# Mary Rees

Susan Mary Rees, FRS (born Cambridge, 31 July 1953[1]) is a British mathematician and a Professor of Mathematics at Liverpool University since 2002, specialising in research in complex dynamical systems.[2][3]

After obtaining her BA in 1974 and MSc in 1975 at St Hugh's College, Oxford, she did research in mathematics under the direction of Bill Parry at Warwick University, obtaining a PhD in 1978. She was awarded a Whitehead Prize of the London Mathematical Society in 1988. The citation[4] notes that, in particular,

Her most spectacular theorem[5] has been to show that in the space of rational maps of the Riemann sphere of degree d ≥ 2 those maps that are ergodic with respect to Lebesgue measure and leave invariant an absolutely continuous probability measure form a set of positive measure.

In recent years, much of Rees's work has focused on the dynamics of quadratic rational maps; i.e. rational maps of the Riemann sphere of degree two, including an extensive monograph.[6] In 2004, she also presented an alternative proof of the Ending Laminations Conjecture of Thurston,[7] which had been proved by Brock, Canary and Minsky shortly before.[8]

## FRS

She was elected to a Fellowship of the Royal Society in 2002.

## Family

Her father David Rees was also a distinguished mathematician, who worked on Enigma in Hut 6 at Bletchley Park.

## Works

• Mary Rees (2010) "Multiple equivalent matings with the aeroplane polynomial". Ergodic Theory and Dynamical Systems, pp. 20
• Mary Rees (2008) "William Parry FRS 1934–2006". Biographical Memoirs of the Royal Society, 54, pp. 229–243
• Mary Rees (2004) "Teichmuller distance is not $C^{2+\varepsilon }$". Proc London Math, 88, pp. 114–134
• Mary Rees (2003) "Views of Parameter Space: Topographer and Resident". Asterisque, 288, pp. 1–418
• Mary Rees (2002) "Teichmuller distance for analytically finite surfaces is $C^{2}$." Proc. London Math. Soc. 85 (2002) 686 – 716.,85, pp. 686–716

## References

1. ^ GRO Register of Births: SEP 1953 4a 294 CAMBRIDGE – Susan M. Rees, mmn = Cushen
2. ^
3. ^ "Dr. Mary Rees". University of Liverpool. 2008-01-18. Retrieved 2014-01-02.
4. ^ Bulletin of the London Mathematical Society 20 (1988), no. 6, p. 639.
5. ^ Positive measure sets of ergodic rational maps, Ann. Sci. École Norm. Sup. 19 (1986), no. 3, 383–407.
6. ^ Views of parameter space: Topographer and resident, Asterisque 288 (2003)
7. ^ The Ending Laminations Theorem direct from Teichmüller geodesics, Preprint, 2004
8. ^