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math.AG2026
Symmetry and solvability: Galois groups of equivariant enumerative problems
Thomas Brazelton, Alberto Landi, Sidhanth Raman
At the genesis of Galois theory at the end of the 19th century, enumerative geometers were concerned with the solvability of various problems: for instance whether one can express…
math.AG2026
The geometry of solutions to the general sextic
Sidhanth Raman
We study the geometry of the three simplest known formulas for roots of a general sextic polynomial. In contrast with work of Green on the quintic, we show that no "simultaneous un…
math.AG2024
Monodromy in the space of symmetric cubic surfaces with a line
Thomas Brazelton, Sidhanth Raman
We explore the enumerative problem of finding lines on cubic surfaces defined by symmetric polynomials. We prove that the moduli space of symmetric cubic surfaces is an arithmetic…