Holly Krieger

Corfield Lecturer, Department of Pure Mathematics and Mathematical Statistics

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, and N.M. Mavraki), in preparation.

A spectral gap of Thurston eigenvalues for unbounded post-critically finite rational maps, in preparation.

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

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.

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.

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.


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.