Kirsten Eisenträger

Associate Professor
Department of Mathematics
The Pennsylvania State University
109 McAllister Building
University Park, PA 16802
Phone: (814) 863-4127

Office: 330 McAllister Bldg.

I am an associate professor in the Department of Mathematics at Penn State. Before that I was an NSF Postdoctoral Fellow/ T.H. Hildebrandt Assistant Professor in the Department of Mathematics at the University of Michigan. In 2003-04 I was a member at the Institute for Advanced Study. I am interested in number theory, arithmetic geometry, and applications to cryptography. Here is my curriculum vitae.

My research is currently supported by a grant from the Department of the Army, and an NSF Career Award. In 2008 I was awarded a Sloan Research Fellowship.


bullet Research articles

bullet Hilbert's Tenth Problem over function fields of positive characteristic not containing the algebraic closure of a finite field, with Alexandra Shlapentokh. To appear in Journal of the European Mathematical Society (JEMS).

bullet Weak Instances of PLWE, with Sean Hallgren, and Kristin Lauter, Selected Areas in Cryptography-SAC 2014, Springer LNCS 8781, pp. 183-194, 2014.

bullet A quantum algorithm for computing the unit group of an arbitrary degree number field, with Sean Hallgren, Alexei Kitaev, and Fang Song, STOC 2014.

bullet Computing the unit group, class group and compact representations in algebraic function fields, with Sean Hallgren. Tenth Algorithmic Number Theory Symposium (ANTS X) Proceedings. Open Book Series, volume 1, Mathematical Sciences Publishers, Berkeley, 2013 (electronic).

bullet Hilbert's Tenth Problem for function fields of varieties over algebraically closed fields of positive characteristic. Monatsh. Math. 168 (2012), no. 1, 1-16, 2012.

bullet Hilbert's Tenth Problem and Mazur's Conjectures in complementary subrings of number fields, with Graham Everest and Alexandra Shlapentokh. Mathematical Research Letters 18, no. 06, 1141-1162, 2011.

bullet Pairings on Hyperelliptic Curves, with Jennifer Balakrishnan, Juliana Belding, Sarah Chisholm, Katherine Stange, and Edlyn Teske. WIN - Women in Numbers: Research Directions in Number Theory, Fields Institute Communications, vol. 60, Amer. Math. Soc., Providence, RI, pages 87-120, 2011.

bullet Quantum algorithms for ray class groups and some subfields of Hilbert class fields, with Sean Hallgren. Symposium on Discrete Algorithms (SODA) 2010 Proceedings, Society for Industrial and Applied Mathematics (SIAM), pages 471-483, 2010.

bullet A CRT algorithm for constructing genus 2 curves over finite fields, with Kristin Lauter. Arithmetic, Geometry and Coding Theory (AGCT-10), Séminaires et Congrès 21 (2009), pages 161-176. Société Mathématique de France, Paris, 2009.

bullet Undecidability in function fields of positive characteristic, with Alexandra Shlapentokh. Int. Math. Res. Not., Vol. 2009: article ID rnp079, 36 pages, doi: 10.1093/imrn/rnp079, 2009.

bullet Descent on elliptic curves and Hilbert's Tenth Problem, with Graham Everest. Proc. Amer. Math. Soc., 137(6):1951-1959, 2009.

bullet Hilbert's Tenth Problem for function fields of characteristic zero. Model Theory with Applications to Algebra and Analysis, Volume 2, Cambridge University Press, 2008, pages 237-254.

bullet On the computation of the Cassels pairing for certain Kolyvagin classes in the Shafarevich-Tate group, with Dimitar Jetchev and Kristin Lauter. Pairing-Based Cryptography - Pairing 2008, Springer LNCS volume 5209, 2008, pages 113-125.

bullet Hilbert's Tenth Problem for function fields of varieties over number fields and p-adic fields, J. Algebra , 310(2007), pages 775-792.

bullet Integrality at a prime for global fields and the perfect closure of global fields of characteristic p>2, J. Number Theory, Volume 114, 2005, pages 170-181.

bullet Hilbert's Tenth Problem for function fields of varieties over C, Int. Math. Res. Not., Issue 59, 2004, pages 3191-3205.

bullet Improved Weil and Tate pairings for elliptic and hyperelliptic curves, with Kristin Lauter and Peter L. Montgomery, in ANTS-VI proceedings, 2004, pages 169-183 (Springer LNCS link).

bullet Hilbert's Tenth Problem and Arithmetic Geometry, Ph.D. thesis, May 2003.

bullet Hilbert's Tenth Problem for algebraic function fields of characteristic 2, Pacific J. Math., 210 (2), 2003, pages 261-281.

bullet Fast elliptic curve arithmetic and improved Weil pairing evaluation, with Kristin Lauter and Peter L. Montgomery, Topics in Cryptology - CT-RSA 2003, (Springer LNCS link).

bullet Other articles
bullet The Theorem of Honda and Tate, presented in VIGRE Number Theory working group, December 2004.


This semester I am teaching Math 567, Number Theory I and Math 485, Graph Theory.

In the Spring of 2015 I taught Math 567, Number Theory I.

In the Fall of 2014 I taught two sections of Math 436, Linear Algebra.

In the Spring of 2013 I taught Math 536, Abstract Algebra.

In the Fall of 2012 I taught Math 567, Number Theory I.

In the Fall of 2011 I taught Math 311M, Honors Concepts of Discrete Mathematics.

In the Spring of 2011 I taught Math 597C, Topics in Number Theory.

In the Fall of 2010 I taught Math 567, Number Theory I.

In the Spring 2010 semester I taught Math 250, Section 3, Ordinary Differential Equations, and Math 536, Algebra II.

In the Spring 2009 semester I taught Math 568, Number Theory II.

In the Fall 2008 semester I taught Math 497A, Elliptic Curves and Applications to Cryptography.

In the Spring 2008 semester I taught Math 536, Algebra II.

In the Fall 2007 semester I taught Math 485, Graph Theory.

bullet Past courses