Nodal domain count for eigenfunctions of dumbbell domains Abstract. The eigenvalues and eigenfunctions of the Laplacian of a plate determine the constant frequencies at which the plate can vibrate. The zero set of the eigenfunction then corresponds to the curves … Read more
On the Donaldson-Scaduto conjecture. Abstract. Donaldson proposed a new method to study manifolds with special holonomy groups, particularly Calabi-Yau 3-folds and G2-manifolds, utilizing a Lefschetz fibration. Motivated by collapsing G2-manifolds with K3 fibrations in the adiabatic setting, Donaldson and Scaduto … Read more
The 2024 UNC PDE Mini-school will feature a series of lectures by Gigliola Staffilani from MIT. We will have additional complementary "satellite" talks by Gonzalo Cao-Labora (MIT), Felipe Hernandez (MIT), and Xueying Yu (Oregon State University). Analysis and PDE Mini-School Website … Read more
Algebraic models of semi-infinite flag manifolds Abstract. We first recall the classical Borel-Weil-Bott theorem and examine its representation-theoretic meaning. Then, we exhibit affine analogue of their representation-theoretic meaning and form several schemes. Finally, we identify the resulting schemes with so-called … Read more
Gravity water waves with constant vorticity at low regularity and balanced energy estimates Abstract. In this talk I will talk about the Cauchy problem of two-dimensional gravity water waves with constant vorticity. The water waves system is a nonlinear dispersive … Read more
The AWM is excited to host Dr. Di Fang of Duke University. Her talk, "Quantum Computing Through the Lens of an Applied Mathematician," will be held on Thursday, April 11th at 3:30 PM in Phillips 332 (the usual day, time, … Read more
Semi-infinite flag manifolds, space of maps, and quantum K-groups of flag manifolds Abstract: We first recall the Plucker relations, that yield a description of a(n open) space of maps from a projective line to a (partial) flag manifolds. Then, we … Read more
Resonances and transmission for waves in truncated media Abstract. In a lot of toy models in quantum mechanics, you can construct “states” that live only at certain ”energies” by trapping things into specific regions, say using an infinite square well … Read more
Mathematical modeling of polymerization processes in physiology Abstract: Polymerization, or aggregation, is essential for many physiological systems. For example, the emergence of a fibrin polymer mesh during the formation of a blood clot is required for a stable clot and … Read more
Interior Hessian estimates for singularities of the Lagrangian mean curvature flow Abstract. In this talk, we discuss the history of the Lagrangian Mean Curvature equation beginning with the special Lagrangian equation of Harvey and Lawson. We consider the hypercritical case … Read more
A geometric flow towards Hamiltonian stationary submanifolds Abstract. In joint work with Jingyi Chen, we introduce a geometric flow for Lagrangian submanifolds in a Kähler manifold which stays in its initial Hamiltonian isotopy class and is a gradient flow for … Read more
