List of sessions
- Model Theory
- Piotr Kowalski
- Antongiulio Fornasiero
- Number Theory
In recent years Number Theory has been a very active area of research, with impressive new contributions coming from young mathematicians such as James Maynard and Peter Scholze. Important contributions have also been given by Polish and Italian number theorists, in some cases even joining forces; we cite as an example the long term and very fruitful collaboration between Alberto Perelli and Jerzy Kaczorowski. We plan to have talks representing the various areas of Number theory which are most actively studied in Italy and in Poland. Indeed, we plan to have talks whose topics range between the Selberg class and the analytic theory of L-functions, additive and computational number theory, the arithmetic aspects of elliptic curves and p-adic analysis and geometry.
- Łukasz Pańkowski
- Sandro Bettin
- Ilaria Del Corso
- Maciej Radziejewski
- Projective Varieties and their Arrangements
One of central problems in algebraic geometry is to describe subvarieties which can be embedded into a given variety and given such a subvariety to decide how “positive” the embedding can be. For example, it is well known that a rational variety cannot be embedded into an abelian variety or that there is just one special class of polarized abelian surfaces which can be embedded into the projective space P^4. One of methods to attack such problems consists of investigations of restriction maps of global sections of some line bundle L on the ambient variety X to a subvariety Y\subset X. In recent years there was increasing interest in arrangements of subvarieties, rather then in single species. It was motivated partly by problems in commutative algebra related to the so called containment problem. Arrangements of hyperplanes are a classical subject of study. Ideals of such arrangements provide interesting examples of ideals with many surprising properties. Important role is played by symmetries of various kinds. In the case of K3 surfaces and their natural generalizations prominent role is played by lattice theory. The purpose of the session is to bring together specialists in geometry and algebra to discuss recent progress and open problems.
- Tomasz Szemberg
- Maria Evelina Rossi
- Alessandra Sarti
- Sławomir Rams
- Algebraic Geometry
Algebraic geometry is a lively research area in both Italy and Poland; the goal of the proposed session is to highlight and share recent advances in the area, and also to foster and strengthen the scientific interactions between researchers from the two countries. We focus on both the classical and modern aspects, which include algebraic surfaces, toric varieties, K3 surfaces and hyperkahler manifolds, abelian and Prym varieties, with the research methods ranking from combinatorial fan-theoretic-considerations to applications of derived categories.
- Joachim Jelisiejew
- Cinzia Casagrande
- Algebraic Geometry and Interdisciplinary Applications
The classical Algebraic Geometry collaboration linking Italy and Poland has found in the last decade a new very productive and interactive path in the direction of Tensor Decomposition. From one side it takes the move from classical studies of Italians mathematicians like Segre and Polish ones like Zariski, from the other side it intersects the more recent necessity of finding a deep understanding to applications like Quantum Information, Phylogenetic, Signal Processing. In this session we want to give international visibility to this very active and collaborating community via some of the most active researchers in the field.
- Weronika Buczyńska
- Alessandra Bernardi
- Arithmetic Algebraic Geometry
Arithmetic algebraic geometry is concerned with the application of geometric ideas to number-theoretical questions. Geometry has proven to be a very rich source of representations of Galois groups of number fields, thus providing tools to handle arithmetical objects which are hard to approach in any other way. In this setting, abelian varieties, and especially Jacobians, have proven to be extremely useful objects: they serve as testing grounds for general conjectures, help with the resolution of Diophatine equations and provide us with ways of constructing not just single Galois representations, but compatible families of them. Arithmetic problems can be studied through the so-called L-functions, cohomology groups and point counts on varieties. This approach leads to still very conjectural motivic approach to varieties. That leads to Gauss-Manin connections associated with families of varieties and considerations of differential equations of algebraic and arithmetic origin.
