Department of Mathematics and Statistical Science Algebra Seminar Series
About the Seminar
The Department of Mathematics and Statistical Science Algebra Seminar is a graduate student led seminar series that provides graduate students and advanced undergraduate students in mathematics the opportunity to give professional mathematical talks. These talks are open to any who would like to attend, and their contents reflect a variety of mathematical disciplines.
Times and Locations
For Spring 2022, the Algebra Seminar meets on alternating Tuesdays, from 11:00am - 12:00pm, on Zoom (occasionally it will also be offered in-person in TLC 249; the in-person offerings will be noted in the schedule below).
- We will use the same Zoom Link each week. Passcode: 818108
- Check the schedule below for more information.
Date |
Speaker / Title / Abstract |
---|---|
January 18, 2022 at 11:00 am Virtual meeting via Zoom |
Dr. Stefan Tohaneanu (Univ Idaho) Abstract: On method for computing the minimum distance of a linear code is to check if certain projective schemes are empty or not. The defining ideals of these schemes are ideals generated by fold products of the linear forms that are dual to the generating matrix of the linear code. Geometrically, the projective varieties defined by these ideals are union of subspaces of various dimensions, and they generalize the more classical objects known as star configurations. |
Please note: Special time and location Friday, February 11 at 4:00 pm In TLC 022 and via Zoom |
Dr. Alex Woo (Univ Idaho) From order statistics to knot theory Abstract: Suppose one wishes to do statistics purely with rank data, inferring the order certain items come in where the only ‘experimental’ data available consists of the order these items come in under various ‘measurements’. Then one needs some notion of ‘distance’ between orderings, or, equivalent, between permutations. Three such notions of distance are known to statisticians as Spearman’s footrule, Kendall’s tau, and transposition distance, and to combinatorialists respectively as total displacement, inversion number, and reflection length. Diaconis and Graham showed in the 1970s that Spearman’s footrule is at least the sum of Kendall’s tau and transposition distance, and asked for a characterization of equality. Recently, Cornwell and McNew gave a way of associating a knot or link to a permutation. Using the results of Cornwell and McNew as well as a recursive answer, due to Hadjicostas and Monico, to the question of Diaconis and Graham, we show that the permutations satisfying equality are precisely the ones associated to an unlinked collection of unknotted loops. |
February 22, 2022 |
Dr. Jennifer Johnson-Leung (Univ Idaho) |
March 1, 2022 | Dr. Ben Breen (Clemson Univ) Computing Hilbert modular forms using a trace formula. Abstract: We present an explicit method for computing spaces of Hilbert modular forms using a trace formula. We describe the main algorithmic challenges and discuss the advantages and shortcomings of this method in comparison to other methods for computing spaces of Hilbert modular forms. We conclude with computations. |
March 22, 2022 | We will watch the Clay lectures given by Fields medalist Akshay Venkatesh at the Arizona Winter School earlier this month. |
March 29, 2022 | We will continue to watch the Clay lectures given by Fields medalist Akshay Venkatesh at the Arizona Winter School earlier this month. |
April 5, 2022 | Dr. Brooks Roberts (Univ Idaho) The group law on binary quadratic forms: Bhargava's new perspective Abstract: The study of integral binary quadratic forms has contributed to the development of many parts of mathematics including algebraic number theory, abelian class field theory, and complex multiplication. As part of this development, Gauss and Dirichlet showed that the set of equivalence classes of primitive integral binary quadratic forms of fixed discriminant has a group law making this set into a finite abelian group. Beginning with his 2001 PhD thesis, Manjul Bhargava presented a new way to describe this group law, and found thirteen other higher composition laws. Bhargava was awarded the Fields Medal in 2014. In this talk we will review Bhargava's remarkable account of the group law for integral primitive binary quadratic forms. |
April 19, 2022 | Jordan Hardy (Univ Idaho) Chains of Large Prime Gaps and Sieve Methods Abstract: Within Mathematics, number theory is a discipline that has become infamous for having problems that are easy to state in a form understandable to most members of the general public, but require incredibly sophisticated mathematical techniques to solve. In this talk, we examine a few versions of a simple question: "How big can the gap between consecutive prime numbers be and how many 'big' gaps can occur in a row?." The easiest versions of this problem, we will see are an accessible exercise for students taking their first course in number theory while more advanced versions have only been tackled using advances in Sieve methods made during the late 20th and early 21st century. |
April 26, 2022 | Jordan Hardy (Univ Idaho) Some Conjectures About Nonprincipally Polarized Abelian Surfaces With Complex Multiplication Abstract: The theory of abelian varieties with complex multiplication was developed for abelian varieties of arbitrary genus in a book called Complex Multiplication of Abelian Varieties and Its Applications to Number Theory in 1961. This is a powerful theory which identifies certain special abelian varieties whose endomorphism rings are as big as possible. These abelian varieties turn out to be computationally easier to do with, and they correspond to special points in the siegel modular variety. When you evaluate a siegel modular function at these points you get algebraic numbers which can be used to generate class fields over the reflex field of CM fields. Almost all of the theory that has been developed in this area concerns abelian varieties which carry a principal polarization. What happens when we shift our focus to abelian varieties with nonprincipal polarizations? Earlier, I developed the theory to identify when it is possible to give an abelian surface with complex multiplication by a given CM field, but the criterion developed is clunky and difficult to quickly verify. In this talk we will discuss some conjectures about simpler necessary and sufficient conditions for there to be an abelian variety with complex multiplication by a given CM field which carries a polarization of a desired type. |
May 3, 2022 | Jake Sapozhnikov (Univ Idaho) Bipackings of Bipartite Graphs Abstract: Let G = G(X_1,X_2) be a bipartite graph. Consider the partite-preserving functions from G to a complete bipartite graph B_{n+1} with the same vertex set and one extra vertex added to one of the partites. We say such a function f is a bipacking of G into B_{n+1} if no edges of G and f(G) coincide. In 2019, Dr. Hong Wang proved that there exists a bipacking for every bipartite graph of girth at least 12 and conjectured that this property holds for all bipartite graphs of girth at least 8. We will discuss the background of the problem, the techniques from Wang(2019), and partial progress toward a proof of the tighter bounds using these techniques. |