personal presentation - university of marylandide/data/teaching/amsc663/14fall/a… · personal...
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Personal
PresentationYIRAN LI
APPLIED MATH, STATISTICS AND SCIENTIFIC COMPUTING
SEP. 18, 2014
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Hometown
Jinan, Shandong China
The Spring City
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Hometown of Confucius
and people like to drink from spring
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Interests and hobbies
Travel
Playing the piano
Some sports
movies and animes
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Favorite Composers
Wolfgang Amadeus Mozart
Ludwig van Beethoven
Claude Debussy
Maurice Ravel
Frédéric Chopin
Johannes Brahms
Yoko Kanno
Joe Hisaishi
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Education
University of Miami 2009-2010 Mathematics,
Economics
Bachelors, Cornell University 2011-2013
Mathematics, Economics
Had a culture/weather shock
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Research Experience
Summer REU, Cornell University 2012 with
Professor Robert S. Strichartz
Hodge-de Rham Theory of K-Forms on Carpet
Type Fractals
Summer Research, University of Maryland 2014
with Professor Maria Cameron
Separation of data sets using Principle
Component Analysis and Stochastic Processes
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Sierpinski Carpet Define real valued functions on 0 forms (vertex), 1 forms (edges) and
2 forms (squares)
Vector spaces of functions of 0, 1, 2 forms
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The Magic Carpet
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Definition of Laplacian on Graphs
and more
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Programmed to calculate eigenvalues
and eigenfunctions of laplacians on 0, 1, 2
forms
Visualized and calculated numerically the
convergence of eigenfunctions when go
into upper level
Found evidence in support for Hodge De
Rham Theory on Fractals (Seirpinski Carpet
and Magic Carpet)
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Weyl ratio of eigenvalues of SC 0
forms
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Eigenfunctions of 0 forms and 2 forms on
Seirpinski Carpet
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Eigenfunctions of 0 forms and 2 forms on
Magic Carpet
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Data Separation method using
markov chains and PCA
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3D Version