Prof. Ross will speak about Nathanson’s “Generalized Egyptian Fractions.” Usual time and place (2:30, K314).

Abstract:

In a paper earlier this year Mel Nathanson generalized the notion of

“Egyptian Fraction” and extended some results of Sierpinski to sets of

these generalized Egyptian fractions. I’ll give short nonstandard proofs of

further generalizations of these results.

Speaker: Ricardo Teixeira (U. Houston-Victoria)

Title: Teaching Precalculus in Hawaii

Abstract: Most students enjoy learning about applications of math concepts. In

this talk, we will show how Precalculus concepts can motivate students

in the University of Hawai`i at Mānoa. Some interesting and recreational

use of certain concepts will be explored. At the end, we will cover

other ideas such as how to develop and maintain an effective culture of

assessment that may be used for future improvement and more.

Speaker: B. Kjos-Hanssen (joint work with Lei Liu)

Abstract:

Campeanu and Ho (2004) stated that it is “very difficult” to compute the number $m_n$ of maximally complex languages (in a finite automata sense) consisting of binary words of length $n$. We show that $m_n=O_{i,n}$, the number of functions from $[2^i]$ to $[2^{2^{n-i}}]$ whose range contains $[2^{2^{n-i}}-1]$, for the least $i$ for which $O_{i,n}>0$. Here, $[a]=${1,…,a}.

Speaker: John Marriott (Boeing)

Title: Data Science Curriculum for Industry

Abstract:

John Marriott earned his PhD from UH Math in 2013 and currently works

at Boeing as a data scientist. He combines mathematical modeling,

statistics, and programming to create data products on logistics,

labor estimates, and workplace safety. He will talk about his current

work, the transition from academia to industry, and suggestions for

curriculum to prepare students for work in this field.

Title: Logic with Probability Quantifiers

Abstract: This talk is based on chapter XIV of Model-Theoretic Logics

(https://projecteuclid.org/euclid.pl/1235417263#toc). I will first give

a brief review of admissible sets and the infinitary logic which is

necessary for probability quantifiers. Then I will present the language

of probability quantifiers, as well as the proof theory, model theory,

and some examples which indicate the expressive power of the language.

Time permitting, my goal is to work towards the main completeness

theorem in section 2.3

Speaker: Kameryn Williams (UHM)

Title: The universal algorithm, the $Sigma_1$-definable universal finite sequence, and set-theoretic potentialism

Abstract: As shown by Woodin, there is an algorithm which will computably enumerate any finite list you want, so long as you run it in the correct universe. More precisely, there is a Turing machine $p$, with the following properties: (1) Peano arithmetic proves that $p$ enumerates a finite sequence; (2) running $p$ in $mathbb N$ it enumerates the empty sequence; (3) for any finite sequence $s$ of natural numbers there is a model of arithmetic $M$ so that running $p$ in $M$ it enumerates $s$; (4) indeed, if $p$ enumerates $s$ running in $M$ and $t$ in $M$ is any finite sequence extending $s$, then there is an end-extension $N$ of $M$ so that running $p$ in $N$ it enumerates $t$. In this talk, I will discuss the universal algorithm, along with an analogue from set theory due to Hamkins, Welch, and myself, which we call the $Sigma_1$-definable universal finite sequence.

These results have applications to the philosophy of mathematics. Set-theoretic potentialism is the view that the universe of sets is never fully completed and rather we only have partial, ever widening access. This is similar to the Aristotelian view that there is no actual, completed infinite, but rather only the potential infinite. A potentialist system has a natural associated modal logic, where a statement is necessary at a world if it is true in all extensions. Using the $Sigma_1$-definable universal finite sequence we can calculate the modal validities of end-extensional set-theoretic potentialism. As I will discuss in this talk, the modal validities of this potentialist system are precisely the theory S4.