A seminar series.
Matthew Krauel
(Sacramento State)
A brief introduction to Monstrous Moonshine.
In the late 1970s a mysterious connection between complex functions related to modular curves and group theory was observed. This mathematical mystery became known as Monstrous Moonshine. Similar mysterious connections, or Moonshines, of all sorts exist today and form a powerful connection between Algebra, Number Theory, and String Theory. In this talk, I will briefly describe Monstrous Moonshine, including brief summaries of the mathematical elements it contains, as well as the history of its development.
Vladislav Taranchuk
(Sacramento State)
Pancyclicity When Each Cycle Contains $K$ Chords.
For integers $n \geq k \geq 2$, let $c(n,k)$ be the minimum number of chords that must be added to a cycle of length $n$ so that the resulting
graph has the property that for every $l \in \{ k , k + 1 , \dots , n \}$, there is a cycle of length $l$ that contains
exactly $k$ of the added chords. Chaouche, Rutherford, and Whitty introduced the function $c(n,k)$. They showed that for every integer $k \geq 2$,
$c(n , k ) \geq \Omega_k ( n^{1/k} )$ and they asked if $n^{1/k}$ gives the correct order of magnitude of $c(n, k)$ for $k \geq 2$. Our main theorem
completely answers this question as we prove that for every integer $k \geq 2$, $c(n , k) \leq k \lceil n^{1/k} \rceil + k$. This upper bound, together
with the lower bound of Chaouche et.\ al., shows that the order of magnitude of $c(n,k)$ is $n^{1/k}$.
Courtney Gibbons
(Hamilton College)
Blank Space.
Sudoku's a game, wanna play? It turns out that algebra is more
than just x's and torturing high school students. Algebra has been used to
solve problems from biology, physics, and economics. In this talk, I'll walk
through an example of using algebra to solve a slightly less ambitious problem:
a 4 by 4 sudoku puzzle. We'll develop many tools used to solve the big problems, too.
Corey Shanbrom
(Sacramento State)
An introduction to the Semple Tower.
We will introduce the Semple tower, a mathematical object of interest to both algebraic and differential geometers for its applications to the singularity theory of curves.