I obtained my first Ph.D. in June 2012 under the supervision of Prof. S. Lakaev from Samarkand State University, Uzbekistan, in Mathematical Physics, and my second Ph.D. in 2017 under the supervision of Prof. G. Bellettini from Scuola Internazionale Superiore di Studi Avanzati (SISSA) and International Centre for Theoretical Physics (ICTP), Trieste, Italy, in Mathematical Analysis.

Since October 2017 I am Postdoctoral Associate in the Faculty of Mathematics of University of Vienna.

Currently, I am a Stand-Alone Grantee of the Austrian Science Fund (FWF). My CV is here.

My general research interests are in calculus of variations and geometric measure theory (CVGMT) and spectral theory (ST). More precisely:

• existence and regularity in CVGMT: free boundary problems (with or without elastic energy) including boundary discontinuities such as partitions, internal cracks, wetting, edge delaminations, debonding, brittle fractures; (anisotropic and crystalline) minimal surfaces; capillarity problems; area functional; higher order problems related to perimeter (such as Willmore problem);
• evolution in CVGMT: geometric evolution problems such as (anisotropic and crystalline) mean curvature flow, mean curvature flow of partitions; quasitatic evolution problems of elastic materials; nonlocal evolution problems;
• discrete Schrodinger operators in ST: coupling constant threshold phenomenon; multiparticle lattice systems, location of essential spectrum, existence of discrete spectrum, Efimov effect; asymptotics of eigenvalues.

• G. Bellettini, Sh. Kholmatov:
  Minimizing movements for the generalized power mean curvature flow.
  Submitted (2024).
• Sh. Kholmatov:
  Consistency of minimizing movements with smooth mean curvature flow of droplets with prescribed contact-angle in $\mathbb{R}^3$.
  Submitted (2024).
• G. Bellettini, Sh. Kholmatov, F. Almuratov:
  Crystalline hexagonal curvature flow of networks: short-time, long-time and self-similar evolutions.
  Submitted (2024).
• Sh. Kholmatov, P. Piovano:
  Existence of minimizers for the SDRI model in $\mathbb{R}^n$: Wetting and dewetting regimes with mismatch strain.
  Submitted (2023).

• Sh. Kholmatov:
  Minimizing movements for forced anisotropic curvature flow of droplets.
  Interfaces Free Bound. (2024).
• Sh. Kholmatov:
  On the minimality of the Winterbottom shape.
  Aequat. Math. (2024).
• Sh. Kholmatov, P. Piovano:
  Existence of minimizers for the SDRI model in 2d: Wetting and dewetting regimes with mismatch strain.
  Adv. Calc. Var. (2023).
• G. Bellettini, Sh. Kholmatov:
  Some aspects of anisotropic curvature flow of planar partitions.
  Ensaios Mat. 38 (2023), 23–76.
• Sh. Kholmatov, A. Khalkhuzhaev, M. Pardabaev:
  Expansion of eigenvalues of rank-one perturbations of the discrete bilaplacian.
  Monats. Math. 197 (2022), 607–633.
• Shokhrukh Kholmatov, Saidakhmat Lakaev, Firdavs Almuratov:
  On the spectrum of Schrödinger-type operators on two dimensional lattices.
  J. Math. Anal. Appl. 514 (2022), 126363.
• Saidakhmat Lakaev, Shokhrukh Kholmatov, Shakhobiddin Khamidov:
  Bose-Hubbard models with on-site and nearest-neighbor interactions: Exactly solvable case.
  J. Phys. A: Math. Theor. 54 (2021), 245201.
• Shokhrukh Kholmatov, Saidakhmat Lakaev, Firdavs Almuratov:
  Bound states of discrete Schrödinger operators on one and two dimensional lattices.
  J. Math. Anal. Appl. 503 (2021), 125280.
• Shokhrukh Kholmatov, Mardon Pardabaev:
  Asymptotics of eigenvalues of the zero-range perturbation of the discrete bilaplacian. .
  Lobachevskii J. Math. 42 (2021), 1285–1292.
• Giovanni Bellettini, Antonin Chambolle, Shokhrukh Kholmatov:
  Minimizing movements for forced anisotropic mean curvature flow of partitions with mobilities.
  Proc. Roy. Soc. Edinburgh Sect. A (2020).
• Shokhrukh Kholmatov, Paolo Piovano:
  A unified model for stress-driven rearrangement instabilities.
  Arch. Rational Mech. Anal. 238 (2020), 415–488.
• Giovanni Bellettini, Shokhrukh Kholmatov:
  Minimizing movements for mean curvature flow of droplets with prescribed contact angle.
  J. Math. Pures Appl. 117 (2018), 1–58.
• Giovanni Bellettini, Shokhrukh Kholmatov:
  Minimizing movements for mean curvature flow of partitions.
  SIAM J. Math. Anal. 50 (2018), 4117–4148.
• Shokhrukh Kholmatov, Zahriddin Muminov:
  Existence of bound states of N-body problem in an optical lattice.
  J. Phys. A: Math. Theor. 51 (2018).
• Giovanni Bellettini, Matteo Novaga, Shokhrukh Kholmatov:
  Minimizers of anisotropic perimeters with cylindrical norms.
  Comm. Pure Appl. Anal. 16 (2017), 1427–1454.
• Saidakhmat Lakaev, Shokhrukh Kholmatov:
  Asymptotics of the eigenvalues of a discrete Schrödinger operator with zero-range potential.
  Izvestiya: Mathematics 76 (2012), 946–966.
• Saidakhmat Lakaev, Shokhrukh Kholmatov:
  Asymptotics of eigenvalues of two-particle Schrödinger operators on lattices with zero-range interaction.
  J. Phys. A: Math. Theor. 44 (2011).