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
Professor
Voice +44 (0) 20 7679
7897
Fax
+ 44 (0) 20 7383 5519
Email: i.petridis at ucl.ac.uk
PUBLICATIONS
`Small Scale Equidistribution of Hecke Eigenforms at Infinity', (with A.C.Nordentoft, M.S.Risager), Journal of the London Math. Society, doi.org/10.1112/jlms.12645.
pdf file
`Bounds on shifted convolution sums for Hecke eigenforms, (with A.C.Nordentoft, M.S.Risager), Res. Number theory 8, 26 (2022).doi.org/10.1007/s40993022003201 pdf file
`Higher order deformations of hyperbolic spectra', (with M.S.Risager)
In: Albeverio S., Balslev A., Weder R. (eds) Schrodinger Operators, Spectral Analysis and Number Theory. p. 223239. Springer Proceedings in Mathematics & Statistics, vol 348. Springer, Cham arxiv version.
`Arithmetic Statistics of modular symbols' (with M. S. Risager), Invent. math. 212 (2018), 9971053. https://doi.org/10.1007/s0022201707847 pdf file
`Averaging over Heegner points in the hyperbolic circle problem' (with M. S.
Risager)
Int. Math. Res. Not. IMRN 2018 49424968. doi: 10.1093/imrn/rnx026 pdf file
`On the value distribution of two Lfunctions' (with N. Laaksonen)
Funct. Approx. Comment. Math. 58 (2018) 4368. pdf file
`Local average in hyperbolic lattice point counting' (with M. S. Risager and an appendix by N. Laaksonen), Math. Z. 285 (2017) 13191344. pdf file
`Hyperbolic point counting for a conjugacy class' (with D. Chatzakos)
Forum Math., 28 (2016), no. 5, 9811003. pdf file
`A double Dirichlet series and applications to QUE of weight 1/2 Eisenstein series' (with N. Raulf and M. S. Risager), Algebra and Number Theory Vol. 8 (2014), No. 7, 15391595 pdf file
`Quantum Limits of Eisenstein Series and Scattering states' (with N. Raulf and M. Risager), Can. Math. Bull. 56 (2013), 814826, Erratum to Quantum Limits of Eisenstein Series and Scattering States Canad. Math. Bull. 56 (2013), 827828.
pdf file
`Instability of cuspidal eigenvalues for hyperbolic surfaces' (with M. Risager)
RIMS Kokyuroku No. 1767, 2011.10, Automorphic forms, trace formulas and zeta functions, ed. Yasuro Gon, (2011), 146160. pdf file
`Dissolving cusp forms: Higher order Fermi's Golden Rules' (with M. Risager), Mathematika 59 (2013), 269301. pdf file
`Hyperbolic latticepoint counting
and modular symbols' (with M. Risager), J. Theor. Nombres Bordeaux 21 (2009), 719732. pdf file
`Geodesics in hyperbolic space and Number Theory' (expository), Jahrbuch der MaxPlanckGesellschaft 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), 783815.pdf file
`Discrete logarithms in free groups' (with M. Risager), Proc. Amer. Math. Soc. 134 (2006), 10021012. pdf file
`The remainder in Weyl's law for ndimensional Heisenberg manifolds' (with M. Khosravi), Proc. Amer. Math. Soc. 133 (2005), 35613571.pdf file
`Lattice counting for deformations of convex domains.' (with J. Toth), J. Differential Geom. 72 (2006) 339352.pdf file
`The distribution of values of the Poincare pairing for hyperbolic Riemann surfaces' (with M. S. Risager), J. Reine Angew. Math. 579 (2005) 159173. pdf file
`Modular symbols have a normal distribution' (with M. Risager),
Geom. Funct. Anal. 14 (2004), 10131043. 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, 9911006. 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), 24972502. pdf file
`The remainder in Weyl's law for random twodimensional flat tori' (with J. Toth), Geom. Funct. Anal. 12 (2002), no. 4, 756775. pdf file
`The remainder in Weyl's law for Heisenberg manifolds' (with J. Toth),
J. Differential Geom. 60 (2002), no. 3, 455483. pdf file
`On Kummer's conjecture' (with Ram Murty), J. Number Theory, 90, (2001), 294303.
pdf file
`Quantum Unique Ergodicity for SL(2,O)\H^3 and estimates for Lfunctions'
(with P. Sarnak), J. Evol.
