The “Friday Afternoon Mathematics Undergraduate Seminar” (FAMUS) is a weekly event consisting of announcements, talks, and faculty interviews. FAMUS takes place most Fridays at 3:00-4:00pm in Room 164 of the Adel Mathematics Building. Typically the first half of FAMUS consists of a talk on a mathematical topic while an interview of a faculty member takes place in the second half. FAMUS is hosted by Jeff Rushall.

Come join us for some entertaining talks! Refreshments always served.

Note that talks are listed in reverse chronological order.

**Date:** December 7, 2018

**Speaker:** Jeff Rushall (NAU)

**Abstract:** A unit fraction is a fraction of the form 1/n, where n is any positive integer. An Egyptian fraction is a sum of unit fractions. It turns out that ANY positive rational number can be written as a sum of distinct unit fractions, and in lots of different ways. Egyptian fractions have curious history, and there are many interesting questions about them, both unsolved and solved (including the very first question on this year’s Putnam Exam!). In this talk, I will give an overview of Egyptian fractions - and show some nice pictures.

The faculty guest interviewee this week is Shannon Guerrero. [PDF of Flyer]

**Date:** November 30, 2018

**Speaker:** Adolfo Escobedo (School of Computing Informatics and Decision Systems Engineering, ASU)

**Abstract:** In this talk, I will give an overview of the diverse research areas (and their mathematical underpinnings) I have worked on formerly as a PhD student and currently an assistant professor. Then, I will give an overview of the School of Computing, Informatics and Decision Systems Engineering (CIDSE) at Arizona State University (ASU), including opportunities for students to enter the PhD program in Industrial Engineering.

**Biography:** Adolfo R. Escobedo joined CIDSE at ASU in 2016 as an assistant professor. Escobedo received a BA in Mathematics from California State University, Los Angeles and a PhD in Industrial and Systems Engineering from Texas A&M University. His research interests are in the theory and application of mathematical programming and algorithm design for computational social choice, power systems operations and planning, circular economy, and optimization software development.

The faculty guest interviewee this week is Adolfo Escobedo - but we won’t do the usual formal interview; we’ll have a more open and loose Q&A related to his presentation. [PDF of Flyer]

**Date:** November 16, 2018

**Speaker:** Jeff Rushall (NAU)

**Abstract:** A Pythagorean triangle is a right triangle - so the triangle side lengths satisfy the Pythagorean Theorem - with INTEGER side lengths. One hypothetical 3-D analogue of a Pythagorean triangle is a “box” whose sides are all pairs of Pythagorean triangles. That is, each of the 6 sides is a rectangle whose diagonal is the hypotenuse of two right triangles - a.k.a. an Euler Brick - provided such a thing even exists. Come and find out if Euler Bricks exist. We will also see if an Euler Brick with an integer internal diagonal - a.k.a. a Perfect Cuboid - exists. And all comers can criticize my use of hyphens - if you dare - during FAMUS.

This week’s guest is Gina Nabours. [PDF of Flyer]

**Date:** November 2, 2018

**Speaker:** Tanner Rosenberg (NAU undergrad)

**Abstract:** One can model a configuration of genes as a permutation of the numbers 1 through n, where each number can be right-side-up or upside-down. In this model, one type of mutation corresponds to performing a 180-degree reversal. The reversal distance between two configurations of genes is the minimum number of reversals needed to convert the permutation corresponding to one gene configuration to the other. Although there are other types of mutations, we focus on reversals since they are the most common mutation and reversal distance provides a good estimate for genetic distance. While the maximal reversal distance among all permutations of 1 through n and the identity permutation is known, in this presentation we discuss our progress toward describing the structure of permutations that attain the maximal reversal distance.

This week’s guest is Nethali Fernando. [PDF of Flyer]

**Date:** October 26, 2018

**Speaker:** Jeff Rushall

**Abstract:** A Heronian triangle is a planar triangle whose side lengths AND area are all integers. For example, every integral Pythagorean right triangle is Heronian. Are there others? Yes - lots. A Super Heronian triangle is a Heronian triangle whose side lengths are CONSECUTIVE integers. One example is a 13-14-15 triangle (I’ll let you figure out the area). How many Super Heronian triangles exist? Are there higher-dimensional analogues? Come to FAMUS and see…

This week’s guest is also Bahattin Yildiz. [PDF of Flyer]

**Date:** October 19, 2018

**Speaker:** Natalie Coston

**Abstract:** Have you ever walked into a room and thought “What did I come in here for?” Well, for Mitsy Markov, this is a way of life. Mitsy is deep into her first semester of graduate school in math, and between classes and teaching, she is getting pretty delirious. Follow Mitsy on a memoryless journey from room to room as she learns about Markov Chains first hand.

