17,683 reputation
22962
bio website math.umn.edu/~garrett
location US
age 62
visits member for 3 years, 2 months
seen 13 hours ago

I am interested in the application of modern analysis to the spectral theory of Eisenstein series and other automorphic forms, L-functions, and number theory. This includes representation theory of (mostly reductive) Lie groups and p-adic 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.


13h
revised Approximation by definite integrals
edited title
14h
answered Banach Spaces: Totally Bounded Subsets
Aug
22
comment Specifying types of variables in pure mathematics and applied mathematics
Echoing @PhillipAndreae's comment, units matter in these situations. "Let the price of X be $p$ dollars."
Aug
21
comment Span of an empty set is the zero vector
In addition to other useful and explanatory answers, observe that Nering says "we agree...". That is, to my interpretation, he expresses disinterest in whether or not this could be proven, or should be a definition, or whatever, ... probably because he sees that it doesn't much matter, and I agree with this. So he is asserting neither, although, as in the answers, your questions can be reasonably addressed, also. In particular, again, in effect he asserts that there is no reason to care much about it, and I agree.
Aug
20
reviewed Close Are there any fundamental new discoveries in Algebraic Number Theory than in ‘traditional’ number theory ?
Aug
20
comment Could I get a critique of this epsilon-delta limit proof?
As in my comment above... it is very important, to avoid impossibly-difficult enterprises, to not aim for the if-and-only-if, which is completely un-necessary... although it is understandably easy to slip into thinking in those terms in the exaggeratedly formulaic version of "mathematics" many people see ("have to have a formula, and it has to be exactly right...")
Aug
20
comment Could I get a critique of this epsilon-delta limit proof?
It is in fact very important to realize that you do not need the "if and only if" at the beginning. It's only that you need to be able to find a delta to give the result for epsilon. Many people think that either it really should be an if-and-only-if, or that it scarcely matters, but the operational point is that in practice it is mostly very hard to find the "exactly right" delta for a given epsilon. But the happy reality is that we don't have to find the optimal/perfect delta for given epsilon. Finding a "too good" delta is completely fine.
Aug
17
revised Is every positive integer the sum of at most 8 pentatope numbers?
edited tags
Aug
16
answered Galois theory, had it solved any major problems beside its original applications to classical problems?
Aug
16
awarded  Nice Answer
Aug
15
reviewed Leave Open Permutation as a product of transposition
Aug
15
comment Motivation and intuition of double cosets
I think Mackey's theorem on intertwining operators among induced representations, and generalizations by Bruhat, Harish-Chandra, and others, is by far the most important way that double cosets arise, and is irresistible.
Aug
15
answered On the square coeffecients of a modular form
Aug
15
reviewed Leave Open What is the most efficient way to calculate the sine of a rational number?
Aug
15
reviewed Leave Open Could anyone help me with the hatcher algebraic topology 1.3.6
Aug
15
reviewed Leave Open Are Singleton sets in $\mathbb{R}$ both closed and open
Aug
15
reviewed Leave Open Question about qoutient groups
Aug
15
reviewed Close $f\in C^\omega ((a-R,a+R),\mathbb{R})$
Aug
15
reviewed Leave Open Does $\gamma(t)=e^{it^2} , t \in [0,\sqrt{2\pi}]$ represent the unit circle?
Aug
14
comment Can integral transforms be viewed as change of basis formulas?
In brief, "yes". The kernel-function of an integral transform (generally known as "Schwartz kernel") is not so much an analogue of a "basis", but an analogue of a "matrix".