All talks are at 4:15 in HH229 HH-231 unless otherwise noted. (Please note the time change from previous semesters!)
To volunteer to give a talk, or for anything else regarding the seminar contact Don Brower.
Date | Speaker | Title |
---|---|---|
Monday, September 10 | Prof. Jeff Diller | Newton's Method and complex dynamical systems |
Monday, September 24 | Stacy Hoehn | The Method of Infinite Repetition in Topology |
Monday, October 15 |
Tom Edgar | Wyld Weyl and Twisted Bruhat |
Monday, October 29 | Jon Hauenstein | Homotopy continuation and intersecting algebraic sets without defining equations |
Monday, November 12 | Sara Quinn | A tour of computable structure theory |
Monday, November 26 | Tanya Salyers | Coupled Oscillators and Biological Synchronization |
Monday, December 10 | Fernando Galaz-Garcia | Riemannian geometry via symmetries |
Monday, January 21 | Daniel Cibotaru | Cohomology of the unitary groups and Morse Theory |
Monday, February 4 | Logan Axon | A Short Tour of Algorithmic Randomness |
Monday, February 18 | Stuart Ambler | A Brief Look at the Dirac Equation of Physics |
Monday, March 10 | Steven Broad | Umbilics and Loewner's Conjecture |
Monday, March 31 |
Chrissy Maher | Math Games People Play |
Monday, April 14 |
Angie Kohlhaas | Pictures of Commutative Algebra |
Monday, April 28 |
Sarah Cotter | Goodstein's Theorem and other abstract nonsense | Goodstein’s Theorem and Incompleteness |
At night, in certain parts of southeast Asia, thousands of male fireflies gather in trees at night and flash on and off in unison in an attempt to attract the females that cruise overhead. When the males arrive at dusk, their flickerings are uncoordinated. As the night deepens, pockets of synchrony begin to emerge and grow. Eventually whole trees pulsate in a silent, hypnotic concert that continues for hours.
Fireflies are the epitome of a "pulse-coupled" oscillator system: they interact only when one sees the sudden flash of another and shifts its rhythm accordingly. Pulse coupling is awkward to handle mathematically because it introduces discontinuous behavior into an otherwise continuous model. In this talk, I will discuss the emergence of synchrony in a population of pulse-coupled oscillators and explain what it tells us about fireflies.
Combining computablility theoretic ideas and measure allows us to identify a collection of ``random'' binary sequences.``Random'' because they are unpredictable, incompressible, and effectively average. The digits of any one random sequence behave pretty much as a sequence of independent identically distributed random variables (taking values 0 or 1).
Effective randomness has been extended to the space of continuous functions on the real interval, a probability space under the Wiener measure. A sequence of random variables taking values 0 or 1 determines a random walk. Taking a random sequence (random as above) determines a sequence of random walks. Limits of random walks have a well established connection with the Wiener measure so it is no surprise that random sequences correspond with ``random'' functions.
Recently some effort has been made to extend algorithmic randomness to the space of closed subsets of $2^{\mathbb{N}}$. Early efforts seemed unnatural and unsatisfying to some. Recently I have been trying to fit that work into the framework of probability theory for this space.
Quoting Wikipedia, "In physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928" that "provides a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity. The equation demands the existence of antiparticles and actually predated their experimental discovery, making the discovery of the positron, the antiparticle of the electron, one of the greatest triumphs of modern theoretical physics."
This talk will explain, using math mostly understandable by engineering undergraduates who learned what they should have in multivariable calculus and linear algebra and differential equations, and with only a few references to physics, how the use of things called spinors allowed Dirac to take the square root of a second order differential operator, obtaining a first order operator, and his equation.