Gwyn Bellamy will show us that algebra isn't really hard - it's just pretty pictures sometimes. He'll tell us what quivers are and how they can be used to define algebras, and how seemingly simple questions can actually turn out to be quite tricky.
Antonella D'Avanzo will tell us what integrable systems are and why they are such good things. In particular we will look at Hamiltonian systems and the Lax equations. Slides to the talk can be found here.
Evgeni Ovcharov will give us an introduction to measure theory using important examples like the Cantor Set, and will tell us why Lebesgue integration is so much better than Riemann integration.
David Urminsky will talk about Hénon's work on the Lorentz attractor (an important example in chaos theory), and how these techniques can be put to use on studying a particular example of a 3-body problem in astronomy. His slides can be found here.
Rosemary Apple will teach us a bit of astronomy with lots of pretty pictures!
Enrique Covorrubias will talk about the Index theorem of Atiyah and Singer, which can help us explain why the Escher drawings are impossible.
Julia Collins will talk about how the techniques of knot theory can be used to give us information about how DNA works. Her slides can be found here.
Jiajia Cui will talk about the Goldbach Conjecture and how close we are to solving it.
Ewan Russell and Qiming Li will give us a biography of Hilbert and tell us about some of the 23 problems he posed in Paris in 1900.
Jan Hilmar will give this semester's final talk, about Gödel's Incompleteness Theorem and the ramifications for current mathematics.
Thomas Köppe will tell us about Poincaré, his famous conjecture and the controversy over the recent proof by Grigory Perelman. His slides can be found here.
Andrew Wilson will give us a brief introduction to Algebraic Geometry; in particular, rational varieties and how they can be used to take a new look at old problems such as Pythagoras' Theorem and the Fundamental Theorem of Algebra.
Mike Kowalski will give a layman's introduction to "Oscillatory Integral Operators and Sublevel Sets", focusing on how one object can provide estimates for the other.
Alberto Palomo-Lozano will discuss the question of whether there is a direct correlation between genius and insanity via quotes, pictures and anecdotes of famous mathematicians and scientists.
Jonathan Hogg will run through important events in mathematics from prehistoric times to the current day, with a special emphasis on Scottish mathematics.
Xi Yang will tell us about Operation Management.
Ewan Russell will tell us all about quantum algebras.
Yu Yuill tells us about how to find an optimal solution to the problem of how a company should deliver its goods most efficiently and within a specified time scale.
