### Research Interest

Dr. Durvudkhan Suragan received his Ph.D. in mathematics from Al-Farabi Kazakh National University in 2013. He has a master degree (with distinction) in theoretical physics from King’s College London. Prior to joining Nazarbayev University in April 2018, he served in the Department of Mathematics at Imperial College London as a research associate and at Institute of Mathematics and Mathematical Modeling (Almaty) as a leading researcher. His current research interests include analysis on Lie groups, applied mathematics (mathematical physics), PDE, potential theory and spectral geometry.

In 2013, Suragan was awarded the Konayev prize for young scientists (in Kazakhstan) for the best work in the field of natural sciences.

In 2018, Suragan won the Ferran Sunyer i Balaguer Prize. The prize is awarded for a mathematical monograph of an expository nature presenting the latest developments in an active area of research in Mathematics, in which the applicant has made important contributions. Suragan won the prize for his (with Professor Michael Ruzhansky, Imperial College London) monograph: Hardy inequalities on homogeneous groups, Progress in Mathematics, Vol. 327, Birkhauser, 2019. xvi+588pp.

Fractional logarithmic inequalities and blow-up results with logarithmic nonlinearity on homogeneous groups

Aidyn Kassymov, Michael Ruzhansky, Durvudkhan Suragan, **2020** In : Nonlinear Differential Equations and Applications. 27 , p 1

Green’s Identities, Comparison Principle and Uniqueness of Positive Solutions for Nonlinear p-sub-Laplacian Equations on Stratified Lie Groups

Michael Ruzhansky, Durvudkhan Suragan, **2019** In : Potential Analysis.

Hardy inequalities on homogeneous groups: 100 years of Hardy inequalities

Michael Ruzhansky, Durvudkhan Suragan, **2019** In : .

Hardy–Littlewood–Sobolev and Stein–Weiss inequalities on homogeneous Lie groups

Aidyn Kassymov, Michael Ruzhansky, Durvudkhan Suragan, **2019** In : Integral Transforms and Special Functions.

L
^{p}
-Caffarelli-Kohn-Nirenberg type inequalities on homogeneous groups

Tohru Ozawa, Michael Ruzhansky, Durvudkhan Suragan, **2019** In : Quarterly Journal of Mathematics. 70 , p 1 , p 305-318

On spectral and boundary properties of the volume potential for the Helmholtz equation

Tynysbek Sharipovich Kalmenov, Michael Ruzhansky, Durvudkhan Suragan, **2019** In : Mathematical Modelling of Natural Phenomena. 14 , p 5

Weighted anisotropic Hardy and Rellich type inequalities for general vector fields

Michael Ruzhansky, Bolys Sabitbek, Durvudkhan Suragan, **2019** In : Nonlinear Differential Equations and Applications. 26 , p 2

Weighted L^{p} -Hardy and L^{p} -Rellich inequalities with boundary terms on stratified Lie groups

Michael Ruzhansky, Bolys Sabitbek, Durvudkhan Suragan, **2019** In : Revista Matematica Complutense. 32 , p 1 , p 19-35

A comparison principle for nonlinear heat Rockland operators on graded groups

Michael Ruzhansky, Durvudkhan Suragan, **2018** In : Bulletin of the London Mathematical Society.

A note on stability of Hardy inequalities

Michael Ruzhansky, Durvudkhan Suragan, **2018** In : Annals of Functional Analysis.

Elements of Potential Theory on Carnot Groups

M. V. Ruzhansky, D. Suragan, **2018** In : Functional Analysis and its Applications. 52 , p 2 , p 158-161

Extended Caffarelli-Kohn-Nirenberg inequalities, and remainders, stability and superweights for Lp-weighted Hardy inequalities

Durvudkhan Suragan, Michael Ruzhansky, Nurgissa Yessirkegenov, **2018** In : Transactions of the American Mathematical Society, Series B. 5 , p 32-62

Green-type identities for Rockland operators on graded Lie groups

Manat Mustafa, Durvudkhan Suragan, **2018** In : Complex Analysis and Operator Theory. , p 1-8

