Seminar

An introduction to the `Box Product Problem', its connection with
nabla products, and an overview of recent results with Hector Barriga
Acosta (UNAM Morelia).

Abstract:

Choose a positive integer. If it is odd, multiply it by three and add one. If it is even, divide it by two. The Collatz conjecture is a decades old conjecture that states that for all positive integers, if you repeat this process, you will eventually reach one. In computer science, a hash function is a function that is used to map data values into organized ``buckets'', so that the information in the buckets can be easily retrieved later. These two concepts are seemingly unrelated.

The logistic map is a classic recursive sequence defined by $x_{n+1}=rx_{n}(1-x_{n})$ and $r$ is a parameter with $0\leq r \leq 4$. It turns out, this innocent sequence is quite strange when $r$ gets closer to 4. For large enough $r$, chaos can even occur. We will investigate the fixed points of this map as well as some of its periodic orbits, and later we will look into some of the numerics with this sequence.

Abstract:

This talk will be about using the Euler characteristic to count words in free partially commutative monoids or acyclic orientations of graphs

Abstract:

Abstract:

In this talk, I will discuss the analytical aspect of some recent work on the long time behaviors of a class of random Hamilton-Jacobi equation.