All Questions
5 questions
7
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1
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Which revolutions in topology and geometry can we expect in the next 20 years? [closed]
In my limited perspective on the history of mathematics, I can name at least two big revolutions in Topology and Geometry (broadly construed): the introduction of Schemes in Algebraic Geometry, and ...
5
votes
1
answer
291
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The Idea of Kroneckerian geometry
Let $X$ be a complex, projective algebraic variety and assume that $X$ has a model $X_0$ over $\mathbb Z$ i.e. $X\cong X_0\times_{\operatorname{Spec }\mathbb Z}\operatorname{Spec }\mathbb C$.
Let's ...
8
votes
1
answer
987
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Steps in Geometric Complexity Theory
GCT purports to provide a program to show that $NP \not \subset P/poly$.
At the high level what are the steps involved in the program and what stage is each step in?
What difficulties currently are ...
- 13.9k
15
votes
4
answers
6k
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What is the interface between functional analysis and algebraic geometry?
This is a very open ended curiosity of mine and I would be grateful to hear any comments in this direction. In particular I am interested in functional analysis/algebraic geometry books/papers ...
- 2,246
23
votes
4
answers
4k
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What information is contained in the Kazhdan-Lusztig polynomials?
The Kazhdan-Lusztig polynomials contain all kinds of representation theoretic (and other kinds of) informations.
For example the character of a simple module over a Lie algebra with Weyl group $W$ ...