Iosif
Polterovich
Contact
information:
Département
de
mathématiques et de statistique
Université
de
Montréal
CP 6128, succ. Centre-ville
Montréal, Québec H3C 3J7
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:
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, SIAM J. Math. Anal. 56 (2024),
no. 6, 7644-7682.
- Mikhail
Karpukhin, Antoine
Métras and Iosif Polterovich, Dirac eigenvalue optimisation and harmonic
maps to complex projective spaces, Int. Math. Res.
Not. 2024 (2024), no. 21, 13758-13784.
- 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 hiver 2025: Équations aux dérivées
partielles (MAT
3162)
Miscellaneous texts: