I was previously at
Institute for Advanced Study and
University of California, Irvine.
Research interestests
My research is supported by the NSF grant
DMS1758326 "Spectral theory of periodic and quasiperiodic quantum systems" (2016  2019, formerly DMS1600422). I am mostly interested in

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

Almost commuting operators and applications to mathematical physics.

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

Transport properties of quantum spin systems and their effective Hamiltonians.
Education
Publications
 Bourgain J., Kachkovskiy I.,
Anderson localization for two interacting quasiperiodic particles, to appear in Geom. Funct. Anal. (2018).
 Kachkovskiy I.,
Localization for quasiperiodic operators with unbounded monotone potentials, submitted (2018).
 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.
 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.
 Kachkovskiy I.,
On transport properties of isotropic quasiperiodic $XY$ spin chains, Comm. Math. Phys. 345 (2016), no. 2, 659  673 (arxiv version)
 Jitomirskaya S., Kachkovskiy I.,
$L^2$reducibility and localization for quasiperiodic operators, Math. Res. Lett 23 (2016), no. 2, 431  444 (arxiv version)
 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)

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)

Kachkovskiy I.,
SteinTomas theorem for a torus and the periodic Schrödinger operator with singular potential,
St. Petersburg Math. J. 24 (2013), 939  948 (Russian version)

Filonov N., Kachkovskiy I.,
Polynomials of almost normal arguments in C*algebras,
J. Spectr. Theory 2 (2012), issue 4, 355  371 (arxiv version)

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)

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)

Filonov N., Kachkovskiy I.,
A HilbertSchmidt analog of Huaxin Lin's Theorem, preprint (2010)

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), no. 1, 77  90
Recent seminar talks

Virginia Tech Mathematical Physics seminar, April 18, 2018

Colloquium, Indiana University – Purdue University Indianapolis, March 23, 2018.

Colloquium talk, University of Alabama, Birmingham, October 2017.

University of Kentucky Mathematical Physics Seminar, November 2017.

Colloquium talk, University of Alabama, Birmingham, October 2017.

UC Irvine Mathematical Physics seminar, July 2017.

King's College Analysis Seminar, King's College London, January 2017.

IAS Mathematical Conversations, April 2017.

IAS Analysis and Mathematical Physics Seminar, November 2016.

UCLA Functional Analysis Seminar, 17 February 2016.

Caltech Mathematical Physics Seminar, October 2015.
Conferences

(upcoming) Spectral Theory of QuasiPeriodic and Random Operators, CRM, Montreal, November 2018.

PCMI Research Program , July 8  14, 2018.

AMS Spring Western Sectional Meeting, Portland State University, April 14  15, 2018.

36th Annual Western States Meeting in Mathematical Physics, UC Irvine, February 2018.

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

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

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

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.

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.
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.