In 2024, Schock constructed several KSBA compactifications of the moduli space of cubic surfaces. More precisely, he considered pairs consisting of a cubic surface and a boundary divisor given by the sum of the 27 lines, all with the same weight value in the interval (1/9, 1] and provided a finite wall-and-chamber decomposition and described the weighted stable pairs parameterized by the moduli spaces in each chamber. In this talk, I will describe recent work where I provide a similar finite wall-and-chamber decomposition for KSBA compactifications where we weight one “heavy” line with weight b, and the other 26 lines uniformly with weight c.
Moduli of (b,c)-weighted stable marked cubic surfaces
Thu, Nov. 20 2:30pm (MATH 3…
Functional Analysis
Karen Strung (Institute of Mathematics of the Czech Academy of Sciences)
X
Orbit-breaking in topological dynamical systems was introduced by Ian Putnam in his study of the C*-algebras associated to Cantor minimal systems. By breaking an orbit at a single point, Putnam was able to construct all simple unital AF algebras as subalgebras by way of a Cantor minimal system. Since then, orbit-breaking algebras have been used to construct dynamical models for many stably finite “classifiable” C*-algebras, most notably the Jiang–Su algebra. In this talk I will highlight these results and also discuss recent work-in-progress with Robin Deeley and Ian Putnam, where we generalize orbit-breaking for a homeomorphism to the setting of a continuous, surjective, local homeomorphism, allowing for purely infinite constructions.
Orbit breaking and C*-algebras Sponsored by the National Science Foundation
Moduli of (b,c)-weighted stable marked cubic surfaces