Dmitry Melnikov

Principal invited lecturer


Professor Dmitry Melnikov graduated from the Lomonossov Moscow State University in 2003. He defended a postgraduate title (Russian PhD equivalent) in 2006 and received PhD from Rutgers University in 2008. Professor Melnikov is a permanent member of the Mathematical Physics Group at the Institute for Theoretical and Experimental Physics (Moscow). HIs current interests are String theory, holography, AdS/CMT correspondence, baryons and QCD at high temperature and density, physics beyond the Standard Model.


Research Field


String Theory

Historically string theory is a branch of theoretical physics which addresses conceptual problems of high energy (particle) physics. In particular, it is an attempt to build a consistent theory of quantum gravity and a candidate theory for the unification of all known physical interactions. Formal string theory employs very advanced mathematical tools. Its developments has often generated a great return impact on various areas of mathematics. It is often viewed as a bridge connecting modern physics and mathematics. One of the breakthrough achievements of string theory is a realization of the holographic principle - a duality between gauge theories and theories of gravity. Holographic duality is currently the most actively developing direction of the theory. It provides a framework, which allows to study physical systems characterized by a strong interaction of its elements. The main example of such a system are quarks bound into mesons and baryons. However recent range of applications of the duality is much wider. Apart from models in particle physics it includes cosmological models, nuclear physics and condensed matter systems. Holography and other string theory methods are expected to bring a new insight and technology to the solution of the complex problems in these independent areas of physics.


Research Project


AGT Relation, Knots and AdS/CFT


Holographic Baryons and Instanton Crystals

Preprints | 2015

Knot invariants from Virasoro related representation and pretzel knots

Preprints | 2015

Chern-Simons Improved Hamiltonians for Strings in Three Space Dimensions

Preprints | 2015

Baryonic popcorn

Published | 2012 | J. High Energ. Phys. - 2012, November 09, 2012

On the AdS/BCFT approach to quantum Hall systems

Published | 2013 | J. High Energ. Phys. - 2013, December 31, 1969

Black holes in AdS/BCFT and fluid/gravity correspondence

Published | 2014 | J. High Energ. Phys. - 2014, November 14, 2014

Colored knot polynomials for arbitrary pretzel knots and links

Published | 2015 | Phys. Lett. B 743 (2015) 71

Matrix integral expansion of colored Jones polynomials for figure-eight knot

Published | 2015 | Jetp Lett. - 101, January 24, 2015

Chern-Simons improved Hamiltonians for strings in three space dimensions

Published | 2016 | Phys. Rev. D - 94, 8 July 2016

Topological transport from a black hole

Published | 2018 | Physics Letters B - 778, December 31, 1969

Circuit Complexity of Knot States in Chern-Simons theory

Published | 2019 | J. High Energ. Phys. (2019) 2019: 16

Lifshitz scaling, microstate counting from number theory and black hole entropy

Published | 2019 | J. High Energ. Phys. - 2019, June 13, 2019

Chern-Simons-Higgs model as a theory of protein molecules

Published | 2019 | Journal of Applied Physics - 126, December 28, 2019

Topological Indices of Proteins

Published | 2019 | Sci Rep - 9, December 10, 2019