Department of Mathematics
University College London
Gower Street
London WC1E 6BT
Phone +44 (0) 20 7679 2839/2894
Fax + 44 (0) 20 7383 5519

Yiannis Petridis

Reader
Voice +44 (0) 20 7679 7897
Fax + 44 (0) 20 7383 5519
E-mail: petridis at member.ams.org, petridis at math.ucl.ac.uk

Spectral Theory and its applications. LMS-EPSRC short Course 26 June - 1 July 2011

Lecture Notes for LTCC course: L-functions

Booker's lecture on Turing and RH

MATH 3109

PUBLICATIONS

  • `Quantum Limits of Eisenstein Series and Scattering states' (with N. Raulf and M. Risager), submitted.
  • `Instability of cuspidal eigenvalues for hyperbolic surfaces' (with M. Risager) submitted to the Proceedings of the conference `Automorphic forms, trace formulas and zeta functions' at RIMS, Kyoto, January 2011.
  • `Dissolving cusp forms: Higher order Fermi's Golden Rules' (with M. Risager), preprint. pdf file
  • `Hyperbolic lattice-point counting and modular symbols' (with M. Risager), J. Theor. Nombres Bordeaux 21 (2009), 719-732. pdf file
  • `Geodesics in hyperbolic space and Number Theory' (expository), Jahrbuch der Max-Planck-Gesellschaft 2006 pdf file in german: pdf file
  • `Equidistribution of geodesics on homology classes and analogues for free groups' (with M.Risager), Forum Mathematicum 20 (2008), 783-815. pdf file
  • `Discrete logarithms in free groups' (with M. Risager), Proc. Amer. Math. Soc. 134 (2006), 1002-1012. pdf file
  • `The remainder in Weyl's law for n-dimensional Heisenberg manifolds' (with M. Khosravi), Proc. Amer. Math. Soc. 133 (2005), 3561-3571.pdf file
  • `Lattice counting for deformations of convex domains.' (with J. Toth), J. Differential Geom. 72 (2006) 339-352.pdf file
  • `The distribution of values of the Poincare pairing for hyperbolic Riemann surfaces' (with M. S. Risager), J. Reine Angew. Math. 579 (2005) 159-173. pdf file
  • `Modular symbols have a normal distribution' (with M. Risager), Geom. Funct. Anal. 14 (2004), 1013-1043. pdf file.
  • `The remainder in Weyl's law for Heisenberg manifolds II' (with D. Chung and J. Toth), Bonner Mathematische Schriften, Nr. 360 (2003) pdf file.
  • `Spectral deformations and Eisenstein series associated with modular symbols', Internat. Math. Res. Notices 2002, no. 19, 991-1006. pdf file .
  • `On the number of Fourier coefficients that determine a Hilbert modular form (with S. Baba and K. Chakraborty), Proc. Amer. Math. Soc. 130 (2002), 2497-2502. pdf file
  • `The remainder in Weyl's law for random two-dimensional flat tori' (with J. Toth), Geom. Funct. Anal. 12 (2002), no. 4, 756--775. pdf file
  • `The remainder in Weyl's law for Heisenberg manifolds' (with J. Toth), J. Differential Geom. 60 (2002), no. 3, 455--483. pdf file
  • `On Kummer's conjecture' (with Ram Murty), J. Number Theory, 90, (2001), 294-303. pdf file
  • `Quantum Unique Ergodicity for SL(2,O)\H^3 and estimates for L-functions' (with P. Sarnak), J. Evol. Equ. 1 (2001), 277-290. pdf file
  • `Perturbation of Scattering Poles for Hyperbolic Surfaces and Central Values of L-series', Duke Math. J., 103 (2000), no. 1, 101-130. pdf file
  • 'Variation of Scattering Poles for Conformal Metrics', Spectral Problems in Geometry and Arithmetic (Iowa City, IA, 1997), 149-158, Contemp. Math., 237, Amer. Math. Soc., Providence, RI, 1999. pdf file
  • `Fourier coefficients of cusp forms', Number Theory (Ottawa, ON, 1996), 297-307, CRM Proc. Lecture Notes, 19, Amer. Math. Soc., Providence, RI, 1999. pdf file
  • `On squares of eigenfunctions for the hyperbolic plane and a new bound on certain L-series', Internat. Math. Res. Notices, 1995, no. 3, 111-127. pdf file
  • `On inner products of eigenfunctions for the hyperbolic plane', Max-Planck-Institut preprint / 95-1, 1995.
  • `Spectral data for finite volume hyperbolic surfaces at the bottom of the continuous spectrum', J. Funct. Anal., 124 (1994), no. 1, 61-94. pdf file
  • `On the singular set, the resolvent and Fermi's Golden Rule for finite volume hyperbolic surfaces', Manuscripta Math., 82 (1994), no. 3-4, 331-347. pdf file
  • `On differences of eigenvalues for flat tori and hyperbolic surfaces', Geometry of the Spectrum (Seattle, WA, 1993), 241-256, Contemp. Math., 173, Amer. Math. Soc., Providence, RI, 1994. pdf file
  • `Scattering poles for SL(2,Z): the case of multiple zeros', in preparation.
  • `On the periodicity of Bell polynomials', in preparation.

    RESEARCH INTERESTS

  • Automorphic forms and their Spectral Theory, Analytic Number Theory, Spectral and Scattering Theory of Manifolds.