- Bartosz Naskręcki
- Davide Lombardo
- Maciej Zdanowicz
- Group Theory
This special session is dedicated to Group Theory in general. Group Theory is a subject with a long tradition in Polish and Italian mathematics, and both countries boast large communities of researchers in this field. As an example, the Italian research project “Group Theory and Applications” has been developed among the Group Theory communities in the universities of Firenze, L’Aquila, Lecce, Milano, Milano Bicocca, Napoli, Padova, Salerno and Trento. The past years have seen many collaborations between the Polish and the Italian Academies, among which it is notable to mention the Conferences “Groups and Group Rings”. The aim of the session is to gather researchers working on different branches of Group Theory: finite groups, infinite groups, finite p-groups, profinite groups, and geometric group theory, representation theory of groups, characters etc. A special focus will be reserved to collecting contributions from the most active lines of research in Group Theory, as well as from new emerging fields. The hope of the organizers is to attract a significant number of young researchers, who will have the opportunity to explore the latest trends of Group Theory.
- Waldemar Holubowski
- Patrizia Longobardi
- Mercede Maj
- Geometric Function and Mapping Theory
In the past century there has been an increasing interest in nonlinear potential theory, analysis in metric measure spaces and their relations and applications to variational calculus and PDE’s. At the core of these topics lies geometric function and mapping theory, with roots in complex analysis. These areas of research attracted a lot of scientific cooperation between Polish and Italian mathematicians in the past; our aim is to bring together people working in the field, encouraging and facilitating further exchange of ideas.
- Tomasz Adamowicz
- Valentino Magnani
- Paweł Goldstein
- Complex Analysis and Geometry
Application of PDE techniques in geometry has a long history and is still a very active field of mathematics today. The proposal aims at presenting new results and research directions dealing with complex nonlinear PDEs and their applications to complex differential and algebraic geometry. Topics will include equations of complex Monge-Ampere type, almost-complex geometry, canonical metrics in complex geometry as well as aspects of hermitian geometry.
- Sławomir Dinew
- Adriano Tomassini
- Giorgio Patrizio
- Sławomir Kołodziej
- Optimization, Microstructures, and Applications to Mechanics
The session will be devoted to analytical and variational studies of topics on fracture, dislocations, microstructures, homogenization which are possibly related to partial differential equations and functional analysis tools.
- Agnieszka Kałamajska
- Elvira Zappale
- Variational and Set-valued Methods in Differential Problems
The planned session will be devoted to recent developments on variational and set-valued techniques and their applications to various differential problems. The use and the importance of such methods stems in particular from their potential applications in studying the existence and multiplicity of solutions and their behavior, dynamics and asymptotics, obtained via analytical or topological methods. The results to be discussed during the session deal with ordinary and partial differential equations and systems also in a non-smooth variational setting, i.e., involving convex or locally Lipschitzian functionals (subgradients, generalized gradients in the sense of Clarke etc.) nonlinear non-smooth optimization and variational inequalities.
- Wojciech Kryszewski
- Pasquale Candito
- Salvatore Marano
- Marek Galewski
- Topological Methods and Boundary Value Problems
The planned session is devoted to recent advances in topological methods and boundary value problems (BVPs). For elliptic problems, the session will be focused on stationary solutions, their bifurcation, multiplicity, localization and stability. For time dependent BVPs, the dynamics problems will be studied, such as: existence and properties of attractors or general invariant sets, periodic solutions or singular limits. Special attention will be paid to geometric and computational aspects of these problems. The topological methods studied and used in this context include homotopy invariants as the topological degree, the fixed point index, Conley-type indices as well as the theory of dynamical systems. Within the session motivations and applications to real world phenomena will also be discussed.
- Aleksander Ćwiszewski
- Gennaro Infante
- Variational Problems and Nonlinear PDEs
Our goal is to bring together young as well as established scientists working on nonlinear PDEs related to variational problems arising in mathematical physics, to exchange ideas, to give the opportunity to report on recent progress and to facilitate cooperation. In particular we want to focus on existence, multiplicity and qualitative properties of solutions of nonlinear differential equations and systems with variational structure, e.g. Schödinger and Maxwell equations as well as other types of elliptic equations
- Jarosław Mederski
- Pietro d’Avenia
- Nonlinear Variational Methods with Applications
The session aims at presenting the state-of-the-art and current research on nonlinear PDEs related to variational problems (variational equations and variational inequalities), with a particular attention to the applications. In particular, our goal is to bring together scholars working on variational inequalities applied to equilibrium problems, duality theory, Lagrange theory as well as on nonlinear boundary value problems, focusing on existence and regularity of the solutions to elliptic and parabolic equations or systems.
