
answered  Equidistribution of Hecke points and $p = (a+bi)(abi) = e^{i\theta}\sqrt{a^2 + b^2}$ 
May 14 
comment 
Langlands reciprocity for C*algebras
It seems to me that the indicated preprint gets so far off the rails so quickly that it's hard to visualize specific details of a plausible, corrected version. E.g., the "convolution" product at the bottom of the first page certainly does not converge, ... but there are many related integrals which do, but, ... And, yes, as @Corbennick comments, not all reductive groups have arithmetic quotients which are algebraic varieties... So the notion of a "corrected" version is too ambiguous to discuss, I fear. 
May 13 
revised 
about subgroup of general linear group
deleted 4 characters in body 
May 13 
answered  about subgroup of general linear group 
May 13 
answered  Connection between the two definitions of Siegel Upper Half Space 
May 11 
comment 
Relation between dual of nuclear space $(\substack{\text{lim} \\ \leftarrow i} H_i)'$ and $\substack{\text{colim} \\ i \rightarrow } H_i$
@JochenWengenroth's edit/addition explains why these maps factor through limitands... 
May 11 
answered  When does a function space allow for point evaluations? 
May 8 
comment 
Meromorphic continuation of Eisenstein series
@GHfromMO, sorry to be so late in responding, but, indeed, if I could usefully clarify, what might it be? 
May 8 
comment 
Primer on Eisenstein series
I hasten to comment that E. Lapid has written many wise notes about Eisenstein series... and has noted some crazy subtleties... but/and there is no trivial resolution/outcome. 
May 8 
answered  Primer on Eisenstein series 
May 7 
comment 
Relation between dual of nuclear space $(\substack{\text{lim} \\ \leftarrow i} H_i)'$ and $\substack{\text{colim} \\ i \rightarrow } H_i$
Did you mean to write the colimit of the duals, rather than just the $H_i$ themselves? If so, then this would be correct, because a continuous linear map to a normed TVS (such as the scalars) from a projective limit of Banach spaces factors through some limitand, for nearly definitional, easy reasons. Are $H_i$'s Banach? Hilbert? It would not be good to identify every Hilbert space with its dual. 
May 5 
awarded  Revival 
Apr 20 
comment 
AtkinLehner theory for nonholomorphic Eisenstein series
For $GL_2$, all Eisenstein series generate principal series (possibly ramified at some places) everywhere locally. So any questions are not only local, but should be explicitly answerable, since there is no supercuspidal stuff interfering. 
Apr 17 
comment 
Primes as uncorrelated random variables
@JonMarkPerry, :) the point is that the notion of "probability" of primality is not wellfounded, although an extremely intuitive/engaging idea. :) That it is not (at this time in history) something that generates causality, that is, that gives true proof, is disappointing, but a contingent fact. 
Apr 17 
comment 
Primes as uncorrelated random variables
@JonMarkPerry, it's not that I have an objection to your remark, but that the terseness of it might mislead naive people. That is, the ramifications of "true facts" are often subtler than people generally understand, etc. That is, the limits of heuristics are notatall widely understood, and, in fact, I do strongly claim, there is no widespread procedure for distinguishing good heuristics from bad, etc. Rhyming is not truth. Catchiness is not truth. Yet we do hope (as humans) that such stuff does correctly suggest truth, etc. That's all I meant... 