Holly Krieger

Corfield Lecturer, Department of Pure Mathematics and Mathematical Statistics

Fellow, Murray Edwards College


I study the arithmetic and algebraic aspects of families of complex dynamical systems.

In preparation

Common preperiodic points for quadratic polynomials (with L. DeMarco and H. Ye)

A spectral gap of Thurston eigenvalues for unbounded post-critically finite rational maps


Uniform Manin-Mumford for a family of genus 2 curves (with L. DeMarco and H. Ye)

To appear in Annals of Math.

Arboreal representations for rational maps with few critical points (with J. Juul, N. Looper, M. Manes, B. Thompson, L. Walton)

To appear in Proceedings of Women in Numbers 4.


Reduction of dynatomic curves (with J. Doyle, A. Obus, R. Pries, S. Rubenstein-Salzedo, L. West)

Ergodic Theory and Dynamical Systems (2019), 39(10), 2717-2768.

Bounded height for unlikely intersections in algebraic dynamical systems (with L. DeMarco, D. Ghioca, K. Nguyen, T. Tucker, H. Ye)

International Mathematics Research Notices (2019) Vol. 2019, Issue 8, 2453 - 2482.

Cohomological conditions on endomorphisms of projective varieties (with P. Reschke)

Bulletin de la SMF (2017) Vol. 145 No. 3, 449 - 468.

The dynamical André-Oort conjecture for unicritical polynomials (with D. Ghioca, K. Nguyen, H. Ye)

Duke Math. J. (2017) Vol. 166 No. 1, 1 - 25.

A case of the dynamical André-Oort conjecture (with D. Ghioca, K. Nguyen)

International Math. Research Notices (2016) Vol. 2016, 738-758.

Uniform boundedness of S-units in arithmetic dynamics (with A. Levin, Z. Scherr, T. Tucker, Y. Yasufuku, M. Zieve)

Pacific Journal of Mathematics (2015) Vol. 274 No. 1, 97-106.

Primitive prime divisors in the critical orbit of z^d+c

International Math. Research Notices (2013) Vol. 2013, 5498-5525.

Some consequences of Schanuel's conjecture (with C. Cheng, B. Dietel, M. Herblot, J. Huang, D. Marques, J. Mason, M. Mereb, S.R. Wilson)

Journal of Number Theory (2009) No. 6, 1464-1467.

Research talks

CIRM, Luminy, France -- September 2018.

CIRM, Luminy, France -- April 2015.