Difference between revisions of "NTS Spring 2012/Abstracts"

From UW-Math Wiki
Jump to: navigation, search
(February 2)
(February 2)
Line 13: Line 13:
 
|}                                                                         
 
|}                                                                         
 
</center>
 
</center>
 +
 +
== March 1 ==
  
 
<center>
 
<center>
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20"
 
|-
 
|-
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Evan Dummit''' (Madison)
+
| bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Shamgar Gurevich''' (Madison)
 
|-
 
|-
| bgcolor="#BCD2EE"  align="center" | Title: Kakeya sets over non-archimedean local rings
+
| bgcolor="#BCD2EE"  align="center" | Title: Computing the Matched Filter in Linear Time
 
|-
 
|-
 
| bgcolor="#BCD2EE"  |   
 
| bgcolor="#BCD2EE"  |   
Abstract: In a forthcoming paper with Marci Habliscek, we constructed a Kakeya set over the formal power series ring '''F'''<sub>''q''</sub><nowiki>[[</nowiki>''t''&thinsp;<nowiki>]]</nowiki>, answering a question posed by Ellenberg, Oberlin, and Tao. My talk will be devoted to explaining some of the older history of the Kakeya problem in analysis and the newer history of the Kakeya problem in combinatorics, including my joint work with Marci. In particular, I will give Dvir's solution of the Kakeya problem over finite fields, and explain the problem's extension to other classes of rings.  
+
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.  
 +
 
 +
In the lecture 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 and arithmetic 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).
 +
 
 +
The lecture is suitable for general math/engineering audience.
  
 
|}                                                                         
 
|}                                                                         

Revision as of 23:12, 26 January 2012

February 2

Evan Dummit (Madison)
Title: Kakeya sets over non-archimedean local rings

Abstract: In a forthcoming paper with Marci Habliscek, we constructed a Kakeya set over the formal power series ring Fq[[t ]], answering a question posed by Ellenberg, Oberlin, and Tao. My talk will be devoted to explaining some of the older history of the Kakeya problem in analysis and the newer history of the Kakeya problem in combinatorics, including my joint work with Marci. In particular, I will give Dvir's solution of the Kakeya problem over finite fields, and explain the problem's extension to other classes of rings.

March 1

Shamgar Gurevich (Madison)
Title: Computing the Matched Filter in Linear Time

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.

In the lecture 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 and arithmetic 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).

The lecture is suitable for general math/engineering audience.


March 29

David P. Roberts (U. Minnesota Morris)
Title: tba

Abstract: tba



April 12

Chenyan Wu (Minnesota)
Title: tba

Abstract: tba


April 19

Robert Guralnick (U. Southern California)
Title: tba

Abstract: tba


April 26

Frank Thorne (U. South Carolina)
Title: tba

Abstract: tba


May 3

Alina Cojocaru (U. Illinois at Chicago)
Title: tba

Abstract: tba


May 10

Samit Dasgupta (UC Santa Cruz)
Title: tba

Abstract: tba


Organizer contact information

Shamgar Gurevich

Robert Harron

Zev Klagsbrun

Melanie Matchett Wood



Return to the Number Theory Seminar Page

Return to the Algebra Group Page