Mathematics Colloquia are presented during the academic year on Thursdays at 4:30pm on Microsoft Teams unless otherwise noted. For more information, contact the Mathematics Colloquium Chair, Professor Mike Wilson at James.Wilson@uvm.edu.

 

Monday, March 4

Innovation E430; 3:25-4:25 PM

Special Loci on Moduli Spaces of Abelian Varieties with Complex Multiplication

Anton Hilado, University of Vermont

Abstract: Moduli spaces of abelian varieties possess very interesting geometry. For instance, they may contain subvarieties which are themselves moduli spaces of what may be viewed as different abelian varieties. The study of the intersections of these special subvarieties with other "special" loci such as the loci where the abelian varieties have certain endomorphism structure is a generalization of the theory of singular moduli studied by Gross and Zagier. The work of Lauter and Yang (and later Lauter and Viray) applies the theory to study certain invariants of cryptographic interest for genus 2 curves. In this talk we will describe ongoing work on a genus 3 version of these pioneering works.

ADA:  Individuals requiring accommodations, please contact Doreen Taylor at (802) 656-3166

View the PDF announcement

 

Thursday, March 21

Innovation E432; 4:00 -5:00 PM

Free is good

James Hefferon, University of Vermont

Abstract: In the culture of Mathematics, we value openness, cooperation, and collaboration.  No one would be surprised to find that a colleague had put all their training and energy into a project, working for months or even years, and then posted the results on arXiv for others to use freely and perhaps extend.  A similar culture of sharing is common among teachers in general, and in particular among teachers of mathematics.

Now that the distribution of significant books no longer requires the production of a physical object, a number of authors and author groups in our subject are producing texts that are open.  We will focus on undergraduate mathematics texts.  These have been getting adopted and we will discuss what to look for if you are considering such a text for a class.  We will also discuss what it takes to produce high-quality work, if you have an idea for making one yourself, including outlining the technical process and some non-technical processes such as licenses.

These works have promise for making things in undergraduate mathematics education better than they are.  We will close by discussing how we can help to develop a mindset that values and promotes this as a professional activity.

ADA:  Individuals requiring accommodations, please contact Doreen Taylor at (802) 656-3166

View the PDF announcement