| Thursday 25 April 2024 | |
| Events for day: Wednesday 24 February 2021 |
| 15:30 - 17:30 Mathtematical Logic Weekly Seminar Partitions of Well-founded Trees and Three Connections with Model Theory School MATHEMATICS in 2003, Komjath and Shelah proved a partition theorem on scattered order types; these in turn could be understood as partition relations for classes of well-founded trees. Recently, two different kinds of applications of the same partition relation have been used in infinitary logic and in model theory: one by Vaananen and Velickovic on games related to Shelah's logic $L^1_kappa$, another by Shelah and myself on the canonical treea of an AEC (a generalization of the Scott sentence for an abstract elementary class). I will describe the Komjath-Shelah result in the first part and then narrow in the applications (with more details on the second ... 19:30 - 20:30 Mathematics Colloquium Set-Theoretic Complete Intersections and Local Cohomology School MATHEMATICS A variety $V$ of codimension $r$ in a projective space $mathbb{P}^n$ is called a set-theoretic complete intersection if $V$, as a set, is the intersection of exactly $r$ hypersurfaces in $mathbb{P}^n$. I will discuss the history of the general problem, which varieties $V$ are s.t.c.i., with special attention to the still open problem, is every irreducible nonsingular curve in $mathbb{P}^3$ a set-theoretic complete intersection? In particular I will mention several algebraic criteria, including local cohomology that can in principle be used to show that certain varieties are not s.t.c.i. To get more information about the colloquium, jo ... |