A seminar series.
Matthew Krauel
(Sacramento State)
Where Heisenberg, Dedekind, and Euler meet:
a connection between algebra, number theory, and combinatorics.
For the inaugural talk of the algebra, number theory,
and combinatorics (ANTC) seminar, I will discuss one intersection among these three areas.
This connection--which centers around an algebraic structure bearing the name of Heisenberg,
and functions named after Euler and Dedekind--will also serve as a platform to explain some possible
future research ideas within the theories of vertex operator algebras and automorphic forms.
Joshua Wiscons
(Sacramento State)
An introduction to relational complexity: background, questions, and a few answers
This talk will introduce a relatively new invariant of finite permutation groups
known as the relational complexity. Relational complexity originated in an area of mathematical
logic known as model theory where it was a crucial ingredient of a very general classification
theory for finite homogeneous relational structures. However, little known about it for
specific examples.
This talk will begin from first principles with a focus on how to compute (or at least bound)
the relational complexities of a handful of familiar structures. Following this, the goals
are to present a few general open problems about the invariant, including Cherlin's conjecture
for finite primitive structures of complexity $2$, and discuss recent progress on them. Parts
of the talk will use methods of finite permutation group theory.
Joshua Wiscons
(Sacramento State)
An introduction to relational complexity: background, questions, and a few answers
Part 2. This is a continuation of the previous talk. The key definitions (in the context of permutation groups) will be reviewed and elaborated on before moving the focus to an open problem regarding the computation of the relational complexities of the actions of the symmetric group on partitions. This part of the talk, perhaps more so than the previous one, will be accessible to mathematicians of all levels
Craig Timmons
(Sacramento State)
Finite Fields and Extremal Graph Theory.
In extremal graph theory, one wants to know the extreme values of a graph parameter taken over a specified family of graphs. For example, one could ask for the maximum number of edges in a graph that does not contain three vertices, all pairwise adjacent. Let us call such a set of vertices a triangle.
It is not too hard to construct a graph with four vertices, four edges, and no triangle. It is impossible, however,
to construct a graph with four vertices, five edges, and no triangle.
In this talk, we will discuss problems in extremal graph theory where the best known construction
methods use polynomials over finite fields. There will be many pictures.
No seminar this week.
Christopher Marks
(Chico State)
The arithmetic of vector-valued modular forms.
In the first part of this talk, I will give an introduction to the theory of modular forms,
both scalar and vector-valued. In the second part I’ll discuss some arithmetic aspects of
the theory that are of interest to me, including the Bounded Denominator Conjecture and
(time permitting) the utility of vector-valued modular forms in computing periods of modular
curves.