Iosif Polterovich            

Professor of Mathematics,  Université de Montréal

Director, Institut des sciences mathématiques   

Tel:: (514) 343-5899                       E-mail: iossif  at dms.umontreal.ca
Fax: (514) 343-5700                       Office:  5229, Pavillon André-Aisenstadt, 2920 Chemin de la Tour

Book:

• Michael Levitin, Dan Mangoubi and Iosif Polterovich, Topics in spectral geometry,  Graduate Studies in Mathematics 237, Amer. Math. Soc., 2023.

Publications since 2005:

• Nikolay Filonov, Michael Levitin, Iosif Polterovich and David Sher, Uniform enclosures for the phase and zeros of Bessel functions and their derivatives,  to appear in SIAM J. Math. Anal.
  
• Mikhail Karpukhin, Antoine Métras and Iosif Polterovich, Dirac eigenvalue optimisation and harmonic maps to complex projective spaces, Preprint.
• Nikolay Filonov, Michael Levitin, Iosif Polterovich and David Sher, Inequalities à la Pólya for the Aharonov-Bohm eigenvalues of the disk, J. Spectral Theory 14 (2024), no. 2, 597-618.
  
• Lev Buhovsky, Iosif Polterovich, Leonid Polterovich, Egor Shelukhin and Vukašin Stojisavljević,  Persistent transcendental Bézout theorems, Forum Math., Sigma 12 (2024), e72.
  
• Lev Buhovsky, Jordan Payette, Iosif Polterovich, Leonid Polterovich, Egor Shelukhin and Vukašin Stojisavljević, Coarse nodal count and topological persistence, to appear in J. Eur. Math. Soc.
  
• Mikhail Karpukhin, Jean Lagacé and Iosif Polterovich, Weyl's law for the Steklov problem on surfaces with rough boundary, Arch. Rat. Mech. Anal. 247 (2023), art. no. 77.
  
• Nikolay Filonov, Michael Levitin, Iosif Polterovich and David Sher, Pólya's conjecture for Euclidean balls,  Invent. Math. 234 (2023), 129-169.
  
• Mikhail Karpukhin, Mickael Nahon, Iosif Polterovich and Daniel Stern, Stability of isoperimetric inequalities for Laplace eigenvalues on surfaces, to appear in J. Diff. Geometry.
  
• Alexander Girouard, Mikhail Karpukhin, Michael Levitin and Iosif Polterovich, The Dirichlet-to-Neumann map, the boundary Laplacian and Hörmander's rediscovered manuscript, J. Spectral Theory 12 (2022), no. 1, 195-225.
  
• Stanislav Krymski, Michael Levitin, Leonid Parnovski, Iosif Polterovich and David Sher,  Inverse Steklov spectral problem for curvilinear polygons, In. Math. Res. Not. 2021 (2021), no. 1, 1-37.
  
• Michael Levitin, Leonid Parnovski, Iosif Polterovich and David Sher, Sloshing, Steklov and corners: Asymptotics of Steklov eigenvalues for curvilinear polygons,  Proc. London. Math. Soc. 125 (2022), no. 3, 359-487.
  
• Michael Levitin, Leonid Parnovski, Iosif Polterovich and David Sher, Sloshing, Steklov and corners: Asymptotics of sloshing eigenvalues, J. Anal. Math. 146 (2022), 65-125.
  
• Mikhail Karpukhin, Nikolai Nadirashvili, Alexei Penskoi and Iosif Polterovich, An isoperimetric inequality for Laplace eigenvalues on the sphere, J. Diff. Geometry 118 (2021), no. 2, 313-331.
  
• Mikhail Karpukhin, Nikolai Nadirashvili, Alexei Penskoi and Iosif Polterovich, Conformally maximal metrics for Laplace eigenvalues on surfaces, Surveys Diff. Geometry 24 (2019), 205-256.
• Iosif Polterovich, Leonid Polterovich and Vukašin Stojisavljević,  Persistence barcodes and Laplace eigenfunctions on surfaces, Geom. Dedicata 201 (2019), no. 1, 111-138.
  
• Alexandre Girouard, Jean Lagacé, Iosif Polterovich and Alessandro Savo, The Steklov spectrum of cuboids, Mathematika 65 (2019), no. 2, 272-310.
  
• Iosif Polterovich, David Sher and John Toth, Nodal length of Steklov eigenfunctions on real-analytic Riemannian surfaces, J. Reine Angew. Math. 754 (2019), 17-47.
  
• Yu Wang, Mirela Ben-Chen, Iosif Polterovich and Justin Solomon, Steklov spectral geometry for extrinsic spectral shape analysis, ACM Transactions on  Graphics 38 (2018), no. 1, Article No. 7.
• Alexandre Girouard and Iosif Polterovich, Spectral geometry of the Steklov problem, J. Spectral Theory 7 (2017), no. 2, 321-359. Reprinted in: Antoine Henrot (Ed.), Shape Optimization and Spectral Theory, 120-148, De Gruyter Open, 2017.
  
• Suresh Eswarathasan, Iosif Polterovich and John Toth,  Smooth billiards with a large Weyl remainder, Int. Math. Res. Not. (2016), no. 12, 3639-3677.
  
• Asma Hassannezhad, Gerasim Kokarev and Iosif Polterovich, Eigenvalue inequalities on Riemannian manifolds with a lower Ricci curvature bound, J. Spectral Theory 6 (2016), no. 4, 807-835.
  
