Departmental Colloquium
Scott Mutchnik & Gwyn Moreland
UIC
Details below
Abstract: Title for Gwyn Moreland: Positive cycles on Hilbert schemes of points
Abstract for Gwyn Moreland: Algebraic geometers are often interested in certain “positive” cones that one can associate to varieties, such as the nef and effective cones. While traditionally studied in the divisor and curves cases, positive cones of cycles of intermediate dimension have recently been the subject of much study. We discuss some results of this kind, and their particular challenges, in the case of Hilbert schemes of points. In particular, we look at the Hilbert scheme of 3 points in P^3, which parametrizes collections of 3 distinct points in 3-space as well as all limits of such subschemes.
Title for Scott Mutchnik: Interactions between the syntactic and the semantic
Abstract for Scott Mutchnik: Model theorists are interested in what the language of logic has to say about mathematical structures. Within model theory, Shelah’s program of classification theory proposes to analyze the universe of mathematical structures according to combinatorial patterns in the syntax of logical theories, at the level of individual formulas. The combinatorics of a theory at the local scale often provides global information on the geometric structure of its models. However, the geometry of general mathematical structures has recently allowed us to solve classical combinatorial problems in the syntax of first-order theories, including the question (asked by Shelah (1999) and Džamonja and Shelah (2004)) of whether NSOP_1 is equal to NSOP_2. We discuss this problem, which makes no explicit mention of anything besides the combinatorics of the formulas themselves, and how our solution reveals the influence of the semantic on the syntactic.
Friday September 8, 2023 at 3:00 PM in 636 SEO