Ilya Kachkovskiy's photo

I was previously at Institute for Advanced Study and University of California, Irvine.

Research interestests

My research is supported by the NSF grant DMS-1758326 "Spectral theory of periodic and quasiperiodic quantum systems" (2016 - 2019, formerly DMS-1600422). I am mostly interested in

Education

Publications

  1. Bourgain J., Kachkovskiy I., Anderson localization for two interacting quasiperiodic particles, to appear in Geom. Funct. Anal. (2018).
  2. Kachkovskiy I., Localization for quasiperiodic operators with unbounded monotone potentials, submitted (2018).
  3. Filonov N., Kachkovskiy I., On the structure of band edges of 2d periodic elliptic operators, Acta Math. 221 (2018), no. 1, 59 - 80, arXiv version.
  4. Jitomirskaya S., Kachkovskiy I., All couplings localization for quasiperiodic operators with Lipschitz monotone potentials, J. Eur. Math. Soc. 21 (2018) no. 3, 777 - 795, arXiv version.
  5. Kachkovskiy I., On transport properties of isotropic quasiperiodic $XY$ spin chains, Comm. Math. Phys. 345 (2016), no. 2, 659 - 673 (arxiv version)
  6. Jitomirskaya S., Kachkovskiy I., $L^2$-reducibility and localization for quasiperiodic operators, Math. Res. Lett 23 (2016), no. 2, 431 - 444 (arxiv version)
  7. Kachkovskiy I., Safarov Yu., Distance to normal elements in C*-algebras of real rank zero, J. Amer. Math. Soc. 29 (2016), 61 - 80. (arxiv version)
  8. Kachkovskiy I., Absence of eigenvalues for the periodic Schrödinger operator with singular potential in a rectangular cylinder, Funct. Anal. Appl., 47 (2013), no. 2, 104 - 112 (Russian version)
  9. Kachkovskiy I., Stein-Tomas theorem for a torus and the periodic Schrödinger operator with singular potential, St. Petersburg Math. J. 24 (2013), 939 - 948 (Russian version)
  10. Filonov N., Kachkovskiy I., Polynomials of almost normal arguments in C*-algebras, J. Spectr. Theory 2 (2012), issue 4, 355 - 371 (arxiv version)
  11. Filonov N., Kachkovskiy I., Absolute continuity of the spectrum of the periodic Schrödinger operator in a layer and in a smooth cylinder, J. Math. Sci. 178 (2011), 274 - 281 (arxiv version, Russian version)
  12. Filonov N., Kachkovskiy I., Absolute continuity of the Schrödinger operator spectrum in a multidimensional cylinder, St. Petersburg Math. J., 21 (2010), 95 - 109 (Russian version)
  13. Filonov N., Kachkovskiy I., A Hilbert-Schmidt analog of Huaxin Lin's Theorem, preprint (2010)
  14. 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), no. 1, 77 - 90

Recent seminar talks

Conferences

  1. (upcoming) Spectral Theory of Quasi-Periodic and Random Operators, CRM, Montreal, November 2018.
  2. PCMI Research Program , July 8 - 14, 2018.
  3. AMS Spring Western Sectional Meeting, Portland State University, April 14 - 15, 2018.
  4. 36th Annual Western States Meeting in Mathematical Physics, UC Irvine, February 2018.
  5. Frontiers in Mathematical Physics, August - September 2016, CRM, Université de Montréal, Canada.
  6. Young Researchers Symposium "Methods of Modern Mathematical Physics", August 2016, Fields Institute, Toronto, Canada.
  7. Simons Center's Workshop: Between Dynamics and Spectral Theory, June 2016, Simons Center for Geometry and Physics, Stony Brook, NY.
  8. Spectral Theory of Periodic, Quasi-periodic, and Random problems, June 2016, University College London.
  9. AMS Fall Western Sectional Meeting, October 2015, California State University, Fullerton.
  10. Spectral Properties of Quasicrystals via Analysis, Dynamics, and Geometric Measure Theory, Banff International Research Station, September 2015, Oaxaca, Mexico.
  11. 26th International Workshop on Operator Theory and its Applications, Tbilisi, Georgia, July 6 - 10, 2015.
  12. Almost Periodic and Other Ergodic Problems, April 2015, University of Cambridge, United Kingdom (co-organizer).
  13. Periodic and Other Ergodic Problems, April 2015, University of Cambridge, United Kingdom.
  14. AMS Sectional Meeting, March 2015, Michigan State University.
  15. Hot Topics: Kadison-Singer, Interlacing Polynomials, and Beyond, March 2015, Mathematical Sciences Research Institute, Berkeley, CA.
  16. The Sixth M. Sh. Birman Conference in Spectral Theory, July 3 - 8, 2014, Euler Institute, St. Petersburg, Russia.
  17. USA-Uzbekistan Conference on Analysis and Mathematical Physics, May 20 - 23, 2014, California State University, Fullerton.
  18. 32nd Annual Western States Mathematical Physics Meeting, February 17 - 18, 2014, California Institute of Technology.

Conference organization

Teaching

Spring Quarter 2020: I'm teaching Math 829.
Fall Quarter 2019: I'm teaching Math 309, Section 4.
Fall Quarter 2018: I'm teaching Math 309, Section 1.
Spring Quarter 2018: I'm teaching Math 234, Section 20.
Fall Quarter 2017: I'm teaching Math 828.