    PROFESSIONAL EXPERIENCE

  • Reader, University College London (2009-)
  • Lecturer, University College London (2007-2009)
  • Associate Professor, City University of New York, Lehman College (2006-2007)
  • Assistant Professor, City University of New York, Lehman College (2002-2005)
  • Research Associate, McGill University (2000-2002)
  • Adjunct Assistant Professor, Queen's University (1999-2000)
  • Postdoctoral Fellow, McGill University (1996-1998)
  • Lecturer, University of California, Santa Barbara (1994-1996)
  • Member, Mathematical Sciences Research Institute (October 1994)
  • Member, Max-Planck-Institut fur Mathematik (1993-1994)
  • Visiting Assistant Professor, Johns Hopkins University (1992-1993)

    EDUCATION

  • Stanford University, Stanford, California (Sept. 1987-Sept. 1992).
    Ph.D. in mathematics, 1993.
    Thesis advisor: Peter Sarnak.
    Thesis title: Scattering Theory for Automorphic Functions and its relation to L-functions.
    M.A. in mathematics, 1989.
  • National University of Athens, Greece, B.Sc. in mathematics (1983-1987).

    SELECTED TALKS

  • Conference on Modular Forms and Related Topics, American University of Beirut, July 2009
  • Prospects in Mathematics, A Symposium for Potential Research Students in Mathematics, Durham University, January 2009
  • Summer school on Spectral Theory of Automorphic Forms, Pohang, Korea, Lecture Series (6 lectures), August 2008,
  • Workshop on spectrum and dynamics, CRM, Montreal, April, 2008.
  • Number Theory Seminar, Cambridge, November, 2007.
  • Asymptotics in Geometry, Tohoku University, Sendai, July 2006 (4 lectures).
  • L-functions and related topics, CRM, Montreal, February 2006
  • Meeting of the Humboldt Foundation, Mathematics, Theoretical Physics and Astrophysics section, Bonn, April 2005.
  • Oberseminar Max-Planck-Institut fuer Mathematik, Bonn, April 2005.
  • Number Theory Seminar, Max-Planck-Institut fuer Mathematik, Bonn, January 2005.
  • Oberseminar Globale Analysis, Universitaet Bonn, January 2005.
  • Analysis seminar, Cambridge University, November 2004.
  • Number Theory Seminar, Oxford University, November 2004.
  • Workshop on Random Matrix theory and Arithmetic Aspects of Quantum Chaos, Isaac Newton Institute for Mathematical Sciences, U. of Cambridge, June 2004.
  • Workshop on Semi-classical theory of eigenfunctions and PDEs, Fields Institute, Toronto, June 2004.
  • Number Theory Seminar, ETH, Zuerich, January 2004.
  • Number Theory Seminar, Johns Hopkins University, Baltimore, November 2003.
  • Workshop on automorphic L-functions, Fields Institute, May 2003.
  • Joint Princeton U./IAS/Rutgers U. Number Theory Seminar, February 2003.
  • Number Theory Seminar, Max-Planck-Institut fuer Mathematik, Bonn, May 2001.
  • Number Theory Seminar, New York University, December 2001.
  • Western Section meeting of AMS, Special Session on Automorphic Forms, Santa Barbara, March 2000.
  • Partial Differential Equations and their Applications to Geometry and Physics, Castelvecchio Pascoli, Italy, June 2000.
  • 54e Colloque des Sciences Mathematiques du Quebec, Montreal, November 2000.
  • Joint Mathematics Meetings AMS-MAA, Special Session on Recent Developments on the Laplace Operator and its Geometric Applications, Baltimore, January 1998.
  • Workshop on Analytic Number Theory, Centre de Recherches Mathematiques, Montreal, Canada, October 1998.
  • Geometric Analysis in Singular and Noncompact Manifolds, San Feliu de Guixols, Spain, June 1997.
  • Tenth annual workshop on automorphic forms and related topics, Stanford U., March 1996.
  • Eastern Section Meeting of AMS, Rider U., Lawrenceville, New Jersey, October 1996.
  • Nevanlinna Colloquium 1993, University of Michigan, Ann Arbor, June 1993.
  • Summer Conference on Spectral Geometry, organized by AMS, U. of Washington, Seattle, July 1993.

    CONFERENCE ORGANIZATION

  • Special session organizer (together with John Toth), AMS meeting in Montreal, September 1997.
  • Organizer (together with D. Jakobson and J. Toth) of the Workshop on Spectral Statistics and High-Energy Eigenstates at CRM, Montreal, August 2001.
  • Organizer (together with D. Jakobson) of a special session on Spectral geometry and analytic aspects of automorphic forms, AMS meeting in Montreal, May 2002.
  • Organizer (together with D. Jakobson) of the Workshop on Spectral Theory and Automorphic Forms, CRM, Montreal, 2004.
  • Organizer (together with C. Sormani and J. Dodziuk) of the 2006 CUNY Geometric analysis workshop (The Laplace and Length Spectra), New York, February 2005
  • Organizer (together with L. Parnovski) of the LMS-EPSRC Short Course in Spectral theory and its applications, UCL, June 2011.

    • LINKS

    LINKS TO TEACHING MATERIAL

    Office Hours: by appointment.

    Tutorials: Friday 12-1 (group 23) and Friday 1-2 (group 12)

    Previous teaching: MATH 6503

    MATH 7502

    Current teaching: MATH 1101 MATH 3109

    LINKS TO SOME OF MY RECENT TALKS

  • Talk in Aarhus U. August 2006 and CUNY, Nov. 2006
  • Talk 1 in Tohoku U. (Sendai) July 2006
  • Talk 2 in Tohoku U. (Sendai) July 2006
  • Talk in Rochester, June 2006
  • Talk in Montreal, February 2006
  • Talk in Clausthal, November 2005
  • Talk at the Humboldt Foundation Meeting, Bonn, April 2005
  • Talk at the Workshop in Random Matrix theory and Number theory, Waterloo, June 2005
  • Talk in Bordeaux, October 2005
  • Talk at Isaac Newton Institute, Cambridge, June 2004
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