Main research topics of the group refer to: variational methods for image segmentation and inpainting; shape optimization: geometric-functional inequalities, optimal partitions; free discontinuity problems; noncoercive minimum problems in continuum mechanics; free boundary problems associated to variational inequalities; convex analysis and control problems. Spectral analysis of scalar operators and functional calculus based on holomorphic functions theory are cornerstones of Functional Analysis with many applications to the theory of differential equations. Since 2006 a new spectral theory was introduced (based on the notion of S-spectrum) for vector-valued operators, providing a hyper-holomorphic vector functional calculus that allows to introduce a new class of fractional diffusion problems.
- Calculus of Variations.
- Variational methods for image segmentation and inpainting.
- Dimension reduction in nonlinear elasticity and recession functional.
- Shape optimization problems and geometric-functional inequalities.
- Free discontinuity problems.
- Optimal partitions.
- Hyper-holomorphic functional calculus and spectral decomposition of vector linear operators.
- Fractional powers of vector-valued operators and new classes of problems related to fractional diffusion.
Purpose of the research group is to to treat various topics ranging from algebraic geometry and complex geometry to representation theory, problems in graph theory, algebraic and enumerative combinatorics and computational topics in commutative algebra. The applications vary in several directions among which image recognition, image processing, code theory, signal processing, neurosciences.
- mathematical analysis applied to mechanical systems
- complex analysis techniques and transforms (Fourier, Laplace,…)
- ordinary and partial differential equations
- geometric analysis and Riemannian geometry
- nonlinear diffusion
|3||DI CRISTO Michele||PA|
The group activity focuses on numerical modeling applied to problems arising from Engineering, Physics, Biomedicine, Earth Sciences. Large part of the activity is carried out within the MOX Laboratory (http://mox.polimi.it) and in particular the activity group numeth@mox (http://numeth.mox.polimi.it). From the applicative side, we deal with biomedical applications (http://bio.mox.polimi.it), computational geosciences (http://compgeo.mox.polimi.it), environmental applications and industrial mathematics (http://fluids.mox.polimi.it), electronic devices and bioelectronics (http://www1.mate.polimi.it/~ricsac/research.html).
Numerical analysis, Scientific computing and data processing, Applications of mathematics in science, Applications of mathematics in industry and society life
|2||ANTONIETTI Paola Francesca||PO|
|4||DE FALCO Carlo||RTDB|
The research activities are devoted to innovative didactics techniques and tools for the dissemination of mathematics (for instance MOOCs) and to the relationships of Mathematics with a variety of fields which include, for instance, architecture, art, theater, astronomy, cultural heritage, history and philosophy of science.
The Nicola Bruti Liberati Quantitative Finance Laboratory (QFinLab) is a high level center for training, research and collaboration with the industry in quantitative finance: asset management, risk management, derivative valuation. It is also active in the field of financial education, through the MOOC "Finance for All" and the activities on the website www.imparalafinanza.it, and in the field of new technologies and regulation analysis, with the dedicated website www.finriskalert.it
The group has expertise in all areas of Quantitative Finance, which includes all applications of quantitative financial instruments (maths, statistics, computational methods) with applications ranging from valuation of derivatives to risk management, portfolio management, and financial product structuring.
|3||BELGIORNO Francesco Domenico||PA|
|8||VIVARELLI Maria Dina||PA|
Main research topics of the group refer to: algebra and theoretical computer science, commutative and computational algebra, complex and hypercomplex analysis, algebraic and enumerative combinatorics, geometric analysis, differential geometry, discrete mathematics, graph theory, representation theory.
Applications range in various directions including image reconstruction and recognition, discrete and geometric tomography, code theory, signal theory, neurosciences, topological data analysis.
|6||MARCHINI Elsa Maria||PA|
Analysis and modeling of random phenomena in physics, biology, finance, econometry. Stochastic optimization, filtering, control, backward stochastic equations. Bayesian inference. Quantum probability and information: quantum open systems, quantum optics applications, quantum uncertainty.
Applications of models based on stochastic processes:
- Optimal control in finite and infinite dimensions of Markovian and non-Markovian processes, of diffusive or pure-jump types; quadratic linear control. Applications to financial modeling.
- Pricing and hedging of financial derivatives, in particular traded on Energy Markets.
- Study of stochastic models of information/epidemic diffusion. This has a natural application, for instance, in the development of strategies to curb epidemics (vaccinations) or to favour the rapid dissemination of information.
- Construction and statistical analysis of Cox-Markov models, construction of Bayesian semi-Markov processes, Bayesian survival analysis with applications to biological and seismