Holly Krieger

Corfield Lecturer, Department of Pure Mathematics and Statistics

Fellow, Murray Edwards College

Research

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


In preparation


A uniform bound on 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


Under review


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


Accepted


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)

To appear in Ergodic Theory and Dynamical Systems.

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

To appear in International Math. Research Notices.


Appeared


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.