Ilya Kachkovskiy's photo

Please note: this is a legacy homepage which is no longer updated (including contact details). I have moved to MSU.

Ilya Kachkovskiy

Visiting Assistant Professor

Department of Mathematics, University of California, Irvine
Irvine, CA, 92697-3875
United States of America


Office : Rowland Hall, 510P
Tel : (949) 824-3153

Research interestests

I'm a member of the Mathematical Physics Group. My research interests include



  1. Filonov N., Kachkovskiy I., On the structure of band edges of 2d periodic elliptic operators, preprint, 2015
  2. Jitomirskaya S., Kachkovskiy I., All couplings localization for quasiperiodic operators with Lipschitz monotone potentials, preprint, 2015
  3. Kachkovskiy I., On transport properties of isotropic quasiperiodic $XY$ spin chains, Communications in Mathematical Physics, 2015 (arxiv version)
  4. Jitomirskaya S., Kachkovskiy I., $L^2$-reducibility and localization for quasiperiodic operators , to appear in Mathematical Research Letters, 2015
  5. Kachkovskiy I., Safarov Yu., Distance to normal elements in C*-algebras of real rank zero, Journal of the American Mathematical Society, 2015 (arxiv version)
  6. 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)
  7. 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)
  8. Filonov N., Kachkovskiy I., Polynomials of almost normal arguments in C*-algebras, Journal of Spectral Theory, 2 (2012), issue 4, 355-371 (arxiv version)
  9. 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)
  10. 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)
  11. Filonov N., Kachkovskiy I., A Hilbert-Schmidt analog of Huaxin Lin's Theorem
  12. 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


  1. (upcoming) Frontiers in Mathematical Physics, August - September 2016, CRM, Université de Montréal, Canada.
  2. (upcoming) Young Researchers Symposium "Methods of Modern Mathematical Physics", August 2016, Fields Institute, Toronto, Canada.
  3. (upcoming) Simons Center's Workshop: Between Dynamics and Spectral Theory, June 2016, Simons Center for Geometry and Physics, Stony Brook, NY.
  4. (upcoming) Spectral Theory of Periodic, Quasi-periodic, and Random problems, June 2016, University College London.
  5. AMS Fall Western Sectional Meeting, October 2015, California State University, Fullerton.
  6. Spectral Properties of Quasicrystals via Analysis, Dynamics, and Geometric Measure Theory, Banff International Research Station, September 2015, Oaxaca, Mexico.
  7. 26th International Workshop on Operator Theory and its Applications, Tbilisi, Georgia, July 6 - 10, 2015.
  8. 7th St. Petersburg Conference in Spectral Theory, dedicated to the memory of M. Sh. Birman, July 3 - 6, 2015, Euler Institute, St. Petersburg, Russia.
  9. Almost Periodic and Other Ergodic Problems, April 2015, University of Cambridge, United Kingdom (co-organizer).
  10. Periodic and Other Ergodic Problems, April 2015, University of Cambridge, United Kingdom.
  11. AMS Sectional Meeting, March 2015, Michigan State University.
  12. Hot Topics: Kadison-Singer, Interlacing Polynomials, and Beyond, March 2015, Mathematical Sciences Research Institute, Berkeley, CA.
  13. The Sixth M. Sh. Birman Conference in Spectral Theory, July 3 - 8, 2014, Euler Institute, St. Petersburg, Russia.
  14. USA-Uzbekistan Conference on Analysis and Mathematical Physics, May 20 - 23, 2014, California State University, Fullerton.
  15. 32nd Annual Western States Mathematical Physics Meeting, February 17 - 18, 2014, California Institute of Technology.

Seminars at UC Irvine


Fall Quarter 2015: I'm teaching Math 3A: Linear Algebra. Links to the class websites: MWF 3pm, MWF 4pm.

Mathematical competitions in Irvine

Since 2013, I have been organizing Tournament of the Towns in Irvine (Russian, English homepage hosted by University of Toronto) and Formula of Unity. Sometimes I run practice sessions in collaboration with UCI Math Circle.