Holly Krieger

Professor of Mathematics, Department of Pure Mathematics and Mathematical Statistics

Corfield Fellow, Murray Edwards College

Research

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

Publications

Dynamical Shafarevich in arbitrary dimension (with J. Juul, N. Looper, N. M. Mavraki), under review.

Birational maps with transcendental dynamical degree (with J. Bell, J. Diller, M. Jonsson), under review.

A uniform bound on common preperiodic points for quadratic polynomials (with L. DeMarco and H. Ye), Journal of Modern Dynamics (2022), Vol. 18, 363-413.

Uniform Manin-Mumford for a family of genus 2 curves (with L. DeMarco and H. Ye), Annals of Math. (2020) Vol. 191, Issue 3, 949-1001.

Arboreal representations for rational maps with few critical points (with J. Juul, N. Looper, M. Manes, B. Thompson, L. Walton), Research Directions in Number Theory, Association for Women in Mathematics Series, Vol. 19, 133-151.

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.

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.

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.

Recorded research talks

VaNTAGe online seminar -- May 2020.

CIRM, Luminy, France -- September 2018.

Temple University Graduate Student Conference -- December 2017.

CIRM, Luminy, France -- April 2015.