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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

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 …
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 …