Skip to main content
Search type Search syntax
Tags [tag]
Exact "words here"
Author user:1234
user:me (yours)
Score score:3 (3+)
score:0 (none)
Answers answers:3 (3+)
answers:0 (none)
isaccepted:yes
hasaccepted:no
inquestion:1234
Views views:250
Code code:"if (foo != bar)"
Sections title:apples
body:"apples oranges"
URL url:"*.example.com"
Saves in:saves
Status closed:yes
duplicate:no
migrated:no
wiki:no
Types is:question
is:answer
Exclude -[tag]
-apples
For more details on advanced search visit our help page
Results tagged with
Search options not deleted user 3709

Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.

15 votes
2 answers
4k views

Learning Arakelov geometry

I have a complex analytic background (Griffiths and Harris, Huybrechts, Demailley etc). Also, I understand some PDE. I want to learn Arakelov geometry (atleast till the point I can "apply" computation …
Vamsi's user avatar
  • 3,383
11 votes

Problems where we can't make a canonical choice, solved by looking at all choices at once

Sard's theorem provides such an example. Given a random smooth map between two manifolds (lets say compact and of the same dimension), there is no canonical way of constructing a regular value. But, S …
9 votes
2 answers
607 views

Hyperbolic PDE in mathematics

Hyperbolic PDE (like the wave equation) are roughly speaking, PDE that satisfy the “finite propagation speed of information” property. They are ubiquitous in mathematical physics (essentially, most fu …
Vamsi's user avatar
  • 3,383
6 votes

Where is number theory used in the rest of mathematics?

If Arakelov geometry counts as number theory, then, http://arxiv.org/pdf/math/0401029v1.pdf demonstrates the computation of the Analytic torsion (a purely analytic object involving the product of dete …
6 votes

Which mathematicians have influenced you the most?

Simon Donaldson. His proofs involve (to quote wikipedia) a creative use of analysis. I loved his proof of the theorem of Narasimhan and Seshadri.
5 votes

What's your favorite equation, formula, identity or inequality?

$(A-\lambda _1) (A-\lambda _2) \ldots = 0$, the Cayley-Hamilton theorem.
3 votes

Why do we need random variables?

Practically everything we measure in real life (for instance the time taken for an apple to fall on Newton's head) is "random" in the sense that if we perform the experiment again, we will not get the …
Vamsi's user avatar
  • 3,383
2 votes

How do you decide whether a question in abstract algebra is worth studying?

This paper has a very nice introduction (it is on "pointless topology"). So apparently, one may come up with very random definitions for their own sake and hope someone "applies" them to more "concret …