Yun Shi, Brandeis University
Authors: Tristan Collins, Jason Lo, Yun Shi, Shing-Tung Yau
2023 AWM Research Symposium
Geometric and Categorical Aspects of Representation Theory and Mathematical Physics [Organized by Mee Seong Im and Xin Jin]

Donaldson and Uhlenbeck-Yau established the classical result that on a compact Kahler manifold, an irreducible holomorphic vector bundle admits a Hermitian metric solving the Hermitian-Yang-Mills equation if and only if the vector bundle is Mumford-Takemoto stable. Motivated by the characterization of supersymmetric B-branes in string theory and mirror symmetry, Collins-Yau asked if a line bundle admits a solution of the deformed Hermitian-Yang-Mills (dHYM) equation is equivalent to it is stable with respect to certain Bridgeland stability conditions. In this talk, we will discuss a partial answer to this question for a set of line bundles on a Weierstrass elliptic K3 surface. This is joint work with Tristan Collins, Jason Lo, and Shing-Tung Yau.

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