Scientific

This triplet of introductory lectures summarizes a few of the most basic biochemical models with the simple rate equations that they satisfy. I describe production-decay, with Michaelis-Menten and sigmoidal terms, showing how the latter can lead to bistable behaviour and hysteresis. I describe two bistable genetic circuits: the toggle switch by Gardner et al (2000) Nature 403, and the phage-lambda gene by Hasty et al (2000) PNAs 97. The idea of bifurcations is discussed. Finally, I introduce
phosphorylation cycles, and show that sharp responses can arise when the enzymes responsible (kinase and phosphatase) operate near saturation. (This is the so called Goldbeter-Koshland ultrasensitivity).

• Cell biology imaging techniques
  • 1. Introduction: Basic optics | Phase contrast | DIC | Mechanism of fluorescence | Fluorophores
  • 2. Fluorescence microscopy: Fluorescent labelling biological samples |
    Epifluorescence microscopy |
    Confocal fluorescence microscopy
  • 3. Advanced techniques: FRAP | FRET | TIRF | Super-resolution imaging
    (time permitting)
  • 4. FRAP data and modelling integrin dynamics

Central to Alan Turing's posthumous reputation is his work with British codebreaking during the Second World War. This relationship is not well understood, largely because it stands on the intersection of two technical fields, mathematics and cryptology, the second of which also has been shrouded by secrecy. This lecture will assess this relationship from an historical cryptological perspective. It treats the mathematization and mechanization of cryptology between 1920-50 as international phenomena. It assesses Turing's role in one important phase of this process, British work at Bletchley Park in developing cryptanalytical machines for use against Enigma in 1940-41. It focuses on also his interest in and work with cryptographic machines between 1942-46, and concludes that work with them served as a seed bed for the development of his thinking about computers.

Turing 2012 - Calgary

This talk is part of a series celebrating the Alan Turing Centenary in Calgary. The following mathtube videos are part of this series

1. Alan Turing and the Decision Problem, Richard Zach.
2. Turing's Real Machine, Michael R. Williams.
3. Alan Turing and Enigma, John R. Ferris.

Many scientific questions are considered solved to the best possible degree when we have a method for computing a solution. This is especially true in mathematics and those areas of science in which phenomena can be described mathematically: one only has to think of the methods of symbolic algebra in order to solve equations, or laws of physics which allow one to calculate unknown quantities from known measurements. The crowning achievement of mathematics would thus be a systematic way to compute the solution to any mathematical problem. The hope that this was possible was perhaps first articulated by the 18th century mathematician-philosopher G. W. Leibniz. Advances in the foundations of mathematics in the early 20th century made it possible in the 1920s to first formulate the question of whether there is such a systematic way to find a solution to every mathematical problem. This became known as the decision problem, and it was considered a major open problem in the 1920s and 1930s. Alan Turing solved it in his first, groundbreaking paper "On computable numbers" (1936). In order to show that there cannot be a systematic computational procedure that solves every mathematical question, Turing had to provide a convincing analysis of what a computational procedure is. His abstract, mathematical model of computability is that of a Turing Machine. He showed that no Turing machine, and hence no computational procedure at all, could solve the Entscheidungsproblem.

Turing 2012 - Calgary

This talk is part of a series celebrating the Alan Turing Centenary in Calgary. The following mathtube videos are also part of this series

1. Alan Turing and the Decision Problem, Richard Zach.
2. Turing's Real Machine, Michael R. Williams.
3. Alan Turing and Enigma, John R. Ferris.

After reviewing ordinary finite-dimensional Morse theory, I will explain how Morse generalized Morse theory to loop spaces, and how Floer generalized it to gauge theory on a three-manifold. Then I will describe an analog of Floer cohomology with the gauge group taken to be a complex Lie group (rather than a compact group as assumed by Floer), and how this is expected to be related to the Jones polynomial of knots and Khovanov homology.