Hardy-Littlewood, Bessel-Riesz, and fractional integral operators in anisotropic Morrey and Campanato spaces

Durvudkhan Suragan, Michael Ruzhansky, Nurgissa Yessirkegenov, **2018** In : Fractional Calculus and Applied Analysis. , p 577-612

Horizontal Weighted Hardy–Rellich Type Inequalities on Stratified Lie Groups

Bolys Sabitbek, Durvudkhan Suragan, **2018** In : Complex Analysis and Operator Theory. 12 , p 6 , p 1469-1480

Isoperimetric inequalities for the cauchy-dirichlet heat operator

Tynysbek Sh Kal’menov, Aidyn Kassymov, Durvudkhan Suragan, **2018** In : Filomat. 32 , p 3 , p 885-892

Isoperimetric inequalities for the heat potential operator

Tynysbek Sh Kal’menov, Aidyn Kassymov, Durvudkhan Suragan, **2018** In : Filomat. 32 , p 3 , p 903-910

$L^{p}$-Caffarelli-Kohn-Nirenberg type inequalities on homogeneous groups

Tohru Ozawa, Michael Ruzhansky, Durvudkhan Suragan, **2018** In : Quarterly Journal of Mathematics.

Sobolev Type Inequalities, Euler–Hilbert–Sobolev and Sobolev–Lorentz–Zygmund Spaces on Homogeneous Groups

Michael Ruzhansky, Durvudkhan Suragan, Nurgissa Yessirkegenov, **2018** In : Integral Equations and Operator Theory. 90 , p 1

Anisotropic L ^{2} -weighted Hardy and L ^{2} -Caffarelli-Kohn-Nirenberg inequalities

Michael Ruzhansky, Durvudkhan Suragan, **2017** In : Communications in Contemporary Mathematics. 19 , p 6

Caffarelli–Kohn–Nirenberg and Sobolev type inequalities on stratified Lie groups

Michael Ruzhansky, Durvudkhan Suragan, Nurgissa Yessirkegenov, **2017** In : Nonlinear Differential Equations and Applications. 24 , p 5

Geometric maximizers of Schatten norms of some convolution type integral operators

Michael Ruzhansky, Durvudkhan Suragan, **2017** In : Journal of Mathematical Analysis and Applications. 456 , p 1 , p 444-456

Hardy and Rellich inequalities, identities, and sharp remainders on homogeneous groups

Michael Ruzhansky, Durvudkhan Suragan, **2017** In : Advances in Mathematics. 317 , p 799-822

Inégalités de Caffarelli–Kohn–Nirenberg étendues et super-poids des inégalités de Hardy L^{p}-pondérées

Michael Ruzhansky, Durvudkhan Suragan, Nurgissa Yessirkegenov, **2017** In : Comptes Rendus Mathematique. 355 , p 6 , p 694-698

Inequalities for the eigenvalues of the Riesz potential

T. Sh Kal’menov, D. Suragan, **2017** In : Mathematical Notes of the Academy of Sciences of the USSR. 102 , p 5-6 , p 770-775

Isoperimetric Inequalities for Some Integral Operators Arising in Potential Theory

Michael Ruzhansky, Durvudkhan Suragan, **2017** In : . 216 , p 320-329

Layer potentials, Kac's problem, and refined Hardy inequality on homogeneous Carnot groups

Michael Ruzhansky, Durvudkhan Suragan, **2017** In : Advances in Mathematics. 308 , p 483-528

Local hardy and rellich inequalities for sums of squares of vector fields

Michael Ruzhansky, Durvudkhan Suragan, **2017** In : Advances in Differential Equations. 22 , p 7-8 , p 505-540

On Green functions for Dirichlet sub-Laplacians on H-type groups

Nicola Garofalo, Michael Ruzhansky, Durvudkhan Suragan, **2017** In : Journal of Mathematical Analysis and Applications. 452 , p 2 , p 896-905

