Monday 7 April 2025, from 2 pm in Room 2109 (2nd Floor) - U5 Building, Annalisa Grossi (University of Bologna) and Andrea Bisterzo (Scuola Normale Superiore, Pisa) will give the following talks
Speaker: Annalisa Grossi
Title: Maximal branes of compact hyper-Kähler manifolds
Abstract: On a hyper-Kähler manifold X, a real structure - or equivalently, an anti-holomorphic involution - is referred to as a brane involution. Up to hyper-Kähler rotation, an anti-holomorphic involution can become an anti-symplectic involution. When the Smith-Thom inequality is realized as an equality, the brane involution is said to be maximal. While examples of non-compact hyper-Kähler manifolds admitting maximal branes are known, the compact case presents a more intriguing picture. In particular, although some K3 surfaces admit maximal brane involutions, the main result that I will show is the non-existence of maximal branes on compact hyper-Kähler manifolds of K3^[n]-type when n=2 or n is odd. This talk is based on a joint work in progress with Simone Billi and Lie Fu.
Speaker: Andrea Bisterzo
Title: Rigidity of an overdetermined heat equation and minimal helicoids in space-forms
Abstract: In the seminal paper "Characterizations of the Mean Curvature and a Problem of G. Cimmino" of 1995, J. C. C. Nitsche proved that if a domain in R^3 is uniformly dense in its boundary, then the boundary must be either a plane or a right helicoid, thereby resolving an open problem proposed by G. Cimmino in 1932. This result, along with the techniques used in its proof, has inspired a significant line of research on rigidity phenomena related to overdetermined differential problems in possibly unbounded domains, with particular regard to those involving the heat equation. The aim of this talk is to present an ongoing work in collaboration with Professor Alessandro Savo, in which we characterize embedded minimal helicoids and totally geodesic hypersurfaces in three-dimensional space-forms through the concept of “constant boundary temperature”, an overdetermined condition involving the Cauchy problem for the heat equation. The result is obtained using a method that differs significantly from Nitsche's technique.
All interested are invited to participate
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