Suppose we lazily slice up the SUM series pizza. How many pieces can we make with just a few slices? What if we had a watermelon? Together we will try to answer this prob- lem and explore some of the beautiful geometry behind it. No background will be assumed and this talk should be ac-…

With a very stretchy square piece of paper, you can make a torus: Glue opposite sides of the square together to make a tube and then stretch and bend the tube to bring the two cir- cular ends together. Since the square can be built out of two triangles, you’ve made a torus out of…

Gerrymandering, the act of drawing political maps to achieve a desirable election outcome, has been increasingly in the news as cases wind their way to the Supreme Court and as the country approaches a new census in 2020. In this talk we’ll look at some of the mathematical strategies and problems that arise in gerrymandering…

Suppose you want to convince someone that you know the solution to a problem, but you don’t want them to learn any- thing about the solution. How can you do it? Such a protocol is called a zero-knowledge proof. In this talk, we’ll define what it means to be a zero-knowledge proof, show several ex-…

Quite a large polygon can squeeze between the integer points in the plane, but what if it has to be symmetric  bout the origin (and avoid all other integer points)? In this talk, I’ll discuss Minkowski’s theorem, which bounds the area of such shapes, and a surprising consequence for the problem of writing integers as sums of squares of other…

Tissues grow, change shape, and differentiate, function normally or abnormally, get diseased or injured, repair themselves, and sometimes atrophy. This complex suite of behaviors is governed by a complex suite of controls. Nonetheless, we can identify some general principles at work in the dynamics of tissues. Our goal is to understand how a tissues mechanics and biology regulate each…

The remarkable Ramanujan’s congruences for the partition function p(n) will be presented. Here is Ramanujan’s own account: “I have proved a number of arithmetic properties of p(n)...in particular that p(5n+4)≡0 (mod 5), p(7n+5)≡0 (mod 7). ... I have since found another method which enables me to prove all of theses properties and a variety of…

“I have traversed this bottomless night, which extinguished all light and joy of my life. I entreat you, leave the science of parallel alone”, wrote a Hungarian mathematician Farkas Bolyai to his son János, horrified at the thought that his son is attracted by the problem of parallels. János was not deterred, however, and discovered,…

In calculus, we study series and learn how to add infinitely many numbers--but how about multiplying infinitely many numbers? In this talk, we'll start with familiar series from calculus, and then move on to study more exotic infinite sums and infinite products and the interactions between them. We'll see some number theory, complex analysis, and…

Need a more private way of sending notes to your friends during class? Elliptic Curve Cryptography is a method of sending secure messages using tools from algebra and geometry. In this talk, I will introduce some of the ideas behind this encryption scheme originally introduced by Diffie and Hellman. This talk will be accessible to…

What is the mathematics behind origami? What can be achieved by just folding paper? We'll talk about the beautiful geometry underlying these questions and more, including a classical algorithm for solving polynomials with a turtle and more modern algorithm for solving cubic polynomials with a piece of paper. No background will be assumed and this…

Dating back to the 1600s modeling has been used to study cardiovascular dynamics enabling scientist to answer essential questions. In fact, todays knowledge that the cardiovascular system is circulating was first discovered via a mathematical model. In this talk I will discuss the role mathematical analysis has played in cardiovascular physiology and how we use…

The Robinson-Schensted-Knuth (RSK) correspondence is an important combinatorial bijection that associates to any permutation a pair of objects called standard Young tableaux. We will describe this correspondence in detail and discuss some interesting connections to combinatorics, algebra, and geometry. This talk will assume no background and will be accessible to all undergraduates.

Polytopes (also known in dimensions zero through three as "points", "line segments", “polygons", and “polyhedra") have been objects of interest to mathematicians throughout the recorded history of mathematics. Most notably, the five Platonic solids were probably known at least a thousand years before Plato. Regular polytopes are "as symmetric as possible" in a sense that…

Chaos refers to seemingly random and unpredictable dynamics of a system that evolves in time. Certain chaotic systems exhibit an additional level of complexity: intermittent extreme events that are noticeably distinct from the usual chaotic dynamics.  These extreme events include ocean rogue waves, extreme weather patterns, and epileptic seizure.  I will discuss several examples of these…

From x-ray machines to luggage scanners, our lives depend on imaging devices that let us “see” what is impossible to observe with the naked eye. I will explain some of the mathematical ideas that make image reconstructions possible. Along the way, we will solve some fun puzzles that are related to image reconstructions. This talk…

We all tackle hard problems everyday, like finding a parking spot in the Dan Allen Deck. However, there are special types of problems which are hard even for a computer to solve. Reductions, conversions of one problem into another, play a critical role in determining the hardness of these computational problems, and lead to philosophical questions…

The 21st century has seen a boom in the production of data as well as methods to analyze data. One such methodology is Topological data analysis (TDA), where concepts from topology are used to infer the patterns underlying data sets. I will provide a basic and accessible introduction to persistent homology, a common type of TDA that is…

Imagine tying up your shoelaces into a knot.  How can we measure the difficulty of unknotting this mess?  In this talk, we will study mathematical knots and various measurements of their complexity with a view towards efficient unknotting.  This talk should be accessible to all undergraduates.