- Anna Zatorska
- Sofia Giuffrè
- Advances in Kinetic Theory
In recent times the study of particle systems has received a considerable attention by the mathematical community in various areas of applications. These range from well-established ones, such as gas and fluid dynamics or multi-component systems, to those including socio-economic systems, vehicular traffic, crowd dynamics, biological systems, to mention just a few. Models typically aim at characterising the aggregate trends of the systems, which emerge spontaneously from the microscopic interactions among the particles. In this respect, the kinetic theory has proved to offer an extremely flexible mathematical framework for describing and linking different manifestations at different scales of such phenomena. The goal of this thematic session is to help disseminate and keep a debate alive around recent advances in modelling, analysis and numerics of multi-agent and fluid systems with the methods of kinetic theory.
- Ewelina Zatorska
- Andrea Tosin
- Mathematical Modelling for Complex Systems: Seeking New Frontiers
As complex system we mean a system composed of several living entities which interact among themselves and with the outer environment. A broad variety of living systems can be considered as complex, spanning from biological systems to systems whose dynamics receives important inputs from human behaviors, as an example crowd and traffic dynamics, swarms, opinion formation, political dynamics. New ideas and new mathematical methods are needed to understand the main features of the behavior of such living, and hence, complex systems: as a consequence, the interest of mathematicians in new structures is a fascinating field of research in mathematical sciences. We propose this thematic session with the main aim to bring together mathematicians which are strongly involved in this broad research topic, sharing different mathematical approach to the modelling issues and different fields of application. In our opinion, a thematic session is a great opportunity to share the knowledge and to contribute to the search of the most appropriate mathematical tools toward the ambitious target of seeking new frontiers for a new mathematical theory.
- Mirosław Lachowicz
- Elena De Angelis
- Advances in Nonlinear Elliptic and Parabolic PDEs: from local to nonlocal problems
We aim to bring together senior and young researchers to interact and expose recent developments on topics in the thriving field of nonlinear and nonlocal, elliptic and parabolic Partial Differential Equations. In this field there are many interesting open questions, both theoretical and inspired by concrete applications: important examples can be found in swarming dynamics in life sciences, LÃ©vy processes in mathematical finance, synchronization phenomena in quantum physics, collective behavior phenomena in social sciences or granular media in engineering. This is an opportunity to overview the latest progress in these directions. Session website
- Miłosz Krupski
- Bruno Volzone
- Matteo Bonforte
- Piotr Biler
- Nonlinear Partial Differential Equations and Related Function Spaces
This mini-symposium will focus on recent developments on the theory of nonlinear elliptic and parabolic partial differential equations. Besides classical nonlinear equations special emphasis will be put on equations governed by unconventional nonlinearities. This includes growth conditions of non-polynomial, possibly anisotropic, type. Equations with data below the regularity of natural dual space will also be a topic of interest. Accordingly, the analysis of nonstandard function spaces that provide a natural functional framework for partial differential equations of these kinds, will fall among our objectives.
- Iwona Skrzypczak
- Angela Alberico
- Nonlinear Diffusion Problems
The aim of the session will be a presentation of recent results concerning large-time and finite- time behaviour of solutions of nonlinear hyperbolic and parabolic partial differential equations and systems of hyperbolic-parabolic type. Included (but not only limited to) will be the porous media equation, Fujita equation, first order hyperbolic conservation laws and systems arising as models of tumor growth and turbulence theory.
- Jan Goncerzewicz
- Alberto Tesei
- Geometric Properties of Solutions of PDEs and Nonlocal Equations
Geometric properties of solutions to elliptic and parabolic equations are a classical subject of investigation. Examples are: convexity and symmetry properties of solutions or their level sets, overdetermined problems, optimization and isoperimetric problems for eigenvalue, etc. Although the related literature is huge, there are still open problems and there is still activity around classical subjects and new perspectives. This session will focus on recent advances in this area, with a special attention to generalizations to the framework of non local equations.
