MATH 297:
Analysis and Probability on Fractals
- Spring 2007

   Alexander Teplyaev

    office: MSB M222
    office hours:   MWF 10-11
    phone: (860)486-3206

course time and room:
officially 9:00-9:50am MWF MSB117
the time can be changed if needed

course web page:


Published papers:

Neil Bajorin, Tao Chen, Alon Dagan, Catherine Emmons, Mona Hussein, Michael Khalil, Poorak Mody, Benjamin Steinhurst, Alexander Teplyaev
Vibration modes of 3n-gaskets and other fractals J. Phys. A: Math. Theor. 41 (2008) 015101 (21pp). pdf file
Vibration Spectra of Finitely Ramified, Symmetric Fractals Fractals 16 (2008), 243--258. pdf file
project web page
older preprint in the Isaac Newton Institute Preprint Series
Mathematica notebooks for the project

More info and other projects:
Fractals web page


Differential Equations on Fractals: A Tutorial by Robert Strichartz
Publisher: Princeton University Press
ISBN: 069112731X

Course description

The course is an introduction to analysis on fractals. This subject can involve such diverse topics as analysis, probability, differential equations, linear algebra, electrical networks etc. It gives a good opportunity to show how different areas of mathematics are combined together to form a unified theory. The exposition is going to be down to earth and require little background beyond the basic courses. Some relevant fractal pictures and applets can be found at

There will be a choice of projects of various types and difficulty, which can be purely theoretical or involve computers. The course itself will be organized to provide background for the chosen projects. The exact format will be determined with the input of the participants. When this course was offered before, the projects resulted in two papers with students as co-authors:

Taking part in a research project like this may be very useful in the future (for instance, when applying to graduate schools). The course satisfies departmental requirements for the math major and minor.