Equ. 1 (2001), 277290. pdf file
`Perturbation of Scattering Poles for Hyperbolic Surfaces and Central Values
of Lseries', Duke Math. J., 103 (2000), no. 1, 101130. pdf file
'Variation of Scattering Poles for Conformal Metrics', Spectral Problems
in Geometry and Arithmetic (Iowa City, IA, 1997), 149158, Contemp. Math., 237, Amer. Math. Soc., Providence, RI, 1999. pdf file
`Fourier coefficients of cusp forms', Number Theory (Ottawa, ON, 1996),
297307, 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 Lseries', Internat. Math. Res. Notices, 1995, no. 3, 111127. pdf file
`On inner products of eigenfunctions for the hyperbolic plane',
MaxPlanckInstitut preprint / 951, 1995.
`Spectral data for finite volume hyperbolic surfaces at the bottom of
the continuous spectrum', J. Funct. Anal., 124 (1994), no. 1, 6194.
pdf file
`On the singular set, the resolvent and Fermi's Golden Rule for
finite volume hyperbolic surfaces', Manuscripta Math., 82 (1994), no. 34,
331347. pdf file
`On differences of eigenvalues for flat tori and hyperbolic surfaces',
Geometry of the Spectrum (Seattle, WA, 1993), 241256, Contemp. Math.,
173, Amer. Math. Soc., Providence, RI, 1994. pdf file
Lecture Notes for LTCC course: Lfunctions
On root 2, Chalkdust Issue 10, 2019
Notes 1 for BB5 course: Quantum Ergodicity and Lfunctions
Notes 2 for BB5 course: Quantum Ergodicity and Lfunctions
Notes 3 for BB5 course: Quantum Ergodicity and Lfunctions
RESEARCH INTERESTS
Automorphic forms and their Spectral Theory, Analytic Number Theory,
Spectral and Scattering Theory of Manifolds.
PROFESSIONAL EXPERIENCE
Professor, University College London (2017)
Reader, University College London (20092017)
Lecturer, University College London (20072009)
Associate Professor, City University of New York, Lehman College (20062007)
Assistant Professor, City University of New York, Lehman College (20022005)
Research Associate, McGill University (20002002)
Adjunct Assistant Professor, Queen's University (19992000)
Postdoctoral Fellow, McGill University (19961998)
Lecturer, University of California, Santa Barbara (19941996)
Member, Mathematical Sciences Research Institute (October 1994)
Member, MaxPlanckInstitut fur Mathematik (19931994)
Visiting Assistant Professor, Johns Hopkins University (19921993)
EDUCATION
Stanford University, Stanford, California (Sept. 1987Sept. 1992).
Ph.D. in mathematics, 1993.
Thesis advisor: Peter Sarnak.
Thesis title: Scattering Theory for Automorphic
Functions and its
relation to Lfunctions.
M.A. in mathematics, 1989.
National University of Athens, Greece, B.Sc. in mathematics (19831987).
SELECTED TALKS
International Conference on Class Groups of Number Fields and related topics, Kerala, India, October 2021
Rutgers Number Theory Seminar, April 2021
Department Colloquium, Stanford U., May 2019i
Analytic Number Theory Seminar, Stanford U., May 2019
Analytic Aspects of Automorphic Forms, Lille, April 2019
LondonParis Number Theory Seminar, November 2018
Elementare und Analytische Zahlentheorie, Bonn, September 2018.
4th EU/US Workshop on Automorphic Forms and Related Topics, Budapest, July 2018.
Canadian Number Theory Association Conference XV, Quebec, July 2018.
A Celebration of CICMA's Postdoctoral Program, CRM, Montreal, July 2018.
