Join us for lots of pizza, conversation, and puzzles as we celebrate the end of the year!
It’s been a pleasure running Math Club these past three years.
-Nico
4/23: Tobias Wilson, “History of Functions (subtitled: Putting the Fun in Functions)”
Abstract:
Although functions are fundamental mathematical objects, they weren’t
actually defined until 1673, by Leibniz. Since that time, the definition
has evolved in a variety of directions- occasionally false, as when Fourier
defined functions to be anything with a Fourier series. In this talk, we’ll
trace the development of the definition through history and then discuss
extending the notion of a function to a variety of branches of modern
mathematics. This talk will be very accessible and (hopefully) entertaining.
actually defined until 1673, by Leibniz. Since that time, the definition
has evolved in a variety of directions- occasionally false, as when Fourier
defined functions to be anything with a Fourier series. In this talk, we’ll
trace the development of the definition through history and then discuss
extending the notion of a function to a variety of branches of modern
mathematics. This talk will be very accessible and (hopefully) entertaining.
4/2: Dan Nichols, “Public-key cryptography and the discrete logarithm problem”
Abstract:
The problem of finding a discrete logarithm in a finite group is the basis for some widely-used cryptographic systems including Diffie-Helman key exchange (DHKE) and elliptic curve cryptography (ECC). You may not be familiar with these encryption methods, but you use them every day when you visit a secure webpage or send a message from your smartphone. I will describe this problem and explain how it is used for secure communication and authentication in web browsers, electronic devices, and more.
3/26: Professor Rob Kusner, “Pi Day Redux”
Abstract:
Because Pi Day fell on the Friday before break, many of you
may have missed out on the festivities. We’ll develop a bit of
integral geometry (a.k.a. geometric probability) that lets us compute
Pi by a random process – the Buffon Needle Problem – as well as the
lengths of curves in the plane and the sphere, eventually leading to
the now-classic theorem of Fenchel-Fary-Milnor about the total
curvature of space curves.
3/12: Stephanie Reinders, “Splines on Cycles”
Abstract:
Start with a graph whose edges are labeled by positive integers. Label each vertex with an integer so that if two vertices are joined by an edge the vertex labels are congruent modulo the edge label. A set of vertex labels satisfying this condition is called a spline. Much of our research pertains to splines on n-cycles. We use the Chinese Remainder Theorem to find particularly nice splines, and we identify two bases for the set of splines on n-cycles.
3/5: Allison Tanguay, “The Needle Problem”
Abstract:
In 1917 a Japanese mathematician named Kakeya posed “the needle problem,” asking: what is the area of the smallest figure in the plane in which a unit line segment (a “needle”) can be rotated 180 degrees? It was conjectured that the smallest such “Kakeya set” was a deltoid with area $\pi/8$. However, in 1928 a Russian mathematician named Besicovitch published a very surprising result: Kakeya sets can be arbitrarily small. More than just a historic and geometric curiosity, Kakeya sets have come to play an important role in analysis today. In this talk, we will construct a Kakeya set with arbitrarily small area and then discuss some problems that are unexpectedly related to these sets.
2/26: Nico Aiello, “Chases and Escapes: Virtue or Vertigo for the Lady in the Lake?”
Chases and Escapes: Virtue or Vertigo for the Lady in the Lake?
The ideas of pursuit and evasion pervade much of human existence and as a result have always been a huge part of human entertainment – it has been said that half of all fictional writing boils down to a single conflict between the hunter and the hunted. But more than just recreational, the study of chases and escapes is also mathematically interesting and has applications to computer science, surveillance, traffic control, and military strategy. After learning some fundamental concepts from game theory, we will discuss the classic pursuit-evasion problem, “The Lady in the Lake,” in which a woman finds herself in a rowboat in the middle of a circular lake while a pursuer waits for her along the shore. If the pursuer runs at four times the woman’s rowing speed, can the woman reach a spot on the shore before her purser does? We will uncover the woman’s optimal escape strategy in order to answer this question and much further, find the minimum speed relative to her pursuer’s that the woman must row to evade capture.
2/19: Jon Judge (UConn), “Euler’s Constant”
Euler’s Constant
Everyone has heard about the number ?, everyone who has taken calculus has heard
about the number e, but there’s a third important number in mathematics that fewer
people have heard about: ? (called gamma, or Euler’s constant). This number, whose
decimal expansion starts out as 0.5772156…, was discovered nearly three centuries
ago when Euler was investigating properties of the harmonic numbers
Hn=1+1/2+1/3+?+1/n. Despite its age, many basic questions about ? remain unsolved.
We will discuss the history of ?, how it can be computed, its connections to
different areas of mathematics, and a long-standing open question about its
(ir)rationality.
2/12: Professor Michael Lavine, “Before You Analyze, Know Y”
“Before You Analyze, Know Y”
Michael Lavine, Professor and Department Head, Department of Mathematics and Statistics, will discuss why choosing a statistical analysis or statistical model without seeing the data is dangerous. He will present a few examples from linguistics, public policy, biology, and ecology that illustrate why.
2/5: Professor Bill Meeks, “From soap films to minimal suraces”
***UPDATE***
Due to the weather, this talk has been cancelled.
——————————————————————————————-
Please join us for Math Club this Wednesday, 5:30-6:30 in LGRT 1528. This week, Professor Bill Meeks will speak on, “From soap films to minimal surfaces” (abstract below). As always, pizza and soda will be provided.
Title: From soap films to minimal surfaces
Abstract: I will present some basic minimization problems in the calculus
of variations. A key problem in this subject is the classical Plateau
problem that asks: Given a simple closed curve in three-space, is it the
boundary of a surface of least area? I will also discuss related problems
such as the Kelvin problem for minimizing perimeter in dimension 3 and
Fermat’s problem of constructing roads of least pavement that connect
three cities in a planar map. However, the focus of my talk will be on
Plateau’s problem and how it is related to the existence of soap films on
a closed wire contour. As an important aside, I will attempt to explain
how this problem leads to the mathematical theory of what are called
minimal surfaces and to applications like the solution of the Positive
Mass Conjecture in the theory of relativity. The talk will be visual with
many colorful slides that illustrate the concepts in nature and in real
life.