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Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.

94 votes
1 answer
11k views

The mathematical theory of Feynman integrals

It is well known that Feynman integrals are one of the tools that physicists have and mathematicians haven't, sadly. Arguably, they are the most important such tool. Briefly, the question I'd like to …
algori's user avatar
  • 23.5k
29 votes
3 answers
5k views

Topologically distinct Calabi-Yau threefolds

In dimensions 1 and 2 there is only one, respectively 2, compact Kaehler manifolds with zero first Chern class, up to diffeomorphism. However, it is an open problem whether or not the number of topolo …
algori's user avatar
  • 23.5k
14 votes
3 answers
1k views

Finite dimensional Feynman integrals

In a sense this is a follow up question to The mathematical theory of Feynman integrals although by all rights it should precede that question. Let $S$ be a polynomial with real coefficients in $n$ v …
algori's user avatar
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