Math Department Colloquium
The colloquium features recent research in the mathematical and statistical sciences. The colloquia are scheduled for Tuesdays from 4pm-5pm, unless noted otherwise. This semester all colloquia will be held virtually on Zoom.
If you wish to be added to the department colloquium mailing list, or if you wish to give a colloquium talk, please contact the organizer Grady Wright.
Schedule for 2020–2021
September 8 – John Clemens, Boise State University
Title: Definable cardinalities and complexity of classification problems
Abstract: The cardinalities of infinite sets can be compared via injections: We say a set B is at least as large as a set A if there is an injection from A into B. In descriptive set theory, we can consider a more nuanced comparison, where we require the injection be suitably definable, e.g., not obtained using the Axiom of Choice. Typically this involves comparing quotient spaces of definable equivalence relation on Polish spaces using injections arising from Borel-measurable maps on the underlying spaces. This presents a rich structure of different definable cardinalities. One can study this structure for its own sake, as well as use it to gauge the complexity of natural classification problems from various areas of mathematics. I will survey some recent work showing the richness of this structure of definable cardinalities, as well as applications to classification problems in areas such as analysis and dynamical systems.
September 11 (Friday, 3:00-4:00pm) – Zach Teitler, Boise State University
Title: Recent advances in Waring rank and symmetric tensor complexity
Abstract: The Waring rank of a homogeneous form is the number of terms needed to write the form as a sum of powers of linear forms. I will give an introduction and overview of the subject,
centered on complexity of the determinant and permanent. I will describe progress in the last ten years on lower and upper bounds for Waring rank; on Strassen’s conjecture, which asserts that Waring rank is additive; and the new study of high-rank loci, initiated in the last 4 years.
September 15 – Jens Harlander, Boise State University
Abstract: Cell complexes are topological spaces that are formed by gluing together Euclidean balls (cells). An n-complex is a cell complex that does contain cells of dimension n, but not higher dimensional ones. Graphs are 1-dimensional cell complexes, the vertices being the 0-cells and the edges being the 1-cells. My talk will be about 2-complexes. On one hand 2-complexes are visually approachable, being just one dimension away from graphs. On the other hand dimension 2 does not place restrictions on the fundamental group, an invariant of central importance in algebraic topology.
I will talk about the status of 2-dimensional conjectures concerning homotopy classification, cohomological dimension, and asphericity.
September 22 – Sasha Wang, Boise State University
Title: An ACE Model for Mathematics Instruction
Abstract: An ACE (Applying, Connecting, Experiencing) model for mathematics instruction is designed to create an active learning environment engaging prospective elementary teachers mathematics learning by (1) Applying learned knowledge and skills to the practice of teaching; (2) Connecting crosscutting concepts through STEM inquiries and practices; and (3) Experiencing community-based experiential learning to increase their attitudes and beliefs toward STEM education. The potential of the ACE model to leverage students learning experience, to build a knowledge base for identifying best practices, and to promote Science, Technology, Engineering, and Mathematics (STEM) learning in our community will be discussed.