Xiao Xiao, Utica College
The Frobenius Problem
Let a, b, . . . , c be positive integers greater than 1 with no common factors. The Frobenius problem studies the largest non-negative integer g(a, b, . . . , c) that cannot be expressed as a non-negative linear combination of a, b, . . . , c. In this talk, I will review some of the old and not so old results of solving the Frobenius problem for g(a, b) and g(a, b, c). If time permits, I will also describe how a closed formula of g(a, b, c) in a special case can be used to solve problems in the classification of F-crystals over algebraically closed field. This talk is accessible to undergraduates.
Thursday, October 11, 4:00 - 4:50pm
Sea battles, Benjamin Franklin's oil lamp, and jellybellies
"During our passage to Madeira, the weather being warm, and the cabbin windows constantly open for the benefit of the air, the candles at night flared and run very much, which was an inconvenience. At Madeira we got oil to burn, and with a common glass tumbler or beaker, slung in wire, and suspended to the ceiling of the cabbin, and a little wire hoop for the wick, furnish'd with corks to float on the oil, I made an Italian lamp, that gave us very good light...." (Benjamin Franklin, December 1, 1762 letter to John Pringle.)
Observations of real phenomena have led to mathematical modeling of surface water waves, interfacial waves, and Lagrangian coherent structures among other examples. This expository talk will provide a quick tour of the (mostly advanced undergraduate level) mathematics needed to describe idealized versions of the rings formed by striking a surface of water with a large object (like a bomb), the oil-water waves observed by Founding Father Benjamin Franklin on his voyage to Madeira, and the motion of nutrient laden water being swept into the underbelly of a swimming jellyfish.
Thursday, November 1, 4:00 - 4:50pm
Ron Taylor, Berry College
The Difference Between a Small Infinity and a Big Zero
Can two people have a different answer to the same question and both be right? Is there room for perspective in mathematics? Most often we find that any given mathematical question will have a single answer, though there are usually many different methods that can be used to find that answer. In this talk we will discuss the Cantor set, a remarkable object that seems to leave room for perspective to play a part in mathematics. Given time we will discuss generalized Cantor sets, a class of sets with interesting properties of size.
Thursday, November 8, 4:00 - 4:50pm
Emilie Weisner, Ithaca College
The mathematics of bead crochet
Creations in the fiber arts are often based in pattern and symmetry. Because of this, the fiber arts and mathematics are a natural pair. In this talk, I'll talk about some of the mathematics related to bead crochet. In particular, I'll discuss the work of Susan Goldstine and Ellie Baker, who use wallpaper groups to understand symmetries in bead crochet patterns. I'll also talk about work on additional mathematical aspects of bead crochet, being carried out by Ithaca College students Rachel Dell'Orto, Sam Reed, and Katie Sheena.
Wednesday, November 14, 2:30 - 3:45pm
Jeff Johannes & Gary Towsley, SUNY Geneseo
A Concise History of Calculus
A lively overview of over two thousand years of calculus history. Not only who-did-what along the way, but the cultural and sociological causes and effects of the calculus. Strongly recommended for anyone who has taken or is taking calculus.
Wednesday, November 28, 2:30 - 3:45pm
Ryan Gantner, St. John Fisher College
The Stochastic Voter Model
In this talk, the stochastic voter model will be introduced and we'll see how it works. After deriving some results about its long-term behavior, we'll turn to some examples of how it can be applied. Some examples include the spread of diseases, the evolution of zombie attacks, ... and elections! The talk will conclude with a simulation to predict the outcome of the 2016 presidential election.
Prerequisites: The major mathematical proof in this talk should be accessible to anyone who has had Calculus 2. All other aspects of the talk involve only intuitive aspects of probability, and should be accessible to all mathematically inclined students.