15 citations · 32 across the 19 of their papers we have counts for
17 papers · 1 filter
The deformed Vortex equations and equivariant stability conditions
Tristan C. Collins, Yukai Zhang
We study the higher rank deformed Hermitian-Yang-Mills (dHYM) equations for -equivariant holomorphic vector bundles over for a compact Riemann sur…
Non-Kähler Special Lagrangian submanifolds and SYZ mirror symmetry
Tristan C. Collins, Francesca Lusetti, Adriano Tomassini
We determine purely algebraic equations to identify \textit{SLags} generated by invariant distributions in a class of non-Kähler Calabi-Yau manifolds. We determine SLag distributio…
An introduction to conifold transitions
Tristan C. Collins
These lecture notes introduce conifold transitions between complex threefolds with trivial canonical bundle from the differential geometric point of view, and with a particular vie…
A free boundary Monge-Ampère equation and applications to complete Calabi-Yau metrics
Tristan C. Collins, Freid Tong, Shing-Tung Yau
Let be a convex body containing the origin in its interior. We study a real Monge-Ampère equation with singularities along $\del P$ which is Legendre dual to a certain free bou…
The Strominger system in the square of a Kähler class
Tristan C. Collins, Sebastien Picard, Shing-Tung Yau
We study the Strominger system with fixed balanced class. We show that classes which are the square of a Kähler metric admit solutions to the system for vector bundles satisfying t…
Complete Calabi-Yau metrics in the complement of two divisors
Tristan C. Collins, Yang Li
We construct new complete Calabi-Yau metrics on the complement of an anticanonical divisors in a Fano manifold of dimension at least three, when consists of two transversel…