Research interestests
I'm a member of the
Mathematical Physics Group. My research interests include
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Spectral theory of quasiperiodic Schrödinger operators: single- and multi-particle Anderson localization.
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Transport properties of quantum spin systems and their effective Hamiltonians.
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Spectral theory of periodic Schrödinger operators: absolute continuity of the spectra, structure of band edges.
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Almost commuting operators and applications to mathematical physics.
Education
Publications
- Filonov N., Kachkovskiy I.,
On the structure of band edges of 2d periodic elliptic operators, preprint, 2015
- Jitomirskaya S., Kachkovskiy I.,
All couplings localization for quasiperiodic operators with Lipschitz monotone potentials, preprint, 2015
- Kachkovskiy I.,
On transport properties of isotropic quasiperiodic $XY$ spin chains, Communications in Mathematical Physics, 2015 (arxiv version)
- Jitomirskaya S., Kachkovskiy I.,
$L^2$-reducibility and localization for quasiperiodic operators , to appear in Mathematical Research Letters, 2015
- Kachkovskiy I., Safarov Yu.,
Distance to normal elements in C*-algebras of real rank zero, Journal of
the American Mathematical Society, 2015
(arxiv version)
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Kachkovskiy I.,
Absence of eigenvalues for the periodic Schrödinger operator with singular potential in a rectangular cylinder,
Functional Analysis and Its Applications, 47 (2013), 104-112 (Russian version)
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Kachkovskiy I.,
Stein-Tomas theorem for a torus and the periodic Schrödinger operator with singular potential,
St. Petersburg Mathematical Journal, 24 (2013), 939-948 (Russian version)
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Filonov N., Kachkovskiy I.,
Polynomials of almost normal arguments in C*-algebras,
Journal of Spectral Theory, 2 (2012), issue 4, 355-371 (arxiv version)
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Filonov N., Kachkovskiy I.,
Absolute continuity of the spectrum of the periodic Schrödinger operator in a layer and in a smooth cylinder,
Journal of Mathematical Sciences, 178 (2011), 274-281
(arxiv version, Russian version)
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Filonov N., Kachkovskiy I.,
Absolute continuity of the Schrödinger operator spectrum in a multidimensional cylinder,
St. Petersburg Mathematical Journal, 21 (2010), 95-109 (Russian version)
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Filonov N., Kachkovskiy I.,
A Hilbert-Schmidt analog of Huaxin Lin's Theorem
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Dechevsky L., Kachkovskiy I.,
Sharp Estimates of the Constants of Equivalence Between Integral Moduli of Smoothness and K-functionals in the Multivariate Case,
Constructive Approximation, 32 (2010), issue 1, 77-90
Invited seminar talks
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UCLA Functional Analysis Seminar, 17 February 2016.
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(upcoming) Special Colloquium, University of Kansas, 9 February 2016.
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(upcoming) Special Colloquium, University of Nebraska - Lincoln, 4 February 2016.
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(upcoming) Special Colloquium, University of Miami, 26 January 2016.
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(cancelled) Interview talk, King's College London, January 2016. Cancelled due to visa/time constraints.
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(upcoming) Special Colloquium, University of Arizona, January 2016.
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(upcoming) Special Colloquium, Université de Montréal, 18 January 2016.
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Special Colloquium, Michigan State University, 13 January 2016.
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Caltech Mathematical Physics Seminar, 7 October 2015.
Conferences
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(upcoming) Frontiers in Mathematical Physics, August - September 2016, CRM, Université de Montréal, Canada.
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(upcoming) Young Researchers Symposium "Methods of Modern Mathematical Physics", August 2016, Fields Institute, Toronto, Canada.
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(upcoming) Simons Center's Workshop: Between Dynamics and Spectral Theory, June 2016, Simons Center for Geometry and Physics, Stony Brook, NY.
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(upcoming) Spectral Theory of Periodic, Quasi-periodic, and Random problems, June 2016, University College London.
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AMS Fall Western Sectional Meeting, October 2015, California State University, Fullerton.
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Spectral Properties of Quasicrystals via Analysis, Dynamics, and Geometric
Measure Theory, Banff International Research Station, September 2015, Oaxaca, Mexico.
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26th International Workshop on Operator Theory and its Applications,
Tbilisi, Georgia, July 6 - 10, 2015.
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7th St. Petersburg Conference in Spectral Theory, dedicated to the memory of M. Sh. Birman,
July 3 - 6, 2015, Euler Institute, St. Petersburg, Russia.
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Almost Periodic and Other Ergodic Problems,
April 2015,
University of Cambridge, United Kingdom (co-organizer).
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Periodic and Other Ergodic Problems,
April 2015,
University of Cambridge, United Kingdom.
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AMS Sectional Meeting, March 2015, Michigan State University.
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Hot Topics: Kadison-Singer, Interlacing Polynomials, and Beyond, March 2015, Mathematical Sciences Research Institute, Berkeley, CA.
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The Sixth M. Sh. Birman Conference in Spectral Theory,
July 3 - 8, 2014, Euler Institute, St. Petersburg, Russia.
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USA-Uzbekistan Conference on Analysis and Mathematical Physics,
May 20 - 23, 2014,
California State University, Fullerton.
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32nd Annual Western States Mathematical Physics Meeting,
February 17 - 18, 2014,
California Institute of Technology.
Seminars at UC Irvine
Teaching
Fall Quarter 2015: I'm teaching Math 3A: Linear Algebra. Links to the class websites:
MWF 3pm,
MWF 4pm.