Some talks:

  • Invited lecture at Fourth European Congress in Matematics STOCKHOLM, SWEDEN, June 27 - July 2, 2004.
  • Plenary talk at British Mathematical Society Colloqium Newcastle upon Tyne 10-13 April 2006.
  • Invited lectures at FRONTIERS IN MATHEMATICS LECTURE SERIES Texas A&M University Department of Mathematics
  • Invited lecture at Cambridge University Kuwait Foundation Lecture
  • Some previous publications:

  • New bounds and conditions for the equation of Nagell-Ljunggren. J. Number Theory 124 (2007), no. 2, 380--395. 11D41 (11R18) MR2321369
  • On the class groups of cyclotomic extensions in presence of a solution to Catalan's equation. J. Number Theory 118 (2006), no. 1, 123--144. 11D61 (11R18 11R29) MR2220266 (2006k:11048)
  • Reflection, Bernoulli numbers and the proof of Catalan's conjecture. European Congress of Mathematics, 325--340, Eur. Math. Soc., Zurich, 2005. 11R18 (11R29) MR2185753 (2006j:11147)
  • (joint with Roberto Maria Avanzi) Generic efficient arithmetic algorithms for PAFFs (processor adequate finite fields) and related algebraic structures. Selected areas in cryptography, 320--334, Lecture Notes in Comput. Sci., 3006, Springer, Berlin, 2004. 94A60 (11T71 68M07) MR2094739 (2005f:94079)
  • Primary cyclotomic units and a proof of Catalan's conjecture. J. Reine Angew. Math. 572 (2004), 167--195. 11D61 (11R18 11R27) MR2076124 (2005f:11051)
  • A class number free criterion for Catalan's conjecture. J. Number Theory 99 (2003), no. 2, 225--231. 11D61 (11R29) MR1968450 (2004b:11040)
  • Security of biased sources for cryptographic keys. Cryptography and computational number theory (Singapore, 1999), 287--302, Progr. Comput. Sci. Appl. Logic, 20, Birkhaeuser, Basel, 2001. 94A60 MR1944733 (2004c:94095)
  • Algorithms for generating, testing and proving primes: a survey. Cryptography and computational number theory (Singapore, 1999), 93--122, Progr. Comput. Sci. Appl. Logic, 20, Birkhaeuser, Basel, 2001. 11Y11 (94A60) MR1944722 (2003h:11158)
  • Recent developments in primality proving. Math. Comput. Simulation 49 (1999), no. 3, 193--204. 11Y11 (11A51 94A60) MR1709170 (2001c:11135)
  • Cyclotomy primality proving---recent developments. Algorithmic number theory (Portland, OR, 1998), 95--110, Lecture Notes in Comput. Sci., 1423, Springer, Berlin, 1998. (Reviewer: Samuel S. Wagstaff, Jr.) 11Y11 (11A51 11T22) MR1726063 (2000j:11195)
  • Fast generation of provable primes using search in arithmetic progressions. Advances in cryptology---CRYPTO '94 (Santa Barbara, CA, 1994), 282--293, Lecture Notes in Comput. Sci., 839, Springer, Berlin, 1994. 11Y11 (94A60) MR1316412 (95j:11122)
  • A primality test using cyclotomic extensions. Applied algebra, algebraic algorithms and error-correcting codes (Rome, 1988), 310--323, Lecture Notes in Comput. Sci., 357, Springer, Berlin, 1989. (Reviewer: H. J. Godwin) 11Y11 (11A51 11R18) MR1008509 (90i:11147)