The wonderful Mathematical Genealogy Project lets one track mathematical ancestry (through PhD advisors). Below is one branch of my ancestry, with year and university of PhD if available. (Where there were two advisors, I don't take the path through the advisor in parenthesis.)

Boyle [University of Washington, 1983] - Lind [Stanford University, 1973]- Ornstein [University of Chicago, 1957] - Kaplansky [University of Chiago, 1941] - Saunders Mac Lane [Gottingen 1934] - Hermann Weyl [Gottingen, 1908] (and I. Paul Bernays) - Hilbert [Konigsberg 1885] - Lindemann [Nurnberg 1873] - Klein [Bonn 1868] - Plucker [Marburg 1823] (and Lipschitz) - Gerling [Gottingen 1812] - Gauss [Helmstedt 1799] - Pfaff [Gottingen 1786] - ...

The next generation:

My PhD students and their doctoral theses

Student Thesis title Year
Danrun Huang Flow equivalence of reducible shifts of finite type,
generalized inverses over Banach algebras
(jointly directed with S. Goldberg )
Nic Ormes Strong orbit realization for minimal homeomorphisms 1997
Sam Lightwood An embedding theorem
for a class of Z^2 shifts of finite type
Inhyeop Yi Canonical symbolic dynamics
for one-dimensional generalized solenoids
(jointly directed with J. Rosenberg)
Ricardo Gomez Finitary isomorphisms of Markov chains
via positive K-theory
Angela Desai Z^d symbolic dynamics:
coding with an entropy inequality
Andrew Dykstra Two equivalence relations in symbolic dynamics 2007
Nicholas Long Involutions of shifts of finite type:
fixed point shifts, orbit quotients and the dimension representation
Kevin McGoff Orders of accumulation of entropy and
random subshifts of finite type
Sompong Chuysurichay Positive rational strong shift equivalence and
the mapping class group of a shift of finite type
Scott Schmieding Strong shift equivalence, algebraic K-theory, and isolating zero-dimensional dynamics on manifolds 2016

Family Photos

May 1992, University of Maryland

Michael Brin and Mike Boyle with their first PhD students. Left to right: Fernando Garibay-Bonales, Michael Brin, Mike Boyle, Danrun Huang.

April 2000, University of Victoria:

Left to right: Sam Lightwood, Ricardo Gomez, Nic Ormes, Danrun Huang, Mike Boyle, Doug Lind.

March 2004, University of Maryland.

Left to right:
FRONT ROW: Nic Ormes, Sam Lightwood, Angela Desai, Andy Dykstra;
BACK ROW: Inhyeop Yi, Mike Boyle, Danrun Huang.

May 2008, University of Maryland:
Nick Long graduates

April 2011 Boylefest banquet, University of Maryland, with most of my PhD students

Left to right:
Ricardo Gomez, Andrew Dykstra, Nic Ormes, Sam Lightwood, Kevin McGoff, Mike Boyle, Nick Long, Brendan Berg, Danrun Huang.
(Missing: Inhyeop Yi, Angela Desai, Sompong Chuysurichay.)
And another take, with Doug "Gramps" Lind

May 2016, University of Maryland, Mike Boyle and Scott Schmieding