# Mathematics

Martin Pergler received a Ph.D. in mathematics from the University of Chicago in 2000 (advisor: Robert Zimmer).

He previously obtained an S.M. in mathematics from the same university in 1994 and a B.Sc. Highest Honours in mathematics from Carleton University in Canada in 1993.

The information in this section is rather obsolete, but there were requests to repost it when I removed it in 2007, and so I am providing access as-is.

**Research/dissertation**

Research summary (2 pages) - my field was group actions on manifolds preserving geometric structures

2 papers presenting the results of my dissertation: Point stabilizers of connection-preserving actions and Epimorphic subgroups of SL(n), trees, and the Tits boundary

Words of wisdom to graduating Ph.D. students on timelines of finishing the degree

Unrelated to my core research, but some musings on Newton's method, Julia and Mandelbrot sets, and complex coloring which some others have since used in their work (Wegert and Semmler, "Phase Plots of Complex Functions: A Journey in Illustration", 2011)

**Teaching and expository writing**

Differentials, the Mean Value Theorem, and the Fundamental Theorem of Calculus

How mathematicians think, a short handout

**Math and music**

I am a clarinetist, recorder player, and singer (bass-baritone - chorister and soloist). I was an active serious amateur and freelancer in the 1990s, predating YouTube and streaming media and so not preserved for posterity online (a performance on NPR's Performance Today occasionally bubbles up in their archives, but doesn't have a consistent address).

However, I did apply maths to some questions of intonation and woodwind playing which appeared on a now-defunct acoustics/music e-journal: note and followup.