Azumaya-type noncommutative spaces and morphisms therefrom: Polchinski¡¯s D-branes in string theory from Grothendieck¡¯s viewpoint

Chien-Hao Liu and Shing-Tung Yau

Morphisms from Azumaya prestable curves with a fundamental module to a projective variety: Topological D-strings as a master object for curves

Si Li, Chien-Hao Liu, Ruifang Song, and Shing-Tung Yau

K-theory from Sen's conjecture Raffaele Savelli