A non-standard framework over a base set A is an extension of a fragment of set theory containing A that realizes many types with parameters from A and preserves bounded quantifier formulas. In particular, if A contains an indexing set I and U is an ultrafilter over I, then a saturated enough non-standard framework over A will contain elements that appear to be principal generators for U. The properties of the ultrafilter are reflected in properties of their hyperprincipal generators in a non-standard framework. In this talk we will go over some background information about non-standard frameworks and then discuss how the properties of being Regular and Good (key properties related to Keisler's Order for countable first-order theories) are reflected in their hyperprincipal generators.
Hyperprincipal generators for regular and good ultrafilters
Oct. 25, 2022 2:30pm (MATH 3…
Lie Theory
Richard Green (CU)
X
After reviewing the character theory of Coxeter groups of types A, B, and D, we will study a particular family of representations of Coxeter groups of type D. Each representation comes equipped with two very different bases, one of which can be described in terms of orthogonal roots.
Orthogonal roots and representations of Coxeter groups
Oct. 25, 2022 3:30pm (MATH 3…
Topology
Vasileios Maroulas (University of Tennessee)
X
Topological data analysis (TDA) studies the shape patterns of data. Persistent homology (PH) is a widely used method in TDA that summarizes homological features of data at multiple scales and stores them in persistence diagrams (PDs). In this talk we will discuss a random persistence diagram generation (RPDG) method that generates a sequence of random PDs from the ones produced by the data. RPDG is underpinned by (i) a model based on pairwise interacting point processes for inference of persistence diagrams, and (ii) by a reversible jump Markov chain Monte Carlo (RJ-MCMC) algorithm for generating samples of PDs. An example on a materials science problem will demonstrate the applicability of the RPDG method.
Random persistence diagram generator and an application to materials Sponsored by the Meyer Fund