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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
7
votes
1
answer
471
views
Combinatorial meaning of Kazhdan-Lusztig-Stanley polynomial
This question is motivated by
Why do combinatorial abstractions of geometric objects behave so well?
The algebraic geometry of Kazhdan-Lusztig-Stanley polynomials
Kazhdan-Lusztig-Stanley polynomial …
5
votes
0
answers
157
views
Higher Cardano formulae in terms of $\Theta$
Consider a polynomial in one variable with complex coefficient
$$f(x) = x^n + a_{n-1} x^{n-1} + \cdots + a_1 x + a_0$$
we are interested in its roots. Babylonian solved for $n = 2$, and Cardano did it …
2
votes
0
answers
266
views
Road map: beyond Artin-Wedderburn theorem
For a noncommutative semisimple ring $R$, its structure and its category of representations can be largely understood using Artin-Wedderburn theorem. Such structure theory is useful, for example, in t …