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The Line Packing Problem by Tin Tran from FIU

This is a past event.

Friday, April 1 at 4:00pm to 5:00pm

DM - Deuxieme Maison, 409A
11200 SW 8th ST 33199, Deuxieme Maison, Miami, Florida 33199

Please join us remotely

Abstract: How can we arrange m lines through the origin in a finite dimensional space F n (F = R or C) in a way that maximizes the minumum angle between pairs of lines? This problem is known as the line packing problem and is one of the most studied problems in applied mathematics. It has numerous applications to quantum information theory, coding theory, wireless communications, and compressive sensing. It also impacts a number of fundamental areas of mathematics including spherical codes, spherical designs, equiangular line sets, equilateral point sets, and strongly regular graphs. If we identify each line with a unit vector spanning the line, then the problem is equivalent to finding a set of unit vectors X = {xi} m i=1 in F n of minimal coherence:= maxi̸=j |⟨xi , xj ⟩|. In this talk, we will present some fundamental results on the problem in the language of frame theory. In the first part, we will introduce some lower bounds on the coherence: the simplex bound and the orthoplex bound. These bounds play a crucial role in constructive solutions of the problem. In the second part, we will give some our recent results to the problem. Several open questions are also presented.

Graduate students are encouraged to attend! 

Dial-In Information

Join Zoom Meeting

https://fiu.zoom.us/j/93053884755?pwd=NWwyMTRBYlF2R29aVDVvdDR6VzU5QT09

 

Meeting ID: 930 5388 4755

Passcode: AAM2022

Event Type

Academics, Lectures & conferences

Audience

Students, Faculty & Staff

Tags

APPLIED MATHEMATICS

Department
Department of Mathematics and Statistics
Hashtag

#GRADUATE STUDENTS

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