List of approved sessions
- Dependence Modelling and Copulas
- Algebraic Geometry
- Stochastic Analysis and Nonlocal PDEs
- Advances in kinetic theory
- Optimization, microstructures, and applications to Mechanics
- Variational and Set-valued Methods in Differential Problems
- Financial mathematics
- Mathematical Modelling for Complex Systems: Seeking New Frontiers
- Topological Methods and Boundary Value Problems
- New perspectives in singular Hamiltonian systems
- Operator theory, Operator algebras and applications
- Variational problems and nonlinear PDEs
Descriptions of sessions
- 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 (P.Jaworski@mimuw.edu.pl)
- Carlo Sempi (firstname.lastname@example.org)
- Fabrizio Durante (email@example.com)
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 (firstname.lastname@example.org)
- Cinzia Casagrande (email@example.com)
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 (firstname.lastname@example.org)
- Enrico Priola (email@example.com)
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 (firstname.lastname@example.org)
- Andrea Tosin (email@example.com)
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 (A.Kalamajska@mimuw.edu.pl)
- Elvira Zappale (firstname.lastname@example.org)
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 (email@example.com)
- Pasquale Candito (firstname.lastname@example.org)
- Salvatore Marano (email@example.com)
- Marek Galewski (firstname.lastname@example.org)
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 Lévy processes.
- Zbigniew Palmowski (email@example.com)
- Marzia De Donno (firstname.lastname@example.org)
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 (email@example.com)
- Elena De Angelis (firstname.lastname@example.org)
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 (email@example.com)
- Gennaro Infante (firstname.lastname@example.org)
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 (email@example.com)
- Alessandro Portaluri (firstname.lastname@example.org)
- Marek Izydorek (email@example.com)
The session will gather specialists from the field of operator theory on Banach and Hilbert spaces. A particular interest will be put on operator algebras. Applications in finance or mathematical physics are welcome.
- Michal Wojtylak (Michal.Wojtylak@im.uj.edu.pl)
- Camillo Trappani (firstname.lastname@example.org)
- Piotr Niemiec (Piotr.Niemiec@im.uj.edu.pl)
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.
- Jarosław Mederski (email@example.com)
- Pietro d’Avenia (firstname.lastname@example.org)