Personal
PresentationYIRAN LI
APPLIED MATH, STATISTICS AND SCIENTIFIC COMPUTING
SEP. 18, 2014
Hometown
Jinan, Shandong China
The Spring City
Hometown of Confucius
and people like to drink from spring
Interests and hobbies
Travel
Playing the piano
Some sports
movies and animes
Favorite Composers
Wolfgang Amadeus Mozart
Ludwig van Beethoven
Claude Debussy
Maurice Ravel
Frédéric Chopin
Johannes Brahms
Yoko Kanno
Joe Hisaishi
Education
University of Miami 2009-2010 Mathematics,
Economics
Bachelors, Cornell University 2011-2013
Mathematics, Economics
Had a culture/weather shock
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
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
The Magic Carpet
Definition of Laplacian on Graphs
and more
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)
Weyl ratio of eigenvalues of SC 0
forms
Eigenfunctions of 0 forms and 2 forms on
Seirpinski Carpet
Eigenfunctions of 0 forms and 2 forms on
Magic Carpet
Data Separation method using
markov chains and PCA
3D Version