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

Spectral theory of quasiperiodic Schrödinger operators: single and multiparticle Anderson localization.

Transport properties of quantum spin systems and their effective Hamiltonians.

Spectral theory of periodic Schrödinger operators: absolute continuity of the spectra, structure of band edges.

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)

Kachkovskiy I.,
Absence of eigenvalues for the periodic Schrödinger operator with singular potential in a rectangular cylinder,
Functional Analysis and Its Applications, 47 (2013), 104112 (Russian version)

Kachkovskiy I.,
SteinTomas theorem for a torus and the periodic Schrödinger operator with singular potential,
St. Petersburg Mathematical Journal, 24 (2013), 939948 (Russian version)

Filonov N., Kachkovskiy I.,
Polynomials of almost normal arguments in C*algebras,
Journal of Spectral Theory, 2 (2012), issue 4, 355371 (arxiv version)

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), 274281
(arxiv version, Russian version)

Filonov N., Kachkovskiy I.,
Absolute continuity of the Schrödinger operator spectrum in a multidimensional cylinder,
St. Petersburg Mathematical Journal, 21 (2010), 95109 (Russian version)

Filonov N., Kachkovskiy I.,
A HilbertSchmidt analog of Huaxin Lin's Theorem

Dechevsky L., Kachkovskiy I.,
Sharp Estimates of the Constants of Equivalence Between Integral Moduli of Smoothness and Kfunctionals in the Multivariate Case,
Constructive Approximation, 32 (2010), issue 1, 7790
Invited seminar talks

UCLA Functional Analysis Seminar, 17 February 2016.

(upcoming) Special Colloquium, University of Kansas, 9 February 2016.

(upcoming) Special Colloquium, University of Nebraska  Lincoln, 4 February 2016.

(upcoming) Special Colloquium, University of Miami, 26 January 2016.

(cancelled) Interview talk, King's College London, January 2016. Cancelled due to visa/time constraints.

(upcoming) Special Colloquium, University of Arizona, January 2016.

(upcoming) Special Colloquium, Université de Montréal, 18 January 2016.

Special Colloquium, Michigan State University, 13 January 2016.

Caltech Mathematical Physics Seminar, 7 October 2015.
Conferences

(upcoming) Frontiers in Mathematical Physics, August  September 2016, CRM, Université de Montréal, Canada.

(upcoming) Young Researchers Symposium "Methods of Modern Mathematical Physics", August 2016, Fields Institute, Toronto, Canada.

(upcoming) Simons Center's Workshop: Between Dynamics and Spectral Theory, June 2016, Simons Center for Geometry and Physics, Stony Brook, NY.

(upcoming) Spectral Theory of Periodic, Quasiperiodic, and Random problems, June 2016, University College London.

AMS Fall Western Sectional Meeting, October 2015, California State University, Fullerton.

Spectral Properties of Quasicrystals via Analysis, Dynamics, and Geometric
Measure Theory, Banff International Research Station, September 2015, Oaxaca, Mexico.

26th International Workshop on Operator Theory and its Applications,
Tbilisi, Georgia, July 6  10, 2015.

7th St. Petersburg Conference in Spectral Theory, dedicated to the memory of M. Sh. Birman,
July 3  6, 2015, Euler Institute, St. Petersburg, Russia.

Almost Periodic and Other Ergodic Problems,
April 2015,
University of Cambridge, United Kingdom (coorganizer).

Periodic and Other Ergodic Problems,
April 2015,
University of Cambridge, United Kingdom.

AMS Sectional Meeting, March 2015, Michigan State University.

Hot Topics: KadisonSinger, Interlacing Polynomials, and Beyond, March 2015, Mathematical Sciences Research Institute, Berkeley, CA.

The Sixth M. Sh. Birman Conference in Spectral Theory,
July 3  8, 2014, Euler Institute, St. Petersburg, Russia.

USAUzbekistan Conference on Analysis and Mathematical Physics,
May 20  23, 2014,
California State University, Fullerton.

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.