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-1600422 "Spectral theory of periodic and quasiperiodic quantum systems" (2016-2019). I am mostly interested in

Education


Publications

  1. Filonov N., Kachkovskiy I., On the structure of band edges of 2d periodic elliptic operators, submitted, 2016
  2. Jitomirskaya S., Kachkovskiy I., All couplings localization for quasiperiodic operators with Lipschitz monotone potentials, to apprear in J. Eur. Math. Soc, 2017
  3. Kachkovskiy I., On transport properties of isotropic quasiperiodic $XY$ spin chains, Comm. Math. Phys. 345 (2016), no. 2, 659 - 673 (arxiv version)
  4. Jitomirskaya S., Kachkovskiy I., $L^2$-reducibility and localization for quasiperiodic operators, Math. Res. Lett 23 (2016), no. 2, 431 - 444 (arxiv version)
  5. 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)
  6. 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)
  7. 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)
  8. Filonov N., Kachkovskiy I., Polynomials of almost normal arguments in C*-algebras, J. Spectr. 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, J. Math. Sci. 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 Math. J., 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), no. 1, 77 - 90

Recent seminar talks

Conferences

  1. Frontiers in Mathematical Physics, August - September 2016, CRM, Université de Montréal, Canada.
  2. Young Researchers Symposium "Methods of Modern Mathematical Physics", August 2016, Fields Institute, Toronto, Canada.
  3. Simons Center's Workshop: Between Dynamics and Spectral Theory, June 2016, Simons Center for Geometry and Physics, Stony Brook, NY.
  4. 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. Almost Periodic and Other Ergodic Problems, April 2015, University of Cambridge, United Kingdom (co-organizer).
  9. Periodic and Other Ergodic Problems, April 2015, University of Cambridge, United Kingdom.
  10. AMS Sectional Meeting, March 2015, Michigan State University.
  11. Hot Topics: Kadison-Singer, Interlacing Polynomials, and Beyond, March 2015, Mathematical Sciences Research Institute, Berkeley, CA.
  12. The Sixth M. Sh. Birman Conference in Spectral Theory, July 3 - 8, 2014, Euler Institute, St. Petersburg, Russia.
  13. USA-Uzbekistan Conference on Analysis and Mathematical Physics, May 20 - 23, 2014, California State University, Fullerton.
  14. 32nd Annual Western States Mathematical Physics Meeting, February 17 - 18, 2014, California Institute of Technology.

Conference organization


Teaching

Fall Quarter 2017: I'm teaching Math 828.