The Department of Mathematics in the College of Arts and Sciences is honored to welcome Dr. Yury Ustinovskiy to deliver the weekly colloquium. Dr. Ustinovskiy is a Courant Instructor at the Courant Institute, where he works in the field of complex and differential geometry, particularly non-Kähler manifolds, canonical metrics and topological properties of such manifolds, complex manifolds admitting large group of symmetries, and generalized Kähler structures.
To apply an analytic flow to any geometric problem, we need to make the first necessary step – classify the stationary points of the flow, and, more generally, its solitons (stationary points modulo diffeomorphisms). For the pluriclosed flow, this question reduces to a non-linear elliptic PDE for an Hermitian metric on a given complex manifold. We will discuss this problem on compact/complete complex surfaces, and provide exhaustive classification under natural extra geometric assumptions. In the course of our classification we will discover a natural extension of the famous Gibbons-Hawking ansatz for hyperKahler manifolds.
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This event was published on March 9, 2021.