Computer Science

The dichotomy between sparse and dense structures is one of the profound, yet fuzzy, features of contemporary mathematics and computer science. We present a framework for this phenomenon, which equivalently defines sparsity and density of structures in many different yet equivalent forms, including effective decomposition properties. This has several applications to model theory, algorithm design and, more recently, to structural limits.

Abstract: We all Google. You may even have found this talk by Googling. What you may not know is that behind the Google's and other search engines is beautiful and elegant mathematics. In this talk, I will try to explain the workings of page ranking and search engines using only rusty calculus.

Bio: Dr. Margot Gerritsen is the Director of the Institute for Computational and Mathematical Engineering at Stanford University. She is also the chair of the SIAM Activity group in Geoscience, the co-director and founder of the Stanford Center of Excellence for Computational Algorithms in Digital Stewardship, and the director of Stanford Yacht Research. She has been appointed to several prestigious positions, including Magne Espedal Professorship at Bergen University, Aldo Leopold Fellow, Faculty Research Fellow at the Clayman Institute and she is also a Stanford Fellow. She is the editor of the Journal of Small Craft Technology and an associate editor of Transport in Porous Media. We are delighted to have Dr. Gerritsen participate in the Mathematics of Planet Earth series.

In the 1940s Alan Turing’s homosexuality was an open secret amongst his co-workers at Bletchley Park. In 1952 the secret became widely known when Turing was arrested on charges of “gross indecency” under the same 1885 law that had led to the imprisonment of Oscar Wilde over half a century earlier. Opting for chemical “treatment” of his “condition” rather than imprisonment, Turing was one of many well-known casualties of a heightened drive against homosexuality in a postwar Britain that drew the line between the normal and the deviant more sharply than ever before. In his talk, Chris Waters will discuss Turing’s sexual proclivities and their meanings in the context of his times, focusing in particular on his arrest and subsequent fate in the context of the sexual politics of the first half of the 1950s. In addition, he will discuss the shaping of Turing’s posthumous reputation, beginning with the attempts made by the Gay Liberation Front in the 1970s to render Turing the gay icon he has become today.

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.