[DMO] Nando Leijenhorst: Rounding SDP solutions to exact fields

26 January 2024 14:00 till 15:00 - Location: EEMCS-Lecture Hall D@ta, 36.HB.01.630 | Add to my calendar

In discrete geometry, we use semidefinite programming to bound quantities such as the maximum size of spherical codes. When these bounds are sharp (that is, there is a construction reaching the bound), complementary slackness can give us information about these constructions. However, to use the complementary slackness, we need exact optimal solutions to the SDP rather than numerical approximations. We improve the rounding procedure of Dostert, de Laat and Moustrou, which works well for small semidefinite programs but is too slow for larger examples. In this talk, I will explain the main difficulties when rounding, and how we approach them. This is joint work with Henry Cohn and David de Laat.