Algebra Seminar
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Tue, 17/01/2012 17:00 |
Professor S Gurevich (Wisconsin) |
Algebra Seminar  |
L2 |
| In the digital radar problem we design a function (waveform) S(t) in the Hilbert space H=C(Z/p) of complex valued functions on Z/p={0,...,p-1}, the integers modulo a prime number p>>0. We transmit the function S(t) using the radar to the object that we want to detect. The wave S(t) hits the object, and is reflected back via the echo wave R(t) in H, which has the form R(t) = exp{2πiωt/p}⋅S(t+τ) + W(t), where W(t) in H is a white noise, and τ,ω in ℤ/p, encode the distance from, and velocity of, the object. Problem (digital radar problem) Extract τ,ω from R and S. I first introduce the classical matched filter (MF) algorithm that suggests the 'traditional' way (using fast Fourier transform) to solve the digital radar problem in order of p^2⋅log(p) operations. I will then explain how to use techniques from group representation theory to design (construct) waveforms S(t) which enable us to introduce a fast matched filter (FMF) algorithm, that we call the "flag algorithm", which solves the digital radar problem in a much faster way of order of p⋅log(p) operations. I will demonstrate additional applications to mobile communication, and global positioning system (GPS). This is a joint work with A. Fish (Math, Madison), R. Hadani (Math, Austin), A. Sayeed (Electrical Engineering, Madison), and O. Schwartz (Electrical Engineering and Computer Science, Berkeley). | |||
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Tue, 24/01/2012 17:00 |
Professor Peter Kropholler (Glasgow) |
Algebra Seminar |
L2 |
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Tue, 31/01/2012 17:00 |
Professor Martin Bridson (Oxford) |
Algebra Seminar |
L2 |
| In this talk I'll describe recent work with Henry Wilton (UCL) in which we prove that there does not exist an algorithm that can determine which finitely presented groups have a non-trivial finite quotient. | |||
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Tue, 07/02/2012 17:00 |
Professor Leo Curry (Tel Aviv) |
Algebra Seminar |
L2 |
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Tue, 28/02/2012 17:00 |
Ashot Minasyan (University of Southampton) |
Algebra Seminar |
L2 |
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Graph products of groups naturally generalize direct and free products and have a rich subgroup structure. Basic examples of graph products are right angled Coxeter and Artin groups. I will discuss various forms of Tits Alternative for subgroups and |
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Tue, 06/03/2012 17:00 |
Dr Kobi Kremnitzer (Oxford) |
Algebra Seminar |
L2 |
| By recent work of Voevodsky and others, type theories are now considered as a candidate for a homotopical foundations of mathematics. I will explain what are type theories using the language of (essentially) algebraic theories. This shows that type theories are in the same "family" of algebraic concepts such as groups and categories. I will also explain what is homotopic in (intensional) type theories. | |||
