Old Main, Penn State
I am interested in algebraic number theory, especially in the theory of Drinfeld modules and related topics.
My research is supported in part by a Collaboration Grant for Mathematicians from the Simons Foundation.
Research Papers
Drinfeld discriminant function and Fourier expansion of harmonic cochains (with Fu-Tsun Wei), Mathematische Annalen 388 (2024), 1379–1435.
Isomorphism classes of Drinfeld modules over finite fields (with Valentijn Karemaker and Jeffrey Katen), Journal of Algebra 644 (2024), 381-410.
The growth of the discriminant of the endomorphism ring of the reduction of a rank 2 generic Drinfeld module (with Alina Cojocaru), Journal of Number Theory 237 (2022), 15-39.
Computing endomorphism rings and Frobenius matrices of Drinfeld modules (with Sumita Garai), Journal of Number Theory 237 (2022), 145-164.
Endomorphism rings of reductions of Drinfeld modules (with Sumita Garai), Journal of Number Theory (special issue in memory of David Goss) 232 (2022), 155–176.
Galois extensions and a conjecture of Ogg (with Krzysztof Klosin), Proceedings of the American Mathematical Society 148 (2020), 3821-3834.
On Ribet's isogeny for J0(65) (with Krzysztof Klosin), Proceedings of the American Mathematical Society 146 (2018), 3307-3320.
Drinfeld-Stuhler modules, Research in the Mathematical Sciences 5 (2018), Paper No. 40, 1-33.
The rational torsion subgroups of Drinfeld modular Jacobians and Eisenstein pseudo-harmonic cochains (with Fu-Tsun Wei), Mathematische Zeitschrift 287 (2017), 521-546.
Optimal quotients of Jacobians with toric reduction and component groups (with Joseph Rabinoff), Canadian Journal of Mathematics 68 (2016), 1362-1381.
Graph Laplacians, component groups and Drinfeld modular curves, Münster Journal of Mathematics 9 (2016), 221-251.
On Garland's vanishing theorem for SL(n), European Journal of Mathematics 2 (2016), 579-613.
On component groups of Jacobians of quaternionic modular curves, Archiv der Mathematik (special issue in honor of Ernst-Ulrich Gekeler) 107 (2016), 315-328.
On the Eisenstein ideal over function fields (with Fu-Tsun Wei), Journal of Number Theory (special issue in honor of Winnie Li) 161 (2016), 384-434.
Drinfeld modules, Frobenius endomorphisms, and CM-liftings (with Alina Cojocaru), International Mathematics Research Notices 17 (2015), 7787-7825.
The Eisenstein ideal and Jacquet-Langlands isogeny over function fields (with Fu-Tsun Wei), Documenta Mathematica 20 (2015), 551-629.
Non-archimedean uniformization and monodromy pairing, Contemporary Mathematics 605 (2013), 123-160.
D-elliptic sheaves and odd Jacobians, Journal of Number Theory (special issue in memory of of David Hayes) 133 (2013), 1012-1026.
Local diophantine properties of modular curves of D-elliptic sheaves, Journal für die reine und angewandte Mathematik 664 (2012), 115-140.
On generators of arithmetic groups over function fields, International Journal of Number Theory 7 (2011), 1573-1587.
On Jacquet-Langlands isogeny over function fields, Journal of Number Theory 131 (2011), 1149-1175.
On finite arithmetic simplicial complexes, Proceedings of the American Mathematical Society 139 (2011), 111-124.
Endomorphisms of exceptional D-elliptic sheaves, Mathematische Zeitschrift 266 (2010), 407-423.
On hyperelliptic modular curves over function fields, Archiv der Mathematik 92 (2009), 291-302.
Genus formula for modular curves of D-elliptic sheaves, Archiv der Mathematik 92 (2009), 237-250.
Modular varieties of D-elliptic sheaves and the Weil-Deligne bound, Journal für die reine und angewandte Mathematik 626 (2009), 115-134.
On eigenvalues of p-adic curvature, Manuscripta Mathematica 127 (2008), 397-410.
Modular curves of D-elliptic sheaves are asymptotically optimal, Mathematical Research Letters 15 (2008), 525-536.
Analogue of the degree conjecture over function fields, Transactions of the American Mathematical Society 359 (2007), 3483-3503.
Abelian subvarieties of Drinfeld Jacobians and congruences modulo the characteristic, Mathematische Annalen 337 (2007), 139-157.
The number of rational points on Drinfeld modular varieties over finite fields, International Mathematics Research Notices Article ID 94356 (2006), 1-36.
On the torsion of optimal elliptic curves over function fields, Mathematical Research Letters 13 (2006), 321-331.
On the variation of Tate-Shafarevich groups of elliptic curves over hyperelliptic curves, Journal of Number Theory 115 (2005), 249-283.
Rigid-analytic geometry and abelian varieties, Contemporary Mathematics 388 (2005), 145-160.
Pesenti-Szpiro inequality for optimal elliptic curves, Journal of Number Theory 114 (2005), 361-393.
On component groups of Jacobians of Drinfeld modular curves, Annales de l'Institut Fourier 54 (2004), 2163-2199.
On the degree of modular parametrizations over function fields, Journal of Number Theory 97 (2002), 317-349.
On coset coverings of solutions of homogeneous cubic equations over finite fields (with Ara Alexanian), Electronic Journal of Combinatorics 8 (2001), #R22.
Preprints
Drinfeld-Stuhler modules and the Hasse principle (with Keisuke Arai and Satoshi Kondo).
Expository Notes (not intended for publication)