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math.AG2025
Tropicalization of super Gromov-Witten invariants
Artan Sheshmani, Shing-Tung Yau, Benjamin Zhou
We show that genus-0, Neveu-Schwarz marked, super Gromov-Witten invariants of a convex, toric variety can be defined and computed using tropical geometry. When is a poi…
math.AG2025
Mirror symmetry for singular double cover Calabi--Yau varieties: quantum test
Tsung-Ju Lee, Bong H. Lian, Shing-Tung Yau
We continue our study on the pairs of singular Calabi--Yau varieties arising from double covers over semi-Fano toric manifolds. In this paper, we first investigate singular CY doub…
math.AG2025
A D-brane fantasy on noncommutative mirror symmetry, prelude: Noncommutative ringed spaces from local noncommutative crepant resolutions of a singular Calabi-Yau space, dynamical D-branes thereupon, and questions beyond
Chien-Hao Liu, Shing-Tung Yau
In contrast to the world-sheet of a fundamental string, the world-volume of stacked D-branes carries an Azumaya noncommutative structure ([L-Y1: Sec.\ 2] (D(1))), allowing it to di…