Kirsten Eisenträger

Assistant Professor
Department of Mathematics
The Pennsylvania State University
109 McAllister Building
University Park, PA 16802
Phone: (814) 863-4127
e-mail:
Office: 422 McAllister Bldg.


I am an assistant 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.

 In 2008 I was awarded a Sloan Research Fellowship.

Papers:


bullet Research articles

bullet Pairings on Hyperelliptic Curves, with Jennifer Balakrishnan, Juliana Belding, Sarah Chisholm, Katherine Stange, and Edlyn Teske. Submitted.

bullet A CRT algorithm for constructing genus 2 curves over finite fields, with Kristin Lauter. To appear in Arithmetic, Geometry and Coding Theory (AGCT-10), Proceedings of the conference AGCT-10, held in Marseille in September 2005. 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 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 Expository articles
 
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 The Theorem of Honda and Tate, presented in VIGRE Number Theory working group, December 2004.


Teaching:

During the Spring 2009 semester I was teaching Math 568, Number Theory II.

During the Fall 2008 semester I was teaching Math 497A, Elliptic Curves and Applications to Cryptography.

During the Spring 2008 semester I was teaching Math 536, Algebra II.

During the Fall 2007 semester I was teaching Math 485, Graph Theory.


bullet Past courses