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International Conference Mathematics Days in Sofia Institute of Mathematics and Informatics Bulgarian Academy of Sciences International Conference Mathematics Days in Sofia July 7–10, 2014, Sofia, Bulgaria Abstracts Sofia, 2014 Programme Committee Mini-symposia Organizers Algebra, Logic, and Combinatorics Advanced Analytical and Numerical Techniques for Applications Vesselin Drensky, Bulgaria – Chair Ludmil Katzarkov, USA Raytcho Lazarov, USA Analysis, Geometry, and Topology Algebraic Methods Oleg Mushkarov, Bulgaria in Quantum Field Theory Luchezar Stoyanov, Australia Vladimir Dobrev, Bulgaria Stanimir Troyanski, Spain Differential Equations Approximation Theory and Special and Mathematical Physics Functions – 2nd series Emil Horozov, Bulgaria Oktay Duman, Turkey Peter Popivanov, Bulgaria Esra Erku¸s-Duman, Turkey Georgi Popov, France Geometry Days in Sofia Mathematical Modeling Vestislav Apostolov, Canada Asen Donchev, USA Johann Davidov, Bulgaria Raytcho Lazarov, USA Gueo Grantcharov, USA Blagovest Sendov, Bulgaria Oleg Mushkarov, Bulgaria Nickolay Yanev, Bulgaria Velichka Milousheva, Bulgaria Mathematical Aspects of Computer Science Transform Methods and Special Functions – 7th Avram Eskenazi, Bulgaria Peter Stanchev, USA Virginia Kiryakova, Bulgaria Organising Committee Variational Analysis Julian Revalski, Bulgaria – Chair Asen Donchev, USA Krassimira Ivanova, Bulgaria Alexander Ioffe, Israel Neli Dimitrova, Bulgaria Mikhail Krastanov, Bulgaria Supported by AMERICAN FOUNDATION FOR BULGARIA NOVA TRADE Ltd. Copyright © 2014 Institute of Mathematics and Informatics of BAS, Sofia Content Preface ............................................ ..........................5 Plenary Talks ....................................... .........................7 Section: Algebra, Logic, and Combinatorics . ....................19 Invited Talks ....................................... ......................19 Communications ..................................... ....................24 Section: Analysis, Geometry, and Topology . ...................45 Invited Talks ....................................... ......................45 Communications ..................................... ....................52 Section: Differential Equations and Mathematical Physics . ..................65 Invited Talks ....................................... ......................65 Communications ..................................... ....................72 Section: Mathematical Modelling . .....................81 Invited Talks ....................................... ......................81 Communications ..................................... ....................84 Section: Mathematical Aspects of Computer Science . ................103 Invited Talks ....................................... .....................103 Communications ..................................... ...................108 Mini-symposium: Advanced Analytical and Numerical Techniques for Applications .................................... .................117 Invited Talks ....................................... .....................118 Communications ..................................... ...................122 Mini-symposium: Algebraic Methods in Quantum Field Theory ............125 Invited Talks ....................................... .....................126 Communications ..................................... ...................130 Mini-symposium: Approximation Theory and Special Functions 2nd series .......................................... .................175 Mini-symposium: Geometry Days in Sofia .................. ...............187 3 Mini-symposium: Transform Methods and Special Functions’14 ............195 Invited Talks ....................................... .....................196 Communications ..................................... ...................202 Mini-symposium: Variational Analysis . ....................225 Index of Speakers.................................... ......................240 List of Participants................................. ........................245 4 Preface The International Conference “Mathematics Days in Sofia” held in Sofia, Bul- garia, in the period July 7-th – July 10-th, 2014 is organized by the Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences. The purpose of this event is to present the current state of the art in all ar- eas of mathematics and computer science and its applications. One of the main goals of the Conference is to bring together Bulgarian mathematicians and com- puter scientists working all over the world. In this way, will expect to enrich the relations between the mathematicians working in Bulgaria and the Bulgarian mathematical diaspora. Our idea is to organize such conferences every 2–3 years and to make them