Burcu Baran

Contact Information: Department of Mathematics     University of Michigan     530 Church Street     Ann Arbor, MI 48109, USA     Office: 4847 East Hall      E-Mail: baran.burcu@gmail.com                   bubaran@umich.edu

Research Interests:

• Arithmetic algebraic geometry: Modular curves and moduli spaces, elliptic curves and Galois representations
• Number theory: Algebraic number theory, Arakelov theory
• Commutative algebra

Teaching:

• Math 217(Winter 2012)

Papers and Preprints:

• Galois-theoretic properties of elliptic curves with non-split Cartan level structure, in preparation.

• An exceptional isomorphism between modular curves of level 13 via Torelli's theorem, preprint. (pdf)

• An exceptional isomorphism between modular curves of level 13 (formerly "Modular curves of level 13"), preprint. (pdf)

• Normalizers of non-split Cartan subgroups, modular curves and the class number one problem, Journal of Number Theory, vol. 130, issue 12 (2010), 2753-2772. (pdf)

• Fitting ideals and the Gorenstein property, Archiv der Mathematik, vol. 94, issue 1 (2010), 11-18. (pdf)

• A modular curve of level 9 and the class number one problem, Journal of Number Theory, vol. 129 (2009), 715-728. (pdf)

Notes:

• Hecke Algebras and Galois Representations (written for 2009-10 modularity lifting seminar). (pdf)