Department of Mathematics
University of California, Santa Cruz
Office: McHenry 4128
E-mail: sdasgup2 (at) ucsc (dot) edu
Department of Mathematics
1156 High Street
Santa Cruz, CA 95064
Math 134, Introduction to Cryptography
Math 202, Graduate Algebra III
UCSC Algebra and Number Theory Seminar
Bay Area Algebraic Number Theory and Arithmetic Geometry Day
|Day 12, April 9, 2016, Berkeley||Day 11, December 5, 2015, Santa Cruz||Day 10, February 21, 2015, Stanford||Day 9, November 15, 2014, Berkeley||Day 8, April 26, 2014, Stanford||Day 7, December 7, 2013, Santa Cruz||Day 6, April 6, 2013, Berkeley||Day 5, November 10, 2012, Santa Cruz||Day 4, March 3, 2012, Stanford||Day 3, October 22, 2011, Santa Cruz||Day 2, April 2, 2011, Berkeley||Day 1, November 6, 2010, Santa Cruz|
| On the Gross-Stark Conjecture, (with Mahesh Kakde and Kevin Ventullo),
| Factorization of p-adic Rankin L-series,
Inventiones Mathematicae, to appear.
| Partial zeta values, Gross's tower of fields conjecture, and Gross-Stark units,
(with Michael Spiess),
| Integral Eisenstein cocycles on GL_n, II: Shintani's Method,
(with Pierre Charollois and Matthew Greenberg),
Commentarii Mathematici Helvetici, 90 (2015), no. 2, 435-477.
| The p-adic L-functions of Evil Eisenstein Series,
(with Joel Bellaiche),
Compositio Mathematica, 151 (2015), no. 6, 999-1040.
| Integral Eisenstein cocycles on GL_n, I: Sczech's cocycle and p-adic L-functions of totally real fields,
(with Pierre Charollois),
Cambridge Journal of Mathematics, 2 (2014), no. 1, 49-90.
| A Conjectural Product formula for Brumer-Stark units over Real Quadratic Fields,
Journal of Number Theory, 133 (2013), no. 3, 915-925 (volume in memory of David Hayes).
| L-Invariants and Shimura Curves,
(with Matthew Greenberg),
Algebra and Number Theory, 6 (2012), no. 3, 455-485.
| Hilbert Modular Forms and the Gross-Stark Conjecture,
(with Henri Darmon and Robert Pollack),
Annals of Mathematics, 174 (2011), no. 1, 439-484.
| A Shintani-Type Formula for Gross-Stark Units over Function Fields,
(with Alison Miller),
Journal of Mathematical Sciences, The University of Tokyo, 16 (2009), no. 3, 415-440.
| Shintani Zeta Functions and Gross-Stark Units for Totally Real Fields,
Duke Mathematical Journal, 143 (2008), no. 2, 225-279.
| Computations of Elliptic Units for Real Quadratic Fields,
Canadian Journal of Mathematics, 59 (2007), 553-574.
| Elliptic Units for Real Quadratic Fields, (with Henri Darmon),
Annals of Mathematics, 163 (2006), no. 1, 301-345.
| Stark-Heegner Points on Modular Jacobians,
Annales Scientifiques de l'École Normale Supérieure, 4e sér., 38 (2005), 427-469.
| Transversals of Additive Latin Squares, (with Gyula Károlyi, Oriol
Serra, and Balázs Szegedy),
Israel Journal of Mathematics, 126 (2001), 17-28.
| A Presentation for the Unipotent Group over Rings
with Identity, (with Daniel Biss),
Journal of Algebra, 237 (2001), no. 2, 691-707.
| On the Size of Minimum Super Arrovian Domains,
SIAM Journal of Discrete Mathematics, 12 (1999), no. 4, 524-534.
| p-adic L-functions and Euler systems: a tale in two trilogies,
(with Massimo Bertolini, Francesc Castella, Henri Darmon, Kartik Prasanna, and Victor Rotger),
submitted to Durham conference Proceedings.
| Heegner Points and Sylvester's Conjecture, (with John Voight),
Arithmetic Geometry, Clay Mathematics Proceedings, 8. American Mathematical Society, Providence, RI, 2009.
| The p-adic Upper Half Plane, (with Jeremy Teitelbaum),
p-adic Geometry: Lectures from the 2007 Arizona Winter School, ed. David Savitt, Dinesh Thakur.
University Lecture Series, 45. American Mathematical Society, Providence, RI, 2008.
| Stark-Heegner Points and Special Values of L-series, (with Massimo Bertolini and Henri Darmon),
L-Functions and Galois Representations, ed. David Burns, Kevin Buzzard, Jan Nekovář.
London Mathematical Society Lecture Note Series, 320. Cambridge University Press, Cambridge, 2007.
| Unités Elliptiques, Corps Quadratiques Réels,
et une Formule Limite de Kronecker, (avec Henri Darmon),
Proceedings de la Troisième Conférence Internationale de Théorie des Nombres Quebec-Maroc, Mai 2003, Casablanca-Marrakech.
Annales des sciences mathématiques du Québec, 28 (2005), no. 1-2, 77-88.
| Gross-Stark Units, Stark-Heegner Points, and Class Fields of
Real Quadratic Fields,
PhD. Thesis, University of California-Berkeley, May 2004.
| Stark's Conjectures,
Senior honors thesis, Harvard University, April 1999.
Talk 2: Trivial zeroes of p-adic L-functions
Talk 3: Factorization of p-adic Rankin L-functions
In 2008, I organized a conference with Frank Calegari, Bjorn Poonen, and Richard Taylor on Modular Forms and Arithmetic at UC-Berkeley and MSRI (June 28-Jul 2, 2008). During the conference we honored Ken Ribet on his 60th birthday.
Here are the slides from my talk at the conference.
Here is the senior thesis of Kaloyan Slavov, which provides computational evidence for the conjecture stated in my paper on Shintani zeta functions above.
Here are my slides from Banff on this topic.
Here are my slides from the UCLA conference on Iwasawa theory about Ribet's method.