Solid, liquid, gas – we see these phases of matter all around us. But physicists have discovered exotic phases with strange properties, such as superfluids and superconductors. What kinds of phase transitions happen in an extremely cold, thin sheet of matter? What does this have to do with the field of math known as topology? In this talk we’ll…
Basic physics suggests that when we stand up, the blood pressure in our brain should drop dramatically. Such a pressure drop should cause us to faint. But most of us don’t faint when we stand up. In this talk I’ll discuss a mathematical model that explains why most of us don’t, and why some people…
1. Ephraim Bililign Title: Measuring the temperature of granular systems Abstract: Granular systems, or collections of athermal mesoscale particles, are immune to temperature in the conventional sense. Thus, to describe the behavior of an jammed assortment of grains, we turn to a modified thermodynamics built on forces and volumes. I will discuss the experimental measurements…
1. Beverly Setzer Title: Detecting Hidden Nodes in Neuronal Networks using Adaptive Filtering Abstract: The identification of network connectivity from noisy time series is of great interest in the study of network dynamics. This connectivity estimation problem becomes more complicated when we consider the possibility of hidden nodes within the network. These hidden nodes act…
A generic rectangulation is a tiling of a rectangle by rectangles, with no four rectangles sharing a single corner (think: no Arizona, Colorado, New Mexico and Utah). For example: We want to ignore lengths of edges and just look at the different configurations of rectangles. In this way of thinking, the rectangulations and are the…
“When am I going to use this?” It’s a question every student has asked at least once. The Modeling Contest in Mathematics (MCM), held annually by COMAP, provides a way for undergraduates to apply the knowledge gained from classes to real world problems. Each year, COMAP presents six interesting prompts on anything ranging…
Knot theory is the subarea of topology that studies math- ematical knots or different ways of placing a circle inside 3- dimensional space. Proving that two knots are distinct (or equivalent) is the main problem knot theorists deal with. In the talk, we will discuss methods used to distinguish knots. For a simple introduction click…
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.