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http://depts.ycp.edu/~cbauer/
cbauer@ycp.edu
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Cryptology on Campus During WW II. Many colleges and universities were involved in offering cryptology classes in the 1940s. There was a tremendous amount of diversity in who delivered the classes. The professors were not all mathematicians, but rather came from departments that included Astronomy, Classics, English, Geology, Greek, Psychology, and Philosophy. Some of these classes were open to all students, while others were run with great secrecy and open only by invitation. These classes are detailed along with the backgrounds of the instructors and the role they played in the war.
The Cryptologic Contributions of Dr. Donald Menzel. Dr. Donald H. Menzel is well known for his work in astronomy, but his cryptologic work (long secret) has attracted much less attention. This talk describes how his interest in this area was first sparked and provides the details of the secret class he led in "Naval Communications" (really cryptanalysis) at Radcliffe College during World War II. This class served as a prototype and was copied elsewhere. A sketch of some of the classified work he carried out during the war, and after, as a consultant, is also included, along with a brief over-view of Menzel’s personality and other interests.
Cracking Matrix Encryption Row by Row. The Hill Cipher, also known as matrix encryption, uses matrices to encipher and decipher text. Various attacks, such as those found by Jack Levine, have been published for this system. This talk reviews a few previous results and presents a powerful new attack in which the rows of the matrix can be determined independent of one another, greatly reducing the amount of time needed for decipherment.
A New Connection Between the Triangles of Stirling and Pascal. An enumeration problem involving matrices is seen to give rise to Pascal's triangle, Stirling's triangle, and infinitely many other new triangles. Some special properties of the better known triangles are related and analogous results for the new triangles are investigated. This is an open problem with much work still to be done and best of all, it is appropriate for undergraduate contemplation!
https://sites.millersville.edu/rbuchanan/
Robert.Buchanan@millersville.edu
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Turing Instability in Pioneer/Climax Species Interactions
Aspects of Financial Mathematics: Options, Derivatives, Arbitrage, and the Black-Scholes Option Pricing Formula
An Introduction to State Space Reconstruction: Applications and Mathematical Prerequisites
https://www.fandm.edu/annalisa-crannell
annalisa.crannell@fandm.edu
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Drawing Conclusions from Drawing a Square. The Renaissance famously brought us amazingly realistic perspective art. Creating that art was the spark from which projective geometry caught fire and grew. This talk looks directly at projective geometry as a tool to illuminate the way we see the world around us, whether we look with our eyes, with our cameras, or with the computer (via our favorite animated movies). One of the surprising results of projective geometry is that it implies that every quadrangle (whether convex or not) is the perspective image of a square. We will describe implications of this result for computer vision, for photogrammetry, for applications of piece-wise planar cones, and of course for perspective art and projective geometry.
Anamorphic distortion: it's closer than you think. What is the difference between Trompe L'Oeil and anamorphic art? One difference is that we think of the former as being surprisingly realistic, and as the latter as a distortion that can morph into being realistic if we stand in the "correct" spot. But both of these perspective art genres employ the same underlying mathematics, and in that sense, one might conclude they are both equally realistic. In this talk, we offer a measure of anamorphic distortion and describe its dependence on the standard measure of viewing distance. We conclude that Trompe L'Oeil and anamorphic art are not truly different in kind, but are rather variations along a spectrum, and that the spectrum varies with relative distances of the image to the viewing target of the particular piece.
In the Shadow of Desargues. Those of us who teach projective geometry often nod to perspective art as the spark from which projective geometry caught fire and grew. This talk looks directly at projective geometry as a tool to illuminate the workings of perspective artists. We will particularly shine the light on Desargues' triangle theorem (which says that any pair of triangles that is perspective from a point is perspective from a line), together with an even simpler theorem (you have to see it to believe it!). Given any convoluted, complicated polygonal object, these theorems allow us to draw that object together with something that is related to it--- its shadow, reflection, or other rigid symmetries---and we'll show how this works. (If you enjoy doodling or sketching, bring your pencil, a good eraser, and a straightedge.)
bdunham@brynmawr.edu
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The Infinitude of Primes: Euclid, Euler, Erdös. The foundation of number theory lies among the primes. It thus seems fitting to examine three different proofs, from across history, of the infinitude of the prime numbers. We first look at Euclid’s argument from 300 BCE, which appears as Proposition 20 of Book IX of the Elements. Although "Euclid’s proof of the infinitude of primes" is a standard in every number theory textbook, some people might be surprised to see his argument in its original form. We next consider Euler’s analytic proof from 1737. Like so much of his work, this features a blizzard of formulas, manipulated with a maximum of agility and a minimum of rigor. But the outcome is spectacular. Finally, we examine Erdös’s combinatorial proof from the 20th century. This is an elementary argument, but it reminds us once again that "elementary" does not mean "trivial." Taken together, these proofs suggest that, to establish the infinitude of primes, it helps to have a two-syllable last name starting with "E." More to the point, they show mathematics as a subject whose creative variety knows no bounds.
