tbranzov

We investigate lattice packings of Minkowski balls and domains. By results of the proof of Minkowski conjecture about the critical determinant we divide the balls and domains on 3 classes: Minkowski, Davis and Chebyshev-Cohn. The optimal lattice packings of the balls and domains are obtained. The minimum areas of hexagons inscribed in the balls and domains and circumscribed around them are given. These results lead to algebro-geometric structures in the framework of Pontrjagin duality theory.

In this introductory talk, I will present some concepts surrounding singularities and why and how we look for their resolutions.

The author explains an approach started by Ciocan-Fontanine and Kapranov.

I will talk about joint work with Shing-Tung Yau, Sergei Gukov, and earlier joint work with Gholampour and Yau on Mathematical definition of Vafa-Witten invariants on 4 and 3 dimensional manifolds.