tradi- tional scientific forums. Similar events were organized by the Institute of Mathe- matics and Informatics in 2007 celebrating the 60-th anniversary of the Institute and about 10 years ago by the Faculty of Mathematics and Informatics of the University of Sofia. The meeting includes the following sections: • Algebra, Logic, and Combinatorics; • Analysis, Geometry, and Topology; • Differential Equations and Mathematical Physics; • Mathematical Modelling (including Approximation Theory, Numerical Math- ematics, Probability and Statistics, Operations Research, and Biomathe- matics); • Mathematical Aspects of Computer Science; and the following mini-symposia: • Advanced Analytical and Numerical Techniques for Applications; • Algebraic Methods in Quantum Field Theory; • Approximation Theory and Special Functions (2nd series); 5 • Geometry Days in Sofia; • Transform Methods and Special Functions’14; • Variational Analysis. The Conference consists of 50-minutes invited plenary talks, 45-minutes invited talks for sections and mini-symposia and 30-minutes communications. The ple- nary and the invited section speakers are established Bulgarian and foreign sci- entists working in international recognized mathematical centers. More than 300 scientists from more than 40 countries will participate at the Conference. They will deliver more than 200 invited talks and communications. Vesselin Drensky Julian Revalski Chairman Chairman of the Programme Committee of the Organising Committee 6 Plenary Talks Cohomologically noetherian modules and rings Luchezar Avramov Department of Mathematics, University of Nebraska Lincoln, NE 68588-0130, USA [email protected] Keywords: Projective resolution, rate of growth, noetherian ring, cohomology products, center of triangulated category A starting point for the homological study of algebraic structures, such as modules or rings, is to “resolve” them by using constructions that involve only standard building blocks. Such resolutions are not uniquely defined, and it is of significant interest to work with “smaller” ones. In order to do this, one needs estimates for the sizes of resolutions, as well as necessary and/or sufficient conditions for the existence of resolutions of prescribed sizes. Various approaches and results, both old and new, will be discussed in the talk. It will be directed to a general mathematical audience. 7 International Conference Mathematics Days in Sofia July 7–10, 2014, Sofia, Bulgaria Optimization problems with stochastic order constraints Darinka Dentcheva Department of Mathematical Sciences Stevens Institute of Technology Castle Point on Hudson, Hoboken, NJ 07030, USA [email protected] Keywords: stochastic dominance, increasing-convex order, risk quantification, du- ality, numerical methods of optimization Stochastic orders formalize preferences among random outcomes and are widely used in statistics and economics. We focus on stochastic optimization problems involving stochastic-order relations as constraints that relate performance func- tionals, depending on our decisions, to benchmark random outcomes. We discuss the relation of univariate and multivariate stochastic orders to utility functions, conditional value at risk, as well as general coherent measures of risk. Necessary and sufficient conditions of optimality and duality theory for problems with sto- chastic order constraints involve expected utility theory, dual (rank-dependent) utility theory, and coherent measures of risk, providing a link between various approaches for risk-averse optimization. Some attention is paid to the numerical treatment of the problems. Several applications will be outlined. Almost complex structures on quaternionic Kaehler manifolds Paul Gauduchon Centre de Math´ematiques, Ecole Polytechnique, France [email protected] Keywords: quaternionic Kaehler manifolds We show that compact quaternionic-Kaehler manifolds of positive type admit no globally defined almost complex structure, even in the stable sense, except for 8 Plenary Talks n+2 the complex Grassmannians Gr2(C ) Acknowledgements. This is joint work with Andrei Moroianu and Uwe Semmelmann. Kac-Moody algebras, Riemann-Hilbert problems and new soliton equations Vladimir S. Gerdjikov Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences Sofia, Bulgaria [email protected] Keywords: Kac-Moody algebras, Riemann-Hilbert problems, soliton equations We start with a Riemann-Hilbert Problem (RHP) with canonical normal- ization whose sewing functions depend on several additional variables. Using Zakharov-Shabat theorem we are able to construct a family of ordinary differ- ential operators for which the solution of the RHP is a common fundamental analytic solution [1–3]. This family of operators obviously commutes. Thus we are able
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