On horizontal Hardy, Rellich, Caffarelli–Kohn–Nirenberg and p-sub-Laplacian inequalities on stratified groups

Michael Ruzhansky, Durvudkhan Suragan, **2017** In : Journal of Differential Equations. 262 , p 3 , p 1799-1821

On Isoperimetric Inequalities for the Cauchy-Robin Heat Operator

A. Kassymov, M. Sadybekov, D. Suragan, **2017** In : Mathematical Modelling of Natural Phenomena. 12 , p 3 , p 114-118

On S-Number Inequalities of Triangular Cylinders for the Heat Operator

Tynysbek Kal’menov, Aidyn Kassymov, Durvudkhan Suragan, **2017** In : . 216 , p 349-362

Some Spectral Geometry Inequalities for Generalized Heat Potential Operators

Aidyn Kassymov, Durvudkhan Suragan, **2017** In : Complex Analysis and Operator Theory. 11 , p 6 , p 1371-1385

Uncertainty relations on nilpotent Lie groups

Michael Ruzhansky, Durvudkhan Suragan, **2017** In : Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 473 , p 2201

Communications of the Moscow mathematical society

M. V. Ruzhansky, D. Suragan, **2016** In : Russian Mathematical Surveys. 71 , p 1 , p 157-158

Isoperimetric inequalities for Schatten norms of Riesz potentials

G. Rozenblum, M. Ruzhansky, D. Suragan, **2016** In : Journal of Functional Analysis. 271 , p 1 , p 224-239

Isoperimetric inequalities for the logarithmic potential operator

Michael Ruzhansky, Durvudkhan Suragan, **2016** In : Journal of Mathematical Analysis and Applications. 434 , p 2 , p 1676-1689

On first and second eigenvalues of Riesz transforms in spherical and hyperbolic geometries

Michael Ruzhansky, Durvudkhan Suragan, **2016** In : Bulletin of Mathematical Sciences. 6 , p 2 , p 325-334

On KAC’S principle of not feeling the boundary for the kohn laplacian on the heisenberg group

Michael Ruzhansky, Durvudkhan Suragan, **2016** In : Proceedings of the American Mathematical Society. 144 , p 2 , p 709-721

On permeable potential boundary conditions for the Laplace–Beltrami operator

T. Sh Kal’menov, D. Suragan, **2015** In : Siberian Mathematical Journal. 56 , p 6 , p 1060-1064

On spectral geometry for the one-speed particle transport operator

D. Suragan, **2015** In : Computational Mathematics and Mathematical Physics. 55 , p 5 , p 844-847

Initial-boundary value problems for the wave equation

Tynysbek Sh Kalmenov, Durvudkhan Suragan, **2014** In : Electronic Journal of Differential Equations. 2014

On eigenvalue problems of the one-speed neutron transport equation for isotropic scattering

D. Suragan, **2013** In : Annals of Nuclear Energy. 62 , p 468-470

On transparent boundary conditions for the high-order heat equation

D. Suragan, N. Tokmagambetov, **2013** In : Siberian Electronic Mathematical Reports. 10 , p 1 , p 141-149

Boundary conditions for the volume potential for the polyharmonic equation

T. Sh Kal'menov, D. Suragan, **2012** In : Differential Equations. 48 , p 4 , p 604-608

On a new method for constructing the Green function of the Dirichlet problem for the polyharmonic equation

T. Sh Kal'menov, D. Suragan, **2012** In : Differential Equations. 48 , p 3 , p 441-445

A boundary condition and spectral problems for the Newton potential

T. Sh Kalmenov, D. Suragan, **2011** In : . , p 187-210

To spectral problems for the volume potential

T. Sh Kal'menov, D. Suragan, **2009** In : Doklady Mathematics. 80 , p 2 , p 646-649

Determination of the structure of the spectrum of regular boundary value problems for differential equations by V.A. Il'in's method of anti-a priori estimates

T. Sh Kal'menov, D. Suragan, **2008** In : Doklady Mathematics. 78 , p 3 , p 913-915