Geneseo Mathematics Colloquium Schedule
Thursday, January 29, 5:00-5:50pm
Tom Tucker, University of Rochester
Solutions to polynomials in two variables
You may remember the quadratic formula for finding solutions to quadratic polynomials in one variable. It is natural to ask: Are there formulas like this for polynomials of higher degree? The answer, roughly speaking, is yes. Going further, one might ask: What about polynomials in more than one variable? Here, the answer is far more complicated, and involves geometry in what may seem a surprising way. One famous example of this type of polynomial equation is the Fermat equation xn + yn = zn.
Thursday, February 5, 2:30-3:20pm
Chris Leary, SUNY Geneseo
Axioms, Models, Infinity, and the Nature of the Universe
Starting from The Elements of Euclid, we discuss the role of logic and set theory in our understanding of mathematics. With a quick trip through some of the most fundamental mathematical results of the 19th and 20th centuries, we end in the 21st, where current research in set theory may decide the truth of the Continuum Hypothesis.
Thursday, February 19
Zubair Dawood, Quantitative Strategies Group at Manning & Napier (SUNY Geneseo, Class of 2012)
Mathematical Methods in Equity Research
At first glance, financial markets are mind-numbingly complex. However, at the root, what is going on is fairly straightforward. The purpose of this talk is to depict the statistical modeling techniques, mathematical methods, and the analytical tools utilized to gain a deeper understanding of the drivers of economic activity, financial markets, and companies' performance in order to generate reasonable investment returns. Mathematical methods taught at the undergraduate level go a long way in lifting the veil on the complexity of financial markets.
Monday, February 23, 4:00-4:50pm
David Dickerson, SUNY Cortland
Mathematics Majors’ Understandings of the Concept of Mathematical Definition
Two qualitative studies of undergraduate mathematics majors examined students’ abilities to write, select, and use mathematical definitions. Findings include that students at the advanced level of undergraduate mathematical study often have difficulty creating definitions that conform to their concept images, and have a fragile understanding of the structure of mathematical knowledge. Further they are likely to argue directly from their concept images rather than from the definitions but are less likely to do so when they supply their own definitions for concepts. The results of this study have implications for college-level mathematics instruction.
Monday, March 2, 4:00-4:50pm
Jonathan Pakianathan, University of Rochester
An Elementary Construction of Tessellated Surfaces
In this talk, we will give an elementary outline of some of the classical work on polyhedra, the classification of surfaces, and the theory of tessellation patterns on surfaces. Given a tessellated surface, a group arises as its symmetry group. We will talk about the converse: given a group, we will explain how to construct a family of tessellated surfaces.
Monday, March 30, 4:00-4:50pm
Julie Croteau, Corning Community College (SUNY Geneseo, Class of 1997)
A fun example of mathematics was discovered after visiting the Fitness Center at Corning CC. This short talk will explore how much someone is really lifting at the gym on the circuit machines via some basic relationships. You may be lifting more (or less) than you think!
After sharing this example, the speaker will discuss her career path since graduating from SUNY Geneseo in 1997.
Monday, April 13, 4:00-4:50pm
Quantum Messages and Quantum Games
What's the shortest message you can send someone? It might seem like the answer is a single bit: a 0 or a 1. But the world is much stranger than that! We can also send quantum bits (or qubits) that can be 0 or 1 or even both 0 and 1 at the same time. These qubits can also be "entangled" with each other, a phenomenon Einstein called "spooky action at a distance". I'll say how these strange quantum messages can be described using straight-forward linear algebra: vectors and matrices. I'll discuss the surprising power of using quantum messages for computing and sending information, and how we can better understand quantum information by studying games that use quantum messages instead of classical ones.
Monday, April 20, 3:30-4:30pm
Silvia Saccon, University of Texas at Dallas
Are Modules Unique?
Integers enjoy a key property: By the Fundamental Theorem of Arithmetic, every nonzero integer can be factored uniquely into a product of primes. What can we say about "factorizations" in other algebraic structures? Does uniqueness always hold? We investigate these questions in the land of rings and modules, and discover some surprising results.