Research

Publications

• A Jacquet-Langlands relation between mod p Hilbert and quaternionic modular forms. (joint with F. Diamond and S. Sasaki)
     To appear in Astérisque.
  

• Minimal weights of Hilbert modular forms: the ramified case. (joint with F. Diamond)
     IMRN , July 2022.
  

• p-adic dynamics of Hecke operators over modular curves. (joint with E. Goren)
     Journal de Théorie des Nombres de Bordeaux , Tome 33, no 2 (2021), p. 387-431.
  

• Mod p Hilbert modular forms of parallel weight one. (arXiv:1711.01680)
  

• Minimal weights of Hilbert modular forms in characteristic p . (joint with F. Diamond)
     Compositio Mathematica Volume 153, Issue 9, 2017, pp. 1769-1778   pdf
  
  
• Analytic continuation of overconvergent Hilbert modular forms.
   Astérisque 382 (2016), pp 1-48.   pdf
  Based on a lecture series I gave at the IHES under Cours d'Arithmétique et de Géométrie Algébriquein October 2012.
  

• Modularity lifting results in parallel weight one and applications to the Artin conjecture: the tamely ramified case (with S. Sasaki, Y. Tian)
     Forum of Mathematics, Sigma. (2014), Vol. 2, e. 18, 58 pages.    pdf

• Companion forms in parallel weight one. (joint with T. Gee)
     Compositio Mathematica. Volume 149, Issue 06, June (2013), pp 903- 913.   pdf
  
  
• Modularity lifting in parallel weight one.
     J. Amer. Math. Soc. (JAMS) 26 (2013), no. 1, 199--225.    pdf
  

• The Artin Conjecture via p-adic Hilbert modular forms. 
Proceedings of the conference in honor of the 70th birthday of Prof. Shahshahani (Dec 2012)  pdf

• Canonical Subgroups Over Hilbert Modular Varieties. (joint with E. Goren)
     J. Reine Angew. Math. (Crelle) 670, 1-63 (2012)    pdf
  
  
• Sous-groupes canoniques sur les variétés modulaires de Hilbert. (Joint with E. Goren)
     C. R. Acad. Sci. Paris, Ser. I, 347 (2009).   pdf
  
  
• Overconvergence and classicality: the case of curves.
     J. Reine Angew. Math. (Crelle) 631 (2009), 109--139    pdf
  
  
• A ``Subgroup-Free'' Approach To Canonical Subgroups. (joint with E. Goren)
     Commentarii Mathematici Helvetici Commentarii 81 (2006), 617-641.    pdf
  
  
• A Gluing Lemma And Overconvergent Modular Forms.
     Duke Math. Journal 132 (2006), no. 3, 509--529.    pdf    typo
  
  
• The Eigencurve: A Brief Survey.
     Mathematisches Institut Seminars, Universitat Gottingen, (2005), 65--73.    pdf
  
  
• P-adic Modular Forms over Shimura Curves over Totally Real Fields.
     Compositio Mathematica. 140 (2004), no. 2, 359--395.    pdf
  
  
• p-adic Modular Forms over Shimura Curves over Q.
     Thesis, Massachusetts Institute of Technology, June 1999.    pdf
  
  
• An introduction to mathematical olympiads.
  Sharif University Press, Tehran, Iran, 1998 (Book co-authored in Persian).