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Special Lagrangian and the deformed Hermitian Yang Mills

Student-Run Research Seminar

Speaker: Yu Hin Chan, UC Davis
Location: 3106 MSB
Start time: Wed, Oct 5 2022, 12:00PM

In this talk, we will introduce the definition of Special Lagrangian and its mirror, the deformed Hermitian Yang Mills (dHYM) on Kähler manifolds. All the definitions will be demonstrated in the simplest setting $\mathbb{C}^n$ with explicit equations. Then, we will introduce the Lagrangian mean curvature (LMC) flow and demonstrate it in $\mathbb{C}^1$, which is the curve shortening flow. If time allows, I will explain how Calabi symmetry reduces the dHYM of the blowup of $\mathbb{P}^n$ into a one-dimensional problem and how LMC may help us understand the dHYM on the blowup of $\mathbb{P}^n$.