DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:** G. Scott Cochran, Mathematics, George Mason University

**Title: ***
Homology Computations of Nodal Domains - Error Estimates, Validation, and Applications
*

**Abstract:**
Pattern formation occurs throughout the natural sciences. Often, these patterns occur as certain nodal domains of certain functions. We can use algebraic topology and in particular homology to investigate coarse topological features of the nodal domains. However, usually we do not have direct access to the nodal domains either through discrete sampling or the patterns are experimentally determined. In either case, we cannot know if the computed homology is correct. I will present results that establish explicit probability bounds for making the correct homology computations for nodal domains of random fields in one and two spatial dimensions. I will also present a modified algorithm that guarantees we compute the correct homology. Lastly, I will present applications of these results.

**Time:** Friday, Feb. 11, 2011, 1:30-2:30 p.m.

**Place:** Science and Tech I, Room 242

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491