## Thomas Pietraho

Associate Professor of Mathematics

### Contact Information

tpietrah@bowdoin.edu

207-725-3568

Mathematics

Searles Science Building - 205

### Teaching this semester

### MATH 2301. Intermediate Linear Algebra

A continuation of Linear Algebra focused on the interplay of algebra and geometry as well as mathematical theory and its applications. Topics include matrix decompositions, eigenvalues and spectral theory, vector and Hilbert spaces, norms and low-rank approximations. Applications to biology, computer science, economics, and statistics, including artificial learning and pattern recognition, principal component analysis, and stochastic systems. Course and laboratory work balanced between theory and application.

### MATH 3603. Advanced Analysis

Measure theory and integration with applications to probability and mathematical finance. Topics include Lebesgue measure and integral, measurable functions and random variables, convergence theorems, analysis of random processes including random walks and Brownian motion, and the Ito integral.

### Education

- B.A. and M.S., University of Chicago
- Ph.D., Massachusetts Institute of Technology

### Research Interests

- Representation theory of reductive Lie groups, geometric quantization, and the combinatorics of representation theory.

### Publications

Drafts of and links to the following articles are available on my personal web page.

- Orbital Varieties and Unipotent Representations of Classical Semisimple Lie Groups, PhD Thesis, MIT.
- Components of the Springer Fiber and Domino Tableaux,
*Journal of Algebra*, 272 (2):711-729, 2004. arXiv:math.RT/0210416 - A Relation for Domino Robinson-Schensted Algorithms,
*Annals of Combinatorics*, 13 (4):519-532, 2010. arXiv:math.CO/0603654. - Orbital Varieties and Unipotent Representations Attached to Spherical Orbits, arXiv:math.RT/0603685
- Cells in the Weyl Groups of type B(n),
*Journal of Algebraic Combinatorics*, 27(2):247-262, 2008. arXiv:math/0607231 - Cells and Constructible Representations in Type B,
*New York Journal of Mathematics*14:411-430, 2008. arXiv: 0710.3846 - Knuth Relations for the Hyperoctahedral Groups,
*Journal of Algebraic Combinatorics*, 29(4):509-535, 2009. - Module Structure of Cells in Unequal Parameter Hecke Algebras, Nagoya Mathematical Journal, 198(2010). arXiv:0902.1907
- Sign under the domino Robinson-Schensted maps, Annals of Combinatorics 18 (2014). arXiv:1301.1356.
- On the Sign Representations for the Complex Reflection Groups G(r,p,n) (with A. Mbirika and W. Silver), arXiv:1303.5021.