Hovik Matevossian^{1}
, Dimitrios Vlachos^{2}

^{1}Russian Academy of Sciences, Federal Research Center "Computer Science and Control", Russian Federation

^{2}University of Peloponnese, Department of Informatics and Telecommunications, Greece

This Workshop contains all the submissions that have not been assigned in other specific Workshops. Upon the finalization of the Technical Program, submissions in the Core Workshop will be assigned to Presentation Slots according to their subject.

Robert Finn^{1}
, Rajat Bhatnagar^{2}

^{1}Stanford University, Mathematics, United States

^{2}Verge Genomics, , United States

The modern theory of capillarity originated in achievements of Laplace in 1806, based on insights introduced by Thomas Young in 1805. There followed a single definitive work of Gauss in 1830, and then an interlude of well over a century, during which the topic received little attention. In contemporary times, the demands of space exploration and also of medicine, of biology and of industrial procedures have been inspiring new developments of varying character. These have been appearing in frequently uncoordinated ways and often in ignorance of related developments from other sources. We note recent announcements of active interest, appearing in journals as disparate in their structures and goals as the J. Am. Chem. Soc., Physics of Fluids, and J. reine angew. Math. Much is now happening, independent new insights are emerging, and a new and broader theory will certainly ensue. The venue of this conference can be expected to be instrumental in that development and to offer opportunities for cooperation among investigators with varying backgrounds and points of view. To that effect we intend to invite explicitly to this Workshop major contributors from all fields, who are known to us. We emphasize additionally that we welcome unaccustomed insights, and we thus encourage others who may wish to speak to send summaries of the material to rfinn@stanford.edu for consideration, based on its perceived relevance and interest for the topic.

Pavel Kurasov^{1}
, Sergey Naboko^{2}
, Andrey Shkalikov^{3}
, Victor Vlasov^{4}

^{1}Stokholm University, , Sweden

^{2}Saint Petersburg State University, Mathematical Physics, Russia

^{3}Lomonosov Moscow State University, Mechanics and Mathematics, Russia

^{4}Lomonosov Moscow State University, Mechanics and Mathematics, Russia

Classical analysis. Real and Complex analysis in one and several variables, potential theory. Asymptotics. Spectral theory, scattering, inverse problems. Variational methods and calculus of variations. Harmonic analysis. Linear and non-linear functional analysis. Banach spaces. Non-commutative geometry, spectra of random matrices. Asymptotic geometric analysis. Metric geometry and applications. Geometric measure theory.

Vincent Caudrelier^{1}
, Hovik Matevossian^{2}
, Mikhail Surnachev^{3}

^{1}University of Leeds, School of Mathematics, United Kingdom

^{2}Russian Academy of Sciences, Federal Research Center "Computer Science and Control", Russian Federation

^{3}Keldysh Institute of Applied Mathematics RAS, Computational AeroAcoustics Laboratory, Russia

Modeling physical systems using PDEs has been the object of science for centuries and has taken a multitude of forms over time. In many situations, one fundamental aspect of this process is to identify and isolate the system of interest from a possible environment. Mathematically, this translates into boundary-value or initial-boundary value problems for nonlinear PDEs whereby the boundary conditions encode the connection between the system and the "rest of the world". A big challenge is to find boundary conditions that are both physically relevant (modeling) and mathematically appropriate (well-posedness problems). This old theme is being actively revived directly or indirectly by several developments that shape the next step of Mathematical Physics: out-of-equilibrium systems, where one can drive a system out of equilibrium by external forcing; PDEs on graphs as models of complex systems, where one can describe evolutionary processes on graphs with certain boundary conditions at the vertices. Integrable and exactly solvable systems are known to play an important role in establishing a better understanding of fundamental issues in Mathematical Physics and these new developments are no exception. This workshop will aim at bringing together some of the latest developments in those areas and related methods.

Filippo Gazzola^{1}
, Alain Haraux^{2}
, Andrej Kon'kov^{3}
, Hovik Matevossian^{4}

^{1}Politecnico di Milano, Department of Mathematics, Italy

^{2}CNRS, Mathematics, France

^{3}Moscow Lomonosov State University, Differential Equations, Russia

^{4}Russian Academy of Sciences, Federal Research Center "Computer Science and Control", Russian Federation

Dynamical systems, including integrable systems. Equilibrium and non-equilibrium statistical mechanics, including interacting particle systems. PDE including fluid dynamics, wave equation, Boltzmann equation and material science. General relativity. Stochastic models and probabilistic methods including random matrices and stochastic PDE. Solvability, regularity, stability and other qualitative properties of linear and non-linear equations and systems. Spectral theory, scattering, inverse problems. Variational methods and calculus of variations. Algebraic methods, including operator algebras, representation theory and algebraic aspects of quantum field theory. Quantum field theory including gauge theories and conformal field theory. Geometry and topology in physics including string theory and quantum gravity.

