The study of "complex systems" spans an enormous range of phenomena so
large that no consensus has even been reached as to what formallyconstitutes 
a "complex system".  My own favourite definition is simply
any "complicated" system, dynamical or not, that involves either
complicated behaviour or large amounts of difficult-to-describe data,
or both.  In this talk, I will discsus my ongoing work in many complex
systems.  On the continuous dynamical systems front, I will discuss two
projects involving the gravitational n-body problem: first, my
recent single-author paper published in _Nature Physics_ that closed a
15-year-old debate on the nature of chaos in the Outer Solar System;
and second, my single-author works, published in Physical Review Letters
and Astrophysical Journal Letters, on the reliability of large galaxy
and cosmological simulations from the standpoint of "Shadowing", which
is a method of backwards error analysis for numerical solutions of
ODEs.  In the contetxt of rigorous study of dynamical systems, I will
discuss my collaborative work, published in SIAM J. Num. Anal. and
DCDS, which involved the computer-aided proof of the existence of
shadows of long-term numerical solutions to ODEs.  On the discrete
complex systems front, I will mention two bio-informatics projects:
a graph-theoretic "network alignment" algorithm that, in collaboration
with Prof. Przulj of UC Irvine, has been used to align noisy biological
networks of several species and produces alignments 1-2 orders of
magnitude more complete than existing algorithms; second, my genome
sequence assembly work done in collaboration with James Yorke at the
University of Maryland, College Park, which has been used to efficiently
and accurately assemble mammalian-sized genomes.