An Eulerian Miracle. This talk features some genuine Eulerian magic. In 1748, Leonhard Euler considered a modification of the harmonic series in which negative signs were attached to various terms by a rule that was far from self-evident. With his accustomed flair, he determined its sum, and the result was utterly improbable. There are a few occasions in mathematics when the term "breathtaking" is not too strong. This is one of them.
The Math Matriarchs of Bryn Mawr. Over its first 50 years, Bryn Mawr College boasted three remarkable mathematicians who, one after the other, left deep footprints on the institution and on the U.S. mathematical community. They were Professors Charlotte Angas Scott (British), Anna Pell Wheeler (American), and Emmy Noether (German). In this lecture, we meet these women and flesh out their biographies with plenty of local color… not to mention a real-life assassin in a supporting role. From 1885 to 1935, they gave Bryn Mawr a record of women in mathematics unsurpassed by any college, anywhere.
drmwecker@aol.com
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Mathemagical Black Holes. Many of the best recreations have a common theme. Start with a number, perform some process over and over, and always arrive at one particular number - the mathemagical black hole.
Paradoxes. How can you pass your body through a postcard? Can a surface really hold a finite volume of paint but not be painted? How does this last example relate to fractals, the von Koch snowflake, and the human intestines? What's the deal with time travel? How can removing balls from an urn lead to no balls or infinitely many?
https://www1.villanova.edu/university/liberal-arts-sciences/programs/mathematics-statistics/faculty.html
timothy.feeman@villanova.edu
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The ART of tomography. We will look at how an algorithm from linear algebra, called Kaczmarz's Method, can be used to create a CAT scan image from X-ray data.
https://www.gettysburg.edu/academic-programs/mathematics/faculty/
dglass@gettysburg.edu
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Cryptography, Coding Theory, and Curve Interpolation. The goal of cryptography is to use mathematics to communicate secrets so that only the people you want to hear the information do in fact hear it. The goal of coding theory is to use mathematics to build redundancy into messages so that they can withstand errors that may occur in the transmission. While much of the mathematics used in these areas is extremely deep, major advancements in both of these areas have come from the simple fact that two points determine a unique line and some generalizations of this fact. In this talk, I will describe these applications of curve interpolation, and discuss broader ideas that come up in the modern theory of communications.
Elliptic Curves and Poncelet's Porism. Elliptic Curves have great interest to mathematicians for a variety of reasons, ranging from cryptography to the proof of Fermat's Last Theorem. In this talk, I will introduce the concept of elliptic curves, talk about some of their properties, and then show a modern proof of the classical result known as Poncelet's Porism, which uses Elliptic Curves in a surprising way.
Arithmetical Structures on Graphs. In this talk, we will introduce the notion of an arithmetical structure on a finite connected graph. These structures were defined by Dino Lorenzini in order to answer some questions in algebraic geometry and have deep structure, but in this talk we will discuss how they can be described only in terms of elementary number theory and linear algebra, and how new results can be obtained with only a little bit of elementary school arithmetic and a lot of doodling. One goal is to count how many different structures one can place on a given graph as well as discuss finite abelian groups that are associated to arithmetical structures. We will fully answer this question for some families of graphs, and discuss why it is a hard but interesting question for other families.
https://montalto.psu.edu/person/kira-hamman
khh11@psu.edu
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Mathematics and Democracy. An overview of the mathematics behind voting methods, apportionment, and/or weighted voting, with an emphasis on applications to the United States. Appropriate for a general, non-mathematical audience.
To Infinity and Beyond! A layperson's introduction to infinite numbers, in which the audience goes to hell and back several times over.
Foundations. The story of the foundational crisis and the search for solid philosophical foundations for all of mathematics. The story of madness, murder, mayhem, and mathematics! Well, maybe not murder. Appropriate for any audience, although mathematical audiences who are not familiar with the story tend to enjoy it most.
http://www.math.drexel.edu/~ahicks/
ahicks@math.drexel.edu
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Controlling Ray Bundles with Reflectors. How does one design a driver side mirror without a blind spot that does not distort the image? This is essentially the fundamental problem of optical design, which is to guide a given collection of light rays to some prescribed target points on a surface via a family of optical components, such as mirrors and lenses. We consider the problem of performing this task for a single 2-parameter ray bundle as typically is generated by a single source, show that a single reflector is not adequate to solve the problem, and give estimates on how bad the situation can. We will describe applications, including a driver-side mirror with no the blind spot problem and mirrors designed for panoramic imaging. Prototypes will be available for inspection.
https://sites.lafayette.edu/mcmahone/
mcmahone@lafayette.edu
☑︎ Face-to-face presentation
☒ No online presentations
The Joy of SET: Mathematics in a Game. The card game SET is played with a special deck of 81 cards. There is quite a lot of mathematics that can be explored using the game; understanding that mathematics enhances our appreciation for the game, and the game enhances our appreciation for the mathematics! We can look at questions in combinatorics, probability, linear algebra, and especially geometry. The deck is an excellent model for the finite affine geometry AG(4,3) and provides an entry to surprisingly beautiful structure theorems for that geometry. If you’d like some practice before the talk, go to www.setgame.com for the rules and a Daily Puzzle.
