Algebra / Number Theory / Combinatorics Seminar

A Fibonomial is what is obtained when you replace each term of the binomial coefficients $ {n \choose k}$ by the corresponding Fibonacci number.  For example, the Fibonomial $${ 6\brace 3 } = \frac{F_6 \cdot F_5 \cdot \dots \cdot F_1}{(F_3\cdot F_2 \cdot F_1)(F_3\cdot F_2 \cdot F_1)} = \frac{8\cdot5\cdot3\cdot2\cdot1\cdot1}{(2\cdot1\cdot1)(2\cdot1\cdot1)} = 60$$ since the first six Fibonacci […]

For centuries finding the determinant of a matrix was considered to be something that took $\Theta(n^3)$ steps.  Only in 1969 did Strassen discover that there was a faster method.  In this talk I'll discuss his finding, how the Master Theorem for divide-and-conquer plays into it, and how it was shown that finding determinants, inverting matrices, […]

In this talk, I will try to give a fun introduction to tropical geometry and Hassett spaces, and show how tropical geometry can be used to compute the Chow rings of Hassett spaces combinatorially. This is joint work with Siddarth Kannan and Shiyue Li.

A triple of natural numbers (a,b,c) is an S-set if a+b=c. I. Schur used the S-sets to show that for n >3, there exists s(n) such that for prime p > s(n), x^p + y^p = z^p (mod p) has a nontrivial solution. A (p,q)-graph G is said to be vertex Ho-Lee-Schur graph if there exists a bijection […]

Augusta Ada Byron King Lovelace (1815-1852) is today celebrated as the first computer programmer in history. This might be confusing to some because in 1852 there were no machines that looked like what we call computers today. In this talk I attempt to explain what Ada really did, and delineate the mathematics involved. Bernoulli numbers […]