Tatiana Shaposhnikova^{1}
, Tatyana Suslina^{2}

^{1}Lomonosov Moscow State University, Mechanics and Mathematics, Russia

^{2}St. Petersburg State University, Department of Mathematics and Mathematical Physics, Russia

Asymptotics. Spectral theory. Variational methods and calculus of variations. Homogenization of differential operators with rapidly oscillating coefficients. Error estimates of operator type. Homogenization and multiscale problems. Relations to continuous media and control. Modeling through PDE. PDEs including fluid dynamics, wave equation, Boltzmann equation and material science.

Gerard Lemaitre^{1}
, Jorge Linares^{2}
, Constantin MEIS^{3}

^{1}Aix Marseille Universite, Laboratoire d'Astrophysique Marseille, France

^{2}Université de Versailles St. Quetin en Yvelines, GEMAC, France

^{3}CEA , National Institute for Nuclear Science and Technology, France

Modeling in Physical Sciences

Hovik Matevossian^{1}

^{1}Russian Academy of Sciences, Federal Research Center "Computer Science and Control", Russian Federation

Mathematical Modeling in Science and Technology

Hovik Matevossian^{1}

^{1}Russian Academy of Sciences, Federal Research Center "Computer Science and Control", Russian Federation

Mathematical Aspects of Computer Science

Hovik Matevossian^{1}

^{1}Russian Academy of Sciences, Federal Research Center "Computer Science and Control", Russian Federation

Expectations from modern medicine are very high and this makes this field very demanding as far as the questions posed and the needed solutions are concerned, related to early diagnosis, effective therapy, accurate intervention, real time monitoring, procedures/systems/instruments optimization, error reduction and knowledge extraction. In parallel, following the explosive production of biological data concerning DNA, RNA and protein biomolecules, a plethora of questions has been raised regarding their structure, their function, the interactions between them, their relationships and their dependencies, their regulation and expression, their location and their thermodynamic characteristics. Furthermore, the interplay between medicine and biology leads to fields like molecular medicine and systems biology which are further interconnected with physics, mathematics, informatics and engineering creating new islands in the ocean of scientific interconnections like medical physics and biophysics, medical informatics, bioinformatics and computational biology, nanobiotechnology and astrobiology. We hope that this workshop will host exciting questions and intelligent algorithmic solutions in these interdisciplinary fields of medicine and biology bringing together scientists from different research fields into a creative and fertile scientific knowledge interchange.

Dimitrios Thomakos^{1}

^{1}University of Peloponnese, Department of Economics, Greece

Owing to masses of digital real-world data it is now possible to create and validate models of human behaviour. Of special interest are human activities connected to use of Internet - their habits, movements or likings. Simple models, basing on fundamental physical laws and phenomena can be of instant use in this case. The Workshop is also open to new techniques connected to data mining and statistics that can facilitate the process of models' input preparation as well as help to discover new non-trivial phenomena.

Dimitrios Vlachos^{1}

^{1}University of Peloponnese, Department of Informatics and Telecommunications, Greece

This workshop will focus on topics of complexity with special emphasis on complex networks and multiplex networks. Complex networks are studied in many diverse fields, such as mathematics, physics, biology, sociology, economics, and computer science. In recent years, the field has seen a tremendous growth. The session will focus on recent advances in the field and will include both theoretical and applied research in complex systems. Particular emphasis will be given to the interdisciplinary nature of complex networks. A wide range of topics will be covered, such as network structure and dynamics on networks, coupled networks, spreading, synchronization, visualization, algorithms, large-scale data analysis, as well as networks of interest to biology, sociology, computer science, economics, medicine, linguistics, etc.

Dimitrios Vlachos^{1}

^{1}University of Peloponnese, Department of Informatics and Telecommunications, Greece

Many differential equations, which are of interest in the physical sciences and engineering, exhibit geometric properties that are preserved by the dynamics. Discrete Lagrangian integrators, as a special type of geometric integration, has been recent interest in developing numerical schemes that preserve as many of these geometric invariants as possible. Such methods are of particular interest for problems that can be described by geometric mechanics, wherein the preservation of physical invariants such as the energy, momentum, and symplectic form can be important when simulating long-time dynamics of such systems. The aim of the session is to bring together researchers in mathematics, computer science, physical sciences, and engineering, who are interested in the broad area of numerical methods (for ordinary differential equations to partial differential equations) that preserve the underlying structure of the governing differential equations.

Dimitrios Vlachos^{1}

^{1}University of Peloponnese, Department of Informatics and Telecommunications, Greece

Computational nanoscience in particular and Computational Material Science in general, are rapidly developing fields providing computer simulational and theoretical background for understanding of nanoscale phenomena and nanotechnology research. Computational nanoscience overarches the whole spectrum of science including biology, physics, engineering, material science and chemistry, describing the behaviour of matter at the scale of individual atoms and molecules. This session will concentrate on novel computational approaches used in nanoscale research, including: Quantum Monte Carlo, Molecular Dynamics, Density Functional Theory, Time-Dependent Quantum Dynamics Simulations, Interaction of Nanoscale Materials and Laser Fields, Quantum Transport in Nanoscale Materials, Multiscale Modeling of Nanoscale Materials, Novel Computational Approaches, Electronic Structure Calculations and Attoscale Dynamics.