Geometry in the Game of SET. The deck of cards for the game of SET is an excellent model for the finite affine geometry AG(4,3); the visualization that the game provides allows us to explore the structure of that geometry. In this talk, we’ll explore AG(4,3), focusing on the collections of cards that have no sets (called maximal caps). Contained within each maximal cap is a road map that leads us to surprisingly beautiful combinatorial structure theorems. There’s a wonderful connection to the outer automorphisms of S6 as well, but you don’t need to know what those are to follow the talk.
Deconstructing the SET Daily Puzzle. The SET Daily Puzzle appears on the SET website https://www.setgame.com/set/puzzle. The puzzle consists of 12 cards that contain exactly six sets; the goal is to find all the sets (as quickly as possible). After playing the puzzle for a while, you may begin to notice some interesting things. Some cards may not appear in any of the sets. What is the largest number of cards that could never get used? What is the largest number of sets one card can be in? How many different card-set incidence structures are possible? Can we use the information we find to understand how the puzzle might be constructed? At present, many of our questions require computer simulations to answer, and the hope is to find direct proofs.
https://webspace.ship.edu/msrenault/
msrenault@ship.edu
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Infinity: It’s Really, Really Big. In this talk we’ll consider some common notions of infinity, and see how mathematicians and philosophers have attempted to understand it. We’ll look at some of the ideas of Georg Cantor (1845-1918), the first mathematician to put the infinite on a solid foundation, and we’ll see that there are in fact different “levels” of infinity!
https://divisbyzero.com/
richesod@dickinson.edu
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Tales of Impossibility—On the Problems of Antiquity
A Romance of Many (and Fractional) Dimensions—A History of Dimension
Euler’s Beautiful Polyhedron Formula
https://www1.villanova.edu/university/liberal-arts-sciences/programs/mathematics-statistics/faculty.html
robert.styer@villanova.edu
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Bouncing balls, Jenga blocks, and infinity. If a ball bounces an infinite number of times, will it bounce an infinite amount of time? We use some elementary physics of a bouncing ball to lead to geometric series. Next, can you pile up Jenga blocks so the top one overhangs the bottom one? Some elementary physics leads to the harmonic series. Along the way we enjoy some paradoxes of calculating with infinite series.
Why I became a mathematician. My seventh-grade math teacher introduced us to the abstract concepts of commutativity, associativity, and the like. The ability to reduce previously arbitrary manipulations to a small list of fundamental principles excited me. We will look at a hard problem, translate it to the geometric context of elliptic curves, then see how my seventh-grade introduction to commutativity applies to elliptic curves. We conclude by briefly indicating why elliptic curves are useful in cryptography.
https://www1.villanova.edu/university/liberal-arts-sciences/programs/mathematics-statistics/faculty.html
klaus.volpert@villanova.edu
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Math and Magic of Financial Derivatives (This talk can be tailored to any level.) Are Financial Derivatives the "Engine of the Economy," as declared by Alan Greenspan, or "Weapons of Mass Destruction," as Warren Buffett views them? Over the last 30 years, financial derivatives have overtaken stocks and bonds as the investment vehicle of choice for many large investors. Derivatives are often behind the spectacular profits of investment banks as well as the mind-boggling losses (e.g. at Citigroup) that we read about in the papers. While CEO’s and hedge fund managers profit handsomely when things are going well, the losses are mostly born by shareholders and small investors. Pension funds, even school districts and townships have suffered from disastrous deals in derivatives. It is therefore no exaggeration to say that taxpayers and investors can no longer afford to not understand derivatives. So what are derivatives? Simply put, they are contracts between two parties that stipulate some cash flow over a certain period of time. The size of that cash flow depends on what happens to some underlying asset, such as a stock prices, interest rates, currency exchange rates or commodity prices. The uncertainty in the development of the underlying creates the key difficulty, which is to properly evaluate the price and the risk inherent in a derivative. In this talk I will give an overview of the three main methods to price derivatives and discuss the advantages and short-comings of each method:
The analytic method by Black and Scholes, based on PDE’s
The discrete approach by Cox-Ross-Rubinstein, based on binomial trees.
Monte-Carlo Methods, which average information obtained from simulating a large number of random walks of the underlying.
The Mathematics of Income Inequality. (This talk will be accessible to all with some knowledge of calculus.) The Gini-Index based on Lorenz Curves of income distributions has long been used to measure income inequality in societies. This single-valued index has the advantage of allowing comparisons among countries and within one country over time. However, being a summary measure, it does not distinguish between intersecting Lorenz curves, and may not detect certain sociological and economic trends over time. We will discuss a new two-parameter model for the Lorenz curves. We will present theoretical and empirical evidence for this model, discuss its mathematical properties, and its potential to discern hidden trends.