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