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Analysis Seminar on "Spatio-spectral limiting on Boolean cubes" by Joe Lakey (NMSU)

Event Type: 
Seminar
Speaker: 
Joe Lakey (New Mexico State University NMSU)
Event Date: 
Friday, April 30, 2021 -
3:00pm to 4:00pm
Location: 
Zoom Meeting ID: 937 6606 4787
Audience: 
General Public

Event Description: 

Title: Spatio-spectral limiting on Boolean cubes

Abstract: Boolean cubes are just Nth powers of the integers mod 2, thought of as graphs.

The composition of an operator that truncates to an interval around the origin and then to low frequencies was studied, on the real line, in the 1960s by mathematicians at Bell Labs. Its eigenvectors are so-called prolate spheroidal wave functions and its eigenvalues, remarkably, are close to one up to a parameter known as the time--bandwidth product, then decay rapidly to zero. Analogues of these operators were studied in finite and discrete settings, thought of as approximations of the continuous setting, and in Euclidean space, where eigenvalue decay is less remarkable.

Here we study instead what happens in higher dimensions of a very discrete setting: the integers mod 2. Specifically, we define and characterize eigenspaces of an analogue of the time- and band-limiting operator on Boolean cubes and outline techniques to compute these objects. Extensions to some other special graphs are also considered.

About the Speaker: Joe Lakey received his PhD in 1991 from the University of Maryland under the supervision of John Benedetto. He has worked at New Mexico State University since 1995, first as a faculty member in Mathematical Sciences, then head of Mathematical Sciences for 8 years (2010-2018). He has been an Associate Dean in the College of Arts and Sciences at NMSU since Summer 2018. Previously he held temporary positions at The University of Texas at Austin (1991-1994 and 2002-2003), working primarily with John Gilbert,  Texas A&M (1994-1995) and Washington University in St. Louis (2009-2010). His research is broadly in applied harmonic analysis, most recently focusing on aspects of spectral graph theory.  He has published over 60 papers and coauthored two books with Jeff Hogan. Joe Lakey is an 2013 Fellow of AMS, part of the Inaugural Class of Fellows. He has had support from multiple agencies (NSF, NIH, DARPA, SNL, LALN).  He has trained five PhD students and several MS students. Joe has organized many conferences, notably two CBMS conferences (featuring Terry Tao in 2005 and Anna Gilbert in 2017) and the NM Analysis Seminar first 12 editions, a joint venture with UNM (from 1998 till 2009 alternating between Albuquerque and Las Cruces).

Event Contact

Contact Name: María Cristina Pereyra

Contact Email: crisp@math.unm.edu