• Iosif Polterovich and David Sher, Heat invariants of the Steklov problem, J. Geom. Analysis 25 (2015), no. 2,  924-950.
• Alexandre Girouard, Leonid Parnovski, Iosif Polterovich and David Sher,  The Steklov spectrum of surfaces: asymptotics and invariants,   Math. Proc. Camb. Philos. Soc. 157 (2014), 379-389.
  
• Nikolay Kuznetsov, Tadeusz Kulczycki, Mateusz Kwaśnicki, Alexander Nazarov, Sergey Poborchi, Iosif Polterovich and Bartłomiej Siudeja, The Legacy of Vladimir Andreevich Steklov,  Notices of the AMS  61 (2014), no. 1, 9-22.
  
• Daniel Elton, Michael Levitin and Iosif  Polterovich, Eigenvalues of a one-dimensional Dirac operator pencil,  Ann. Henri Poincaré 15 (2014), no. 12, 2321-2377.
  
• Mikhail Karpukhin, Gerasim Kokarev and Iosif Polterovich, Multiplicity bounds for Steklov eigenvalues on Riemannian surfaces,  Ann. Inst. Fourier  64 (2014), no. 6,  2481-2502.
  
• Andrei Artemev, Leonid Parnovski and Iosif Polterovich, Inverse electrostatic and elasticity problems for checkered distributions, Inverse Problems, 29 (2013), 075010.
• Alexandre Girouard and Iosif Polterovich, Upper bounds for Steklov eigenvalues on surfaces, Electron. Res. Announc. Math. Soc. 19 (2012), 77-85.
• Dmitry Jakobson, Stephane Nonnenmacher and Iosif Polterovich (Editors),  Spectrum and Dynamics: Proceedings of the workshop held in Montreal, QC, April 7-11, 2008, CRM Proceedings and Lecture Notes, Vol. 52, AMS, 2010.
  
• Rodrigo Bañuelos, Tadeusz Kulczycki, Iosif Polterovich and Bartłomiej Siudeja,  Eigenvalue inequalities for mixed Steklov problems,  Amer. Math. Soc. Transl., Vol. 231 (2010), 19-34.
• Alexandre Girouard and Iosif Polterovich,  Shape optimization for low Neumann and Steklov eigenvalues,  Special issue on ``Complex-Analytic Methods", Math. Meth. Appl. Sci. 33, no. 4 (2010),  501-516.
  
• Alexandre Girouard and Iosif Polterovich,  On the Hersch-Payne-Schiffer inequalities for Steklov eigenvalues,  Func. Anal. Appl.  44:2 (2010), 106–117.  (Russian translation is available here)
  
• Hugues Lapointe, Iosif Polterovich and Yuri Safarov,   Average growth of the spectral function on a Riemannian manifold,  Comm. Partial Differential Equations, 34 (2009), no. 6, 581-615.
  
• Alexandre Girouard, Nikolai Nadirashvili and Iosif Polterovich,  Maximization of the second positive Neumann eigenvalue for planar domains,  J. Diff. Geometry 83, no. 3 (2009), 637-662.
  
•  Iosif Polterovich,  Pleijel's nodal domain theorem  for free membranes,  Proc. Amer. Math. Soc. 137 (2009), 1021-1024.
• Dmitry Jakobson, Iosif Polterovich and John Toth,  A lower bound for the remainder in Weyl's law on negatively curved surfaces,  Int. Math. Res. Not. (2008), no. 2, Art. ID rnm142, 38 pp.
  
• Iosif Polterovich,  Spectral asymptotics and dynamics  on Riemannian manifolds, a short survey in Oberwolfach Reports 41 (2007),  2365-2367.
  
• Dmitry Jakobson and Iosif Polterovich,  Estimates from below for the spectral function and for the remainder in local Weyl's law,  Geom. Funct. Anal. 17, no. 3 (2007), 806-838.
• Michael Levitin, Leonid Parnovski and Iosif Polterovich, Isospectral domains with mixed boundary conditions, J. Phys. A: Math. Gen. 39 (2006) 2073-2082.
  
• Dmitry Jakobson, Michael Levitin, Nikolai Nadirashvili and Iosif Polterovich,  Spectral problems with mixed Dirichlet-Neumann boundary conditions: isospectrality and beyond,  J. Comp. Appl. Math. 194 no. 1 (2006), 141-155.
• Dmitry Jakobson, Nikolai Nadirashvili and  Iosif Polterovich, Extremal metric for the first eigenvalue on a Klein bottle, Canad. J. Math. 58 no. 2 (2006), 381-400.  (2008 G. de B. Robinson Award of the Canadian Mathematical Society).
  
• Dmitry Jakobson,  Michael Levitin, Nikolai Nadirashvili, Nilima Nigam and Iosif Polterovich,  How large can the first eigenvalue be on a surface of genus  two ?, Int. Math. Res. Not. 2005:63 (2005), 3967-3985.

Most of my earlier papers are available at  http://arxiv.org/

Enseignement en automne 2024:  Géométrie différentielle (MAT 2300)

Séminaire de mathématiques supérieures

GEoMetric Spectral Theory Online NEtwork (GEMSTONE)

Spectral geometry in the clouds

Nirenberg Lectures in Geometric Analysis

Annales Mathématiques du Québec

Miscellaneous texts:

• Хвостик и Малышастик (a collection of children's stories with mathematical problems, in Russian, illustrated by Tanja Russita), 2020.
  
• Thank you letter (with Leonid Polterovich) to the Notices of the AMS concerning an article by Abigail Thompson, November 2019.
  
• Valery Senderov, a righteous among the nations (in Russian),  Polit.ru, November 2012.
  
• Mathematics and hockey: how to maintain a decent level  (in Russian),  Polit.ru,  February 2011.