75 citations · 334 across the 43 of their papers we have counts for
5 papers · 1 filter
The SYZ mirror symmetry conjecture for del Pezzo surfaces and rational elliptic surfaces
Tristan C. Collins, Adam Jacob, Yu-Shen Lin
We prove a version of the Strominger-Yau-Zaslow mirror symmetry conjecture for non-compact Calabi-Yau surfaces arising from, on the one hand, pairs of a del…
Emergent Sasaki-Einstein geometry and AdS/CFT
Robert J. Berman, Tristan C. Collins, Daniel Persson
We consider supergravity in five-dimensional Anti-De Sitter space with minimal supersymmetry, encoded by a Sasaki-Einstein metric on a five-dimensional compact manifold $…
On the degeneration of asymptotically conical Calabi-Yau metrics
Tristan C. Collins, Bin Guo, Freid Tong
We study the degenerations of asymptotically conical Ricci-flat Kähler metrics as the Kähler class degenerates to a semi-positive class. We show that under appropriate assumptions,…
Stability and the deformed Hermitian-Yang-Mills equation
Tristan C. Collins, Yun Shi
We survey some recent progress on the deformed Hermitian-Yang-Mills (dHYM) equation. We discuss the role of geometric invariant theory (GIT) in approaching the solvability of the d…
The space of almost calibrated forms on a compact Kähler manifold
Jianchun Chu, Tristan C. Collins, Man-Chun Lee
The space of "almost calibrated" forms on a compact Kähler manifold plays an important role in the study of the deformed Hermitian-Yang-Mills equation of mirr…