Talks

It is a well-known fact that in the class of regular non-zero constant mean curvature (CMC) surfaces in the Euclidean space, spheres and the right circular cylinders are the only examples of CMC surfaces which are algebraic. In this talk, first we will show for every spacelike CMC surface of revolution (except spacelike cylinders and standard hyperboloids), which is either an unduloid or a nodoid, in the Lorentz-Minkowski space E 3 1 , there is an associated Weierstrass-℘ function. Next, using this association, we will show unduloid and nodoid cannot be algebraic and hence concluding only spacelike cylinders and standard hyperboloids are algebraic.

Third Talk (90 minutes) I would like to give a brief introduction of zero mean curvature surfaces as the analytic extension of maximal surfaces to timelike minimal surfacces. Then I would like to give numerous examples of zero mean curvature surfaces and discuss some properties of them such as embeddedness and symmetries.

In this talk, I will provide an overview of neutron star (NS) mergers, highlighting the insights gained through numerical relativity simulations. I will mainly focus on the role of the cocoon shock breakout emission as a key early electromagnetic counterpart of NS mergers, with special relevance to events like GW170817. I will explore how the properties of the merger ejecta and the nature of the central engine influence the resulting emission. Additionally, I will present recent advancements in the development of our new general relativistic magnetohydrodynamics (GR-MHD) code GR-Athena++, and share ongoing research efforts on the evolution of magnetic fields in the post-merger remnant.