Index computations in FJRW theory

Fjrw-rings and Landau-ginzburg Mirror Symmetry

Abstract. In this article, we study the Berglund–Hübsch transpose construction W T for invertible quasihomogeneous potential W . We introduce the dual group G and establish the state space isomorphism between the Fan–Jarvis–Ruan–Witten A-model of W/G and the orbifold Milnor ring B-model of W T /G . Furthermore, we prove a mirror symmetry theorem at the level of Frobenius algebra structure for G...

Selecting Computations: Theory and Applications

Sequential decision problems are often approximately solvable by simulating possible future action sequences. Metalevel decision procedures have been developed for selecting which action sequences to simulate, based on estimating the expected improvement in decision quality that would result from any particular simulation; an example is the recent work on using bandit algorithms to control Mont...

Observations and Computations in Sylvester-Gallai Theory

We bring together several new results related to the classical Sylvester-Gallai Theorem and its recently noted sharp dual. In 1951 Dirac and Motzkin conjectured that a configuration of n not all collinear points must admit at least n/2 ordinary connecting lines. There are two known counterexamples, when n = 7 and n = 13. We provide a construction that yields both counterexamples and show that t...

Localization in Matrix Computations: Theory and Applications

Many important problems in mathematics and physics lead to (nonsparse) functions, vectors, or matrices in which the fraction of nonnegligible entries is vanishingly small compared the total number of entries as the size of the system tends to infinity. In other words, the nonnegligible entries tend to be localized, or concentrated, around a small region within the computational domain, with rap...

Computations in Complex Equivariant Bordism Theory