"Can You Hear the Shape of a Drum?" - SURIM 2012



This webpage will serve as a reference to those students taking part in the "Can You Hear the Shape of a Drum?" project for SURIM in the summer of 2012. All group meetings and references will be listed here throughout the summer. Contact info for the graduate mentors is listed below. The main webpage for SURIM is here.


Graduate Mentors
NAME
OFFICE
EMAIL
Chris Henderson
380N
chris
Seungki Kim
380H
seungki
Sam Lichtenstein
381N
saml
Khoa Nguyen
380U1
khoan

Notice, all emails above are of the form "local @ domain" where "local" is given above and "domain" is math.stanford.edu. Because of limited space, for lectures, meet in the "On-Call" mentor's office at the posted time.


SURIM 2011 SCHEDULE
Monday Tuesday Wednesday Thursday Friday
Week 1
June 25		 SURIM:
Welcome: 9:30 am 381T
DRUM:
Group Meeting (after)
Lecture (after): Intro
On-Call: Khoa 		SURIM:
NA
DRUM:
On-Call: Khoa
Lecture: 11am
Measure and Integration 		SURIM:
Venkatesh: 11am 383N
DRUM:
On-Call: Seungki
Lecture: 1pm
Hilbert Spaces 		SURIM:
NA
DRUM:
On-Call:Khoa 		SURIM:
Brian Thomas
Mentor/Mentee
11am 383N
DRUM:
On-Call: Khoa
Lecture: 1pm, 381T
Fourier Series/Transform
Week 2
July 2nd		 SURIM:
NA
DRUM:
Lecture: 11am
Banach Spaces and
(Un)Bounded Operators
On-Call: Chris
CHRIS'S BDAY 		SURIM:
NA
DRUM:
On-Call: Chris 		Happy 4th! SURIM:
Msoer: 11am 383N
Effective Presentation
DRUM:
On-Call: Seungki
Lecture: 1:30pm 381T
Compact Operators
and Spectral Theory 		SURIM:
NA
DRUM:
On-Call: Chris
Lecture: 11am 381T
Analytic Prop.
of the Spectrum
Week 3
July 9		 SURIM:
NA
DRUM:
Lecture: 1pm
Spectral Theory for
the Laplacian
On-Call: Sam 		SURIM:
R: IO and Functions
12 am Sequoia 200
DRUM:
On-Call: Chris 		SURIM:
Conrad: 11am 383N
Geometry of Numbers
DRUM:
On-Call: Sam
Lecture: 1pm
Spectral Theory
of the Laplacian 		SURIM:
R: ggplot2
12 am Sequoia 200
DRUM:
On-Call: Seungki 		SURIM:
Weekly Group Meeting
Oral Prog. Reports
11am 383N
DRUM:
On-Call: Seungki
Lecture: 1 pm
Intro. to
Transplantation
Week 4
July 16		 SURIM:
NA
DRUM:
On Call: Chris
Lecture: Isospectral Graphs
11 am, 381U 		SURIM:
R: loops, apply
vectorization
12 pm Sequoia 200
DRUM:
On-Call: Seungki 		SURIM:
Michael Manapat
2 pm 281U
DRUM:
On-Call: Chris
MEETING! Discuss
future projects
All Mentors/students
need to attend!
11 am, 380N 		SURIM:
Intro to Latex
12 pm Sequoia 200
DRUM:
On-Call: Sam 		SURIM:
Weekly Group Meeting
Oral Prog. Reports
11am 383N
DRUM:
On-Call: Sam
Week 5
July 23		 SURIM:
NA
DRUM:
On Call: Chris
Group Meeting
11 am, 380N 		SURIM:
Latex:mathmode/ref
12 pm Sequoia 200
DRUM:
On-Call: Seungki 		SURIM:
Nancy Rodriguez
11 am 383N
DRUM:
On-Call: Sam 		SURIM:
Latex: Beamer
12 pm Sequoia 200
DRUM:
On-Call: Chris 		SURIM:
Weekly Group Meeting
Oral Prog. Reports
11am 383N
DRUM:
On-Call: Seungki
Week 6
July 30		 SURIM:
Brittany Erickson
11 am, 381T
DRUM:
On Call: Chris
Group Meeting
1 pm, 380N 		SURIM:
R: Batch submission
12 pm Sequoia 200
DRUM:
On-Call: Seungki 		SURIM:
NA
DRUM:
On-Call: Khoa 		SURIM:
Latex: Bib
12 pm Sequoia 200
DRUM:
On-Call: Chris 		SURIM:
Weekly Group Meeting
Oral Prog. Reports
11am 383N
DRUM:
On-Call: Khoa
Week 7
August 5		 SURIM:
NA
DRUM:
On Call: Chris
Group Meeting
1 pm, 380N 		SURIM:
R: Rpubs
12 pm Sequoia 200
DRUM:
On-Call: Seungki 		SURIM:
Dan Bump
11am 381T
DRUM:
On-Call: Khoa 		SURIM:
LaTeX: pre-ambles and
multi-file compiling
12 pm Sequoia 200
DRUM:
On-Call: Chris 		SURIM:
Weekly Group Meeting
Oral Prog. Reports
11am 383N
DRUM:
On-Call: Sam
Week 8
August 12		 SURIM:
Gunnar Carlsson
11 am, 381T
DRUM:
On Call: Chris
Group Meeting
1 pm, 380N 		SURIM:
R: making packages
12 pm Sequoia 200
DRUM:
On-Call: Seungki 		SURIM:
NA
DRUM:
On-Call: Khoa 		SURIM:
NA
DRUM:
On-Call: Sam 		SURIM:
Final Presentations
All Day
DRUM:
On-Call: Everyone!



References
TOPIC
AUTHOR(S)
TITLE
Computational
Levitin, Parnovski, Polterovich
Isospectral Domains With Mixed Boundary Conditions
General
Giraud, Thas
Hearing Shapes of Drums - Mathematical and Physical Aspects of Isospectrality
General
Graduate mentors
Project Description
General
Kac
Can One Hear The Shape of a Drum?
General
Protter
Can One Hear The Shape of a Drum? revisited
Isospectral Graphs
Biyikoglu, Leydold, Stadler
Laplacian Eignvectors of Graphs: Perron Frobenius and Faber-Krahn Type Theorems
Isospectral Graphs
Shlapentokh-Rothman
An Asymptotic Faber-Krahn Inequality for the Laplacian on Z^2
Real Analysis
Folland
Real Analysis: Modern Techniques and Their Applications
Real Analysis
Loomis, Sternber
Advanced Calculus
Real Analysis
Melrose
Introduction to Functional Analysis
Real Analysis
Rudin
Real and Complex Analysis, Principles of Mathematical Analysis
Real Analysis
Shakarchi, Stein
Any book of theirs but "Complex Analysis"
Real Analysis
Sternberg
Theory of Functions of a Real Variable
Spectral Theory
Kowalski
Spectral Theory in Hilbert Spaces
Spectral Theory
Saito
Laplacian Eigenfunctions: Theory, Applications, and Computations
Transplantation
Buser, Doyle, Conway, Semmler
Some Planar Isospectral Domains
Transplantation
Giraud, Thas
See above
Transplantation
Levitin, Parnovski, Polterovich
See above