This week’s guest is also Natalie Coston. [PDF of Flyer]

**Date:** October 12, 2018

**Speaker:** Brent Pohlmann (Cal State University Maritime Academy)

**Abstract:** In this talk we will give an overview of number systems, eventually dening the quaternions. There is very interesting, current research involving the quaternions, which will also be presented. Along the way we’ll talk about Sir William Rohan Hamilton, perhaps the only famous mathematician to come from Ireland.

This week’s guest is also Brent Pohlmann. [PDF of Flyer]

**Date:** October 5, 2018

**Speaker:** Jeff Rushall (NAU)

**Abstract:** Many real-life scenarios involving “public” privacy situations have been mathematized. These include where to sit in a theater to avoid having people beside or in front of you, where to sit on an open-seat flight to maximize the chances of having an extra/empty seat next to you, etc. Another such situation is urinal selection in a bathroom. I will discuss how this situation gets mathematized, its connection to other math problems, and show plenty of pictures (the result of exhaustive fieldwork on my part). And yes, there will be a “Part II” sometime in the not-too-distant future.

This week’s guest is Sal Vera (NAU). [PDF of Flyer]

**Date:** September 28, 2018

**Speaker:** Jeff Rushall (NAU)

**Abstract:** Prime numbers are positive integers greater than 1 with exactly two distinct positive integer divisors. The distribution of primes amongst the rest of the natural numbers is something of a mystery, but some types of primes are easy and fun to ponder. One semi-interesting subset of primes are integer pairs of the form $(n, n+6)$ where both $n$ and $n+6$ are prime, which are known as “sexy primes.” I will present some entertaining facts about primes in general, and sexy primes in particular.

This week’s guest is Ellie Kennedy (NAU). [PDF of Flyer]

**Date:** September 21, 2018

**Speaker:** Riley Waechter (NAU)

**Abstract:** This past summer I traveled to Muhlenberg College in Allentown, Pennsylvania to participate in a Research Experience for Undergraduates (REU) program (now that you know what REU stands for, gold star to anybody who can figure out all 3 acronyms in the title). I will detail what the program was like in many aspects: day-to-day life, “extracurricular” activities, and of course, the math. As far as the math is concerned, I worked on two different projects this summer. We will begin by briefly diving into combinatorial game theory to discuss nimbers (or Sprague-Grundy values) of the game of Node-Kayles played on certain families of graphs. We will then switch gears to discuss the domination number of permutation graphs on n vertices. Finally, we will conclude by examining the application process for REU programs.

This week’s guest is Ian Williams (NAU). [PDF of Flyer]

**Date:** September 14, 2018

**Speaker:** Dana Ernst (NAU)

**Abstract:** You’re single and looking for love. In front of you are three doors. Behind each door is a prospective partner. Let’s assume that of the three people who are waiting behind the doors, there is a best match, a not so good match, and a least good match for you. Your mission is to couple up with your best possible match. Thankfully, I’m going to let you open some doors. But there are rules! To start, you select a door. It will open to reveal one of your potential suitors. If you want to choose this person as your match, you’re done and you don’t get to see either of the others. Risky! If you decide to move on, you discard the first person and they’re history. You select one of the two remaining doors. It opens to reveal someone else and again, you can choose this person as your match. But just like before, if you choose this person, you don’t get to see who is behind the final door. Nor are you allowed to return to the person you discarded behind the first door. If you decide to move on a second time, you select the final door. You must choose the person behind it as your match, whatever you think of them. Also risky! What strategy gives you the best chance of finding your best match?

This week’s guest is also Dana Ernst - but his interview is going to be more of a “telling stories about his summer,” most notably some little bike race he did in Colorado. [PDF of Flyer]

**Date:** September 9, 2018

**Speaker:** Jeff Rushall (NAU)

**Abstract:** I will talk about the math I did, the traveling I did (to some semi-exotic places), and show you some really neat pictures (involving both math and traveling).

The guests this week are department staff Bea Gallegos, Melina Miller and Mary Fule. [PDF of Flyer]