GSAC Colloquium

Fall 2019
Tuesdays, 4:35-5:35 PM, JWB 335
MATH 6960-001

Date Description
August 20 Organizational Meeting
August 27 Proofs Without Words | Hannah Hoganson
Abstract: A proof without words, or picture proof, is as it sounds: A proof of a mathematical identity or statement which can be demonstrated as self-evident by a diagram without explanatory text. Many argue that proofs without words are not really proofs, and are thus not acceptable as real mathematics. I will instead argue the viewpoint of popular mathematics and science writer Martin Gardner: "In many cases a dull proof can be supplemented by a geometric analogue so simple and beautiful that the truth of a theorem is almost seen at a glance." We will start with picture proofs that one could use in trigonometry and calculus courses, and conclude with a picture proof about serial isogons of 90 degrees.
September 3 Billiards in Polygons | Matt Smith
Abstract: Mathematical billiards are particles which move without friction or other external forces within some rigid container. Despite being relatively simple to define, some problems about billiards have been open for over a hundred years. Recent progress towards solving these problems unites several fields of mathematics in surprising and beautiful ways. The goal of this talk is to give a gentle introduction to ergodic theory and some other tools that have been used to attack open problems in billiards.
September 10 Which numbers are divisible by 5? | Daniel McCormick
Abstract: Many of us learned a simple test for divisibility by 5 sometime during early education: check if the last digit is 0 or 5. The key property which makes these divisibility tricks easy to apply is that they exploit patterns in the way we represent numbers with symbols, allowing us to reduce computation to pattern matching. It turns out that these patterns can be understood through the lens of grammar. This talk will explore the deep connection between computation and the theory of formal languages, using divisibility by 5 as a guiding example.
September 17 Control Stability in Aerodynamics | Justin Baker
Abstract: Lyapunov stability is a recurrent theme in the design of modern aircraft, and Lyapunov control is fundamental to many autopilot systems. These techniques are implemented to determine the stability of the feedback control system. Various feed back control systems are optimized for various aerodynamic situations, using gains-scheduling to seamlessly transition between them. We will explore Lyapunov stability and control during the aerodynamics of tail wing flutter, icing conditions and flat spins.
September 24 If you give a random-walking mouse a cookie | Claire Plunkett
Abstract: If a mouse is following a simple random walk on the number line, we can determine many properties and statistics about its walk. But if we give a mouse some cookies by placing cookies at each number, the mouse eats the cookies and gets excited and no longer obeys just a simple random walk. By formulating how the mouse moves according to the cookies it's eating, we define the "cookie random walk." We investigate how the properties of a cookie random walk are different from those of a simple random walk.
October 1 When the needles turn around the mystery remains | Carlos Ospina Trujillo
Abstract: The question of our seminar is simple: what is the minimum area of a plane region on which it is possible to rotate a needle freely? At first glance, this question may seem a fool one with no mathematical content, but as usual in mathematics, this is not the case. We will see several examples of such class of figures, and we will explore more questions related to these objects.
October 8 Fall Break | No talk
Abstract: Have fun! :)
October 15 Fundamental Solutions and D-modules | Cameron Zhao
Abstract: Fundamental solutions give us a way to solve PDEs with constant coefficients. Their existence was proved in the 50s, but different proofs have emerged, providing new perspectives to many areas. We will discuss how the existence problem is related to analytic continuations of generalized functions, how it was solved using resolution of singularities, and how D-modules came into play.
October 22 Should Mathematicians Care About Biology? | Jake Madrid
Abstract: The short answer to this question is yes! But why? The advancement of applied techniques in mathematics in the twentieth century along with recent advances in observational tools in biology has led to an increase in applications of a variety of mathematical fields to biology. In addition, several problems in biology have inspired the development on new mathematics in many disciplines. Here we will discuss the history of mathematics in biology as well as several examples that illustrate the importance of the interface between the two fields.
October 30 (Special day) Outer Space is Full of Aliens but Life is Impossible | Alex Beams
Abstract: Francis Drake proposed an equation to estimate the number of extraterrestrial societies on other planets which are detectable by radio telescope. If the equation suggests that there is another intelligent civilization in our own galaxy, why can’t we find any evidence? This is the “Fermi Paradox”. Aside from a plethora of conspiracy theorists’ claims to the contrary, is it rational to think there could be non-Earth life in our own solar system right now? There are many angles to this issue, and “abiogenesis”, how life begins on planets, is one of them. This is also where things get really strange. At the heart of the inquiry into the origins of life lives another paradox that has been around for decades, and it seems that it has to be resolved in order for life to evolve in the first place. It’s called “Eigen’s Paradox”, and we’re going to run straight into it.
November 5 TBA | AWM Speaker
November 12 TBA | Professor panel
November 19 Down-to-earth topology | Jose Yanez
Abstract: For more than two millennia, humanity has known that the earth is spherical, but in the recent years some people decided to be wrong about it. In this talk, I’ll introduce some basic concepts from topology, and provide some (practically impossible) topological experiments to settle this non-debate once and for all.
November 26 TBA | Ryleigh Moore
December 3 TBA | Peter McDonald