8 May 2012

17:00

8 May 2012

17:00

1 May 2012

17:00

Professor R. Marsh

Abstract

Finite reflection groups are often presented as Coxeter groups. We give a

presentation of finite crystallographic reflection group in terms of an

arbitrary seed in the corresponding cluster algebra of finite type for which

the Coxeter presentation is a special case. We interpret the presentation in

terms of companion bases in the associated root system. This is joint work with

Michael Barot (UNAM, Mexico)

24 April 2012

17:00

6 March 2012

17:00

Dr Kobi Kremnitzer

Abstract

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.

28 February 2012

17:00

Ashot Minasyan

Abstract

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

their stability under graph products. The talk will be based on a joint work with Yago Antolin Pichel.

7 February 2012

17:00

Professor Leo Curry

Abstract

31 January 2012

17:00

Professor Martin Bridson

Abstract

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.

24 January 2012

17:00

Professor Peter Kropholler

Abstract

17 January 2012

17:00

Professor S Gurevich

Abstract

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).