# Calendar of Events

- Thursday, 25 August, 2016
- A Time for Healing and Reflection 10:00 AM
- A Time for Healing and Reflection 12:00 PM
- Mobile Learning In and Out of Class (Make It, Take It) 1:00 PM
- A Time for Healing and Reflection 10:00 AM
- What's New in Qualtrics: Introducing the Qualtrics Insight Platform 10:00 AM
- A Time for Healing and Reflection 2:00 PM
- Wednesday, 31 August, 2016
- Dr. Bennet Omalu 7:00 PM
- Thursday, 25 August, 2016
- A Time for Healing and Reflection 12:00 PM
- Monday, 29 August, 2016
- Microbiology General Seminar Series Fall 2016 11:15 AM
- Tuesday, 30 August, 2016
- Exploring Chilean Food and Wine 6:00 PM

- Friday, 09 September, 2016
- Let's Talk QUAL 4:00 PM
- Thursday, 01 December, 2016
- Faculty Pub 4:00 PM
- Thursday, 27 October, 2016
- Faculty Pub 4:00 PM
- Thursday, 08 September, 2016
- Faculty Pub 4:00 PM
- Thursday, 25 August, 2016
- Mobile Learning In and Out of Class (Make It, Take It) 1:00 PM
- Friday, 26 August, 2016
- Getting to Know Canvas 9:00 AM
- BYOD Wirelessly with Wolfvision Cynap 3:00 PM
- BYOD Wirelessly with Wolfvision Cynap 4:00 PM
- Monday, 29 August, 2016
- BYOD Wirelessly with Wolfvision Cynap 1:20 PM
- Tuesday, 30 August, 2016
- BYOD Wirelessly with Wolfvision Cynap 3:00 PM

# Junior Colloquium: Counting Integer Points in Rational Polyhedra: Popoviciu's Theorem and Beyond

**SPEAKER: **Prof. Murad Ozaydin, University of Oklahoma

**ABSTRACT: **Chicken McNuggets are sold in boxes of 6, 9 and 20. How many ways are there of buying n pieces? This is in fact a special case of a geometric question: In a given planar triangle whose vertices have rational coordinates, how many points are there with integer coordinates? What constitutes a good answer to this question?

An excellent answer one dimension lower is provided by a theorem of Popoviciu giving a short, computable formula for f(n):= the number of ways of getting n blah, if blah is sold only in boxes of sizes a and b, with the gcd(a,b)=1. No similar formula is known even for three (coprime) sizes a, b and c. There are algorithms that compute f(n) in polynomial time, due to Barvinok and others, but no explicit computable formula.

The usual proofs of Popoviciu's theorem uses the Discrete Fourier Transform, instead I'll present a short elementary geometric proof. Then I hope to discuss what is known in higher dimensions and where the difficulties lie.

Pizza will be available at 3:10 p.m.