Colloque de mathematiques, U. de Geneve, May 2018.
Celebrating Peter Sarnak's Honorary Degree, KCL, October 2017.
ETH, Zurich, Number Theory Seminar, March 2017.
MaxPlanckInstitut fur Mathematik, Number Theory Lunch, February 2017.
Humboldt Universitat, Forschungsseminar Arithmetische Geometrie, January 2017.
Seminaire dâ€™Algebre et de Theorie des Nombres, EPFL Lausanne, April 2016.
Oxford Number Theory Seminar, February 2016.
Arithmetique en Plat Pays, Lille, February 2016.
First Nisyros Conference on automorphic representations and related topics, July 2015.
Building Bridges: 2nd EU/US Summer School and Workshop on Automorphic Forms and Related Topics, July 2014.
A Scientific Celebration in honour of Ram Murty's 60th birthday CRM, Montreal, October 2013
Workshop on Geometry of Eigenvalues and Eigenfunctions, CRM, Montreal, June 2012.
Analytic theory of automorphic forms, Oberwolfach, Sept. 2011
Automorphic forms, trace formulas and zeta functions RIMS Conference, January 2011.
Durham modular form days, September 2010.
Global Analysis and Automorphic Forms, Hebrew University of Jerusalem, March 2010
Heilbronn Seminar, U. of Bristol, March 2010
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).
Lfunctions and related topics, CRM, Montreal, February 2006
Meeting of the Humboldt Foundation, Mathematics, Theoretical Physics and Astrophysics section, Bonn, April 2005.
Oberseminar MaxPlanckInstitut fuer Mathematik, Bonn, April 2005.
Number Theory Seminar, MaxPlanckInstitut 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 Semiclassical 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 Lfunctions, Fields Institute, May 2003.
Joint Princeton U./IAS/Rutgers U. Number Theory Seminar, February 2003.
Number Theory Seminar, MaxPlanckInstitut 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 AMSMAA, 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
EghamReadingLondon Arithmetic Statistics Seminar
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 HighEnergy 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 LMSEPSRC Short Course in Spectral theory and its applications, UCL, June 2011.
Coorganizer of the LondonParis Number Theory Seminar (2012) webpage of the seminar
LINKS
LINKS TO TEACHING MATERIAL
Office Hours:
Tutorials:
Previous teaching:
MATH2101 Complex Analysis, MATH3703 Prime Numbers and their distribution
MATH 6503
MATH 7502
Current teaching: MATH0019 Multivariable Analysis
STUDENTS
PhD supervision
Niko Laaksonen (20112016) Quantum Limits, counting and Landautype formulae in hyperbolic space
Dimitris Chatzakos (20122016) Lattice point problems in the hyperbolic plane
Dimitris Lekkas (2017)
Petru Constantinescu (20182021) Distribution results for automorphic forms, their periods and masses
Marios Voskou (2020)
MPhil supervision
Francois Crucifix: Some applications of the spectral theory of automorphic forms, 20092011.
MSci supervision
Henry McTighe, GaussKuzmin statistics for regulators of real quadratic fields, 2009.
Ben Vaidya: AKS algorithm and Sieve theory, 2011.
Niko Laaksonen, Discrete Mean Values of Dirichlet Lfunctions, 2011. Finalist for Science, Engineering and Technology awards in Mathematics for Europe
Andrei Simionescu, Van der Corput's method on exponential sums and latticepoint counting, 2012
Alexandre Peyrot, Small gaps between primes, 2012
George Leadbetter, The Gauss class number one problem, 2013
Christoph Haeusser, The ternary Goldbach conjecture, 2014
Andreea Mocanu, Bounded gaps between primes, 2015
Tom Steeples, The hyperbolic lattice point problem, 2016
Chris Malcolm, The Hyperbolic Prime Number Theorem, 2018.
Jagjeet Sehmi, Van der Corput's method of exponential sums, 2020.
Zhefan Zhou, Class number one and estimates of $L$functions, 2021.
Joshua Heckroodt, GaussKuzmin statistics, 2023.