# Danya Rose

Postdoctoral Research Associate in the School of Mathematics and Statistics at the University of Sydney.

Postal address: Dr Danya Rose School of Mathematics and Statistics F07 University of Sydney NSW 2006 Australia danya.rose@sydney.edu.au

Curriculum Vitae (July 2016).

I am a member of the Applied Mathematics Research Group.

## Current Teaching (Semester 2, 2016)

My consultation hours (S2 2016) are generally 1400-1500 Tuesday and 1000-1100 Friday, Carslaw room 534.

# PHAR1822 Calculus for Pharmacy II

Course material is available to enrolled students through the Blackboard system.

# MATH1013 Mathematical Modelling (second half)

Course material can be accessed through Ed if you are enrolled in the course.

My pre-exam consultations hours are Tuesday 1st Nov 1100-1200, and Friday 4th Nov 1000-1100.

## Research Interests

Currently working on Human longevity: Modelling social changes that propelled its evolution, funded by the ARC Discovery Program, under Dr Peter Kim in association with Prof Kristen Hawkes. In this project we seek to unravel what factors of human social behaviour have influenced the evolution of our life history as distinct from most other mammals. What role does grandmothering play in this context? Does male "showing off" and costly signaling play a role? To what extent (and how) are these behaviours related to one another? This is a question of evolutionary dynamics, approached from an applied mathematical perspective.

My doctoral work was on Geometric phase and periodic orbits of the equal-mass, planar three-body problem with vanishing angular momentum, supervised by Prof Holger Dullin. The thesis had two main branches: studying the symmetries of the reduced, regularised three-body problem with vanishing angular momentum, and producing a simple criterion to determine whether or not a periodic orbit of this system has vanishing geometric phase (that is, whether or not it is absolutely or relatively periodic in physical space); and a numerical survey of periodic orbits of the reduced, regularised three-body problem with vanishing angular momentum and equal masses, turning up 363 orbits, unique up to discrete symmetry, of which some are known in the literature and many are new.

## Publications

Danya Rose and Holger R. Dullin, A symplectic integrator for the symmetry reduced and regularised planar 3-body problem with vanishing angular momentum , Celestial Mechanics and Dynamical Astronomy 117 (2013) 169-185. (arXiv mirror)

## Presentations

Chaotic Motion in the Asteroid Belt. Seminar presented at the Postgraduate Seminar Series (2010).

Symbolic dynamics of the reduced planar 3-body problem. Talk delivered at AustMS, Sydney (2013).

Binary collisions in the planar 3-body problem with vanishing angular momentum. Talk delivered at ANZIAM, Rotorua (2014).

Geometric phase and periodic orbits of the equal-mass, planar three-body problem with vanishing angular momentum. Seminar presented to a mixed audience at the Mathematics Postgraduate Seminar Series (2015).

## Teaching

From 2008 to 2016 I have tutored the following subjects at various times:

From 2011 to 2016 I was a tutor for the Sydney Uni Sport & Fitness Elite Athletes Program.

## Other things

Transcription of Ms Jenny Henderson's excellent handwritten notes for MATH1901 Differential Calculus (Advanced) to $$\rm\LaTeX$$ (2016).

Coming Soon™! A web page showcasing the periodic orbits featured in my doctoral thesis (and eventually hopefully more - in collaboration with Holger Dullin)!