- Tadeusz Kulczycki
- Paolo Salani
- New Perspectives in Singular Hamiltonian Systems
The aim of this session is to bring together top researches from Italy and Poland, working mainly in Hamiltonian and Lagrangian dynamics, as well as graduate students who had the opportunity to learn from and connect with the experts in the field. The emphasis of the talks will be on singular Lagrangian systems or singular Hamiltonian systems and especially on the relation between the variational and the dynamical properties as well as the role of the singularities. A central role will be played by the N-body and the N-vortex problem (and their variants) and will be discussed potential applications of the obtained results to celestial mechanics, and dynamical systems in general. A lot of efforts will be devoted to develop new topological and analytical techniques, methods and tools necessary in order to tackle the most challenging and hard problems in the field.
- Joanna Janczewska
- Alessandro Portaluri
- Marek Izydorek
- Ergodic Theory and Topological Dynamics
The goal of the session is to bring together Italian and Polish specialists in the widely understood area of dynamical systems, with the focus on results and methods relying on ergodic theory of measure-preserving transformations and topological dynamics on compact metric spaces.
- Tomasz Downarowicz
- Anna Giordano Bruno
- Stafano Marmi
- Krzysztof Frączek
- Hutchinson-Barnsley Theory of Fractals
The session is devoted to some aspects of the Hutchinson-Barnsley theory of fractals. In particular, we are going to discuss the problem of detecting those compact spaces which are/are not fractals generated by iterated function systems. We will be also interested in topological properties of families of fractals generated certain types of IFSs. Last but not least, proposed session will be a great chance to gather together and share experience between mathematicians from Italy and Poland who have been working on IFS theory in the last years.
- Grażyna Horbaczewska
- Emma D’Aniello
- Magdalena Nowak
- Filip Strobin
- Harmonic Analysis
The session is devoted to harmonic analysis. Italian and Polish harmonic analysts have been collaborating for many years. These collaborations have involved other European mathematical centers. The goal of the session is to continue and strengthen these interactions and open them for new topics. During the session we shall discuss recent developments in subjects such as: spectral multipliers and multilinear multipliers, maximal functions, singular integrals and flag kernels, analysis on Lie groups and manifolds, Hardy spaces. We shall also discuss connections of harmonic analysis with partial differential equations, number theory and probability.
- Błażej Wróbel
- Andrea Carbonaro
- Jacek Dziubański
- Fulvio Ricci
- Nonlinear Operators, Approximation Algorithms for Operator Equations and Related Problems
The goal of the session is to present some topics related to the existence of fixed points of nonlinear mappings, to the approximation of fixed points of nonlinear operators and of zeros of nonlinear operators and to the approximation of solutions of variational inequalities. Topics of interest include also differential equations and their infinite systems, nonlinear integral equations and their infinite systems, optimization problems and their algorithmic approaches, iterative approximations of zeros of accretive-type operators, iterative approximations of solutions of variational inequalities problems or split feasibility problems and applications. We will focus on the latest achievements and present newest and extended coverage of the fundamental ideas, concepts and important results on the above topics.
- Agnieszka Chlebowicz
- Giuseppe Marino
- Tomasz Zając
- Noncommutative Harmonic Analysis, Noncommutative Probability and Quantum Groups
The session will be a forum for presentation of recent results and developments in Levy processes on quantum groups, models of noncommutative independences, relations of classical and free probability, positive definite functions on Coxeter groups, quantum Markov semigroups, ergodic properties in quantum probability.
- Marek Bożejko
- Franco Fagnola
- Janusz Wysoczański
- Topology and Logic in Algebra and Functional Analysis
The purpose of the session is to bring together well-known specialists and young researchers working in set theory, topology and logic, with applications to selected topics of modern algebra and functional analysis, especially including theory of Banach spaces and lattices, algebras of operators, spaces of measurable functions, spaces of continuous functions C(X) over compact X, and including also some various situations where these research areas interact.
- Jerzy Kąkol
- Libor Vesely
- Clemente Zanco
- Grzegorz Plebanek
- Operator Theory, Operator Algebras and Applications
The session will gather Polish and Italian specialists from the field of operator theory. The main topic will be operators on Banach and Hilbert spaces and operator algebras. The following topics are of interest: Fredholm theory, perturbation theory, unbounded operators, normal operators and related classes, special operators (e.g. Toeplitz operators), semigroup theory, positivity, C*-algebras, von Neumann algebras and partial O*-algebras. Applications in finance or mathematical physics are welcome.
- Michal Wojtylak
- Camillo Trapani
- Piotr Niemiec
- Operator Semigroups: New Challenges and Applications
The theory of strongly continuous operator semigroups is a mature but at the same steadily evolving field serving as a common denominator for many other areas of mathematics, such as for instance the theory of partial differential equations, complex analysis, harmonic analysis, topology and stochastic processes. The aim of the meeting is to bring together top-rank researchers from Italy and Poland whose main interests are concentrated around the study of qualitative and quantitative properties of operator semigroups as well as world leading experts in various applications of semigroups ranging from mathematical biology to mathematical physics and to initiate a fruitful interchange of ideas from complementary areas of expertise in semigroup theory. In particular, experts from PDE theory will learn new abstract methods to treat concrete equations arising in applications and experts in abstract parts of evolution equations and semigroup theory will get a new set of attractive concrete problems to handle by operator semigroups machinery. Other goals of the mini-symposium include the assessment of the state of the art of the theory of operator semigroups as well as the identification of new challenges.
- Yuri Tomilov
- Diego Pallara
- Set Theory and Topology
Set theory and set-theoretical topology are traditional areas of research in Poland and in Italy with active research groups in Wroclaw and Turin. The proposed session will concern current topics in descriptive set theory, infinite combinatorics, forcing, cardinal characteristics of the continuum, topological applications of set theory.
- Robert Rałowski
- Matteo Viale
- Paweł Krupski
- Computational Aspects of Applied Topology
Algebraic topology is gaining a lot of attention and visibility as a rigorous mathematical tool to understand the shape of data and subsequently to solve many fundamental and practical problems in mathematics, sciences and beyond. The topological descriptor of data turned out to be useful in engineering, dynamical systems, material and life sciences and many other disciplines. This session will bring together scientists to discuss new algorithms to compute existing topological invariant and to discover new, commutable and stable topological and geometrical invariant. It will also summarize new and existing applications of topological tools.
- Pawel Dlotko
- Massimo Ferri
- Maurizio Garrione
- Geometric Aspects of Applied Topology
The proposed session aims at presenting theoretical methods in topology that focus on applications in the sciences and engineering. The following broad research themes will be covered: (a) Topological analysis of shapes, images, and signals; (b) Topogical methods for motion planning and the study of configuration spaces of mechanical systems; (c) Topological study of systems and networks; (d) Topological Data Analysis and visualization; (e) Combinatorial Algebraic Topology; (f) Directed homotopy and concurrency problems. Research on these themes is currently spread worldwide, but Polish and Italian researchers play a major role established by their pioneering work in the last thirty years and currently even increasing.
- Jose Carrasquel
- Claudia Landi
- Wacław Marzantowicz
- Ulderico Fugacci
- Geometric Topology, Manifolds, and Group Actions
One goal of this session is to present topics from geometric topology. In particular, recent developments in the study of low-dimensional manifolds will be discussed, focusing on geometric structures and presentations of manifolds via combinatorial and topological methods such as branched coverings, spines, polyedra, and Dehn surgery. Topics concern also related research areas such as knot theory (classical and high-dimensional) and geometric group theory.
Another goal of this session is to present constructions of quasimorphisms on the groups of area preserving diffeomorphisms of oriented surfaces, and relate them to the topological entropy and conjugacy invariant norms.
One more goal of this session is to study the structure of single automorphisms and automorphism groups of free groups. On the groups side, the focus is on stable and unstable twisted cohomology groups and the property (T), and on the single automorphism side — on the induced extensions of free groups, mostly inspired by Thurston’s approach to fundamental groups of 3-manifolds.
This session includes also a discussion about solvable compact Clifford-Klein forms on non-compact homogeneous spaces. In particular, some conditions will be presented, under which a semisimple homogeneous space does not admit any solvable compact Clifford-Klein form.
Moreover, group actions on manifolds will be discussed, including Hamiltonian group actions on symplectic manifolds, smooth finite group actions on spheres with isolated fixed points, group actions on Cartesian products of spheres and asymmetric manifolds, the existence and nonexistence problems for equivariant maps between representation spheres, and the related Borsuk-Ulam property for finite group actions on spheres, as well as some Borsuk-Ulam type property of virtual representation spaces of finite groups.
- Światosław Gal
- Carlo Petronio
- Mattia Mecchia
- Krzysztof M. Pawałowski
- Stochastic Analysis and Nonlocal PDEs
The session is devoted to stochastic and analytic methods for local and nonlocal operators, including stochastic differential equations, estimates and construction of semigroups of operators, potential theory, variational methods, boundary value problems, Markov processes.
- Krzysztof Bogdan
- Enrico Priola
- Financial Mathematics
This session will be devoted to applications of advanced stochastic calculus and probability theory to solve problems arising in finance and insurance. This may include (but not be limited to) stochastic integration, martingale theory, variational inequalities, and LÃ©vy processes.
- Zbigniew Palmowski
- Marzia De Donno
- Differential Inclusions and Controlled Systems
The scope of the session will focus on the recent developments in the theory of differential inclusions and control problems for dynamical systems as well as their broad applications. Topics of the session include also (but are not limited to) systems with stochastic perturbations, optimization problems and related topics including real life problems of mechanics, biology, economy and other applications.
- Mariusz Michta
- Irene Benedetti
- Jerzy Motyl
- Tiziana Cardinali
- Stochastic Models of Molecular Anomalous Diffusion and Fractional Dynamics
Three Nobel Prizes awarded within a short five year period (2009 in Physiology or Medicine, 2012 and 2014 in Chemistry) were related to the biological mechanisms in living cells and the fluorescence-based techniques of observing these mechanisms under the microscope. This caused a dramatic increase of experimental and theoretical achievements in the study of living cells worldwide. In this session we focus on an anomalous diffusion phenomenon observed recently in single-molecule experiments, which largely departs from the classical Brownian diffusion theory. The concept of anomalous diffusion and related notion of fractional dynamics has deeply penetrated the statistical and chemical physics communities, yet the subject has also become recently a major field in applied mathematics. The main objective of the session is to bring together researchers, practitioners of physics, biology and mathematics whose work is related to anomalous diffusion, fractional dynamics, intercellular biology, single particle tracking experiments and stochastic processes.
- Krzysztof Burnecki
- Carlo Manzo
- Gianni Pagnini
- Aleksander Weron
- Probability Measures – Structures, Identification and Characterizations
In the session a wide range of topics of modern probability theory will be covered. Special emphasis will be on structural properties of probability measures defined on different algebraic structures. In particular, the following themes will be discussed: characterizations related to independence of random matrices; time change for stochastic processes with a relation to fractional differential equations; identifiablity of distributions by properties of random walks; generalized convolutions and related random walks; geometry of random eigenfunctions; multivariate root inverse Gaussian distribution with its relation to some integrals in Rn; generalizations of gamma random matrices.
- Jacek Wesołowski
- Mauro Piccioni
- Dependence Modelling and Copulas
The session will deal with copula methods in multivariate stochastic modeling. The special emphasis will be put to financial, risk management and hydrological applications. Copulas are mathematical objects that fully capture the dependence structure among random variables and offer a great flexibility in building multivariate stochastic models. Since their discovery in the early 50 s, copulas have led to a much better understanding of stochastic dependence and allowed to break away from the multivariate Normal distribution, which generally underestimates the probability of joint extreme risks. Copula-based dependence models are rapidly gaining considerable popularity in several fields and are becoming indispensable tools in biostatistics, econometrics, hydrology, finance, insurance, and risk management. Several challenging problems are related to favor these models. First, the discrete nature of the dimensionality typically introduces non-trivial combinatorial problems, especially if the dimension of the problem is large. Constructing a multivariate distribution function required a matching stochastic model or unfeasible computations. Constructing multivariate stochastic processes with an intuitive and flexible dependence structure is also difficult. On the other hand, the financial and insurance industry (among many other fields of applications) have recognized miss-specified dependence structures as a major risk. For instance, pricing and risk management of portfolios is impossible without a firm understanding of the interactions between the involved objects.
- Piotr Jaworski
- Carlo Sempi
- Fabrizio Durante
- Challenges and Methods of Modern Statistics
This session will gather speakers representing different areas of modern statistics. The speakers will present a wide variety of talks concerning advanced methods of the analysis of contemporary data, ranging from advanced mathematical theory behind modern methods of data analysis to the applications for real life data problems. The specific topics will include the statistical analysis of graphical models and large data sets, contemporary Bayesian statistics and mathematical algorithmic developments behind advanced methods of data analysis.
- Malgorzata Bogdan
- Fabrizio Ruggeri
- Piotr Zwiernik
- Recent Advances in Numerical Modeling for Differential Problems
This session is focused on illustrating recent advances in the numerical modeling of evolutionary problems, mainly given by differential systems arising from the spatial semidiscretization of partial differential equations. The contributions highlight modern approaches providing a significantly better balance between accuracy and stability properties with respect to existing numerical methods (this is possible, for instance, within the general class of multivalue numerical methods) and efficiently retain qualitative properties of the solution of the problem (this is the case, for instance, of adapted numerical methods for oscillatory problems, which are able to accurately preserve the oscillatory character with a lower computational effort with respect to standard numerical schemes).
- Zbigniew Bartoszewski
- Raffaele D’Ambrosio
- Computational Mathematics: Discrepancy and Complexity
Computational mathematics has been a constantly growing field driven by the need to solve numerically more and more complicated problems of physics, chemistry, economics, or finance. A particular role play high-dimensional problems that occur almost everywhere and are best exemplified by multivariate integration. The focus of this session is on multivariate integration and discrepancy, as well as on computational complexity and algorithms for solving such important problems of computational mathematics as function approximation and (ordinary and stochastic) differential equations.
- Leszek Plaskota
- Giancarlo Travaglini
- Grzegorz Wasilkowski
- Stefano De Marchi
- Quantitative Techniques for Complex Real-Life Applications
Several applications in real-life context imply decisions in complex environment. The decision maker have to choose the best solution among several options leading to combinatorial optimization problems. The intrinsic complexity of the environment, forces the decision maker to take into account several criteria simultaneously, leading with multi-objective optimization. In addition, often, data are not known with precision, rather a probability distribution is available allowing the decision maker to handle stochastic programming problem. In others applications, it is not possible to define probability distribution. In this context, robust optimization is applied which solutions remain optimal/feasible in the case of changing in the data given a risk aversion of the decision maker. The aim of the session is to collect works leading with mathematical formulation and solution approaches for combinatorial optimization problems arising in real-life applications in multi-objective, constrained, and uncertain environment.
- Piotr Bilski
- Francesca Guerriero
- Luigi Di Puglia Pugliese
- Janusz Granat
- Multiscale Models in Mathematical Biology
Biological processes involve many different phenomena which occur at various scales. Usually we distinguish three main scales: the molecular scale (including genes expression and the genome modification), the cellular scale, and the macroscopic scale which describes the physiological systems of cells, tissues etc., but in ecological modeling we also consider populational and environmental scales. The changes on one scale can influence or can be influenced by processes acting in other scales. Cancer is one of processes in which coupled mechanisms interact across multiple scales. We will discuss singular perturbation techniques and time delays in stochastic dynamical systems. Our models include gene expression and regulation and anticancer models and therapies.
- Jacek Miękisz
- Luigi Preziosi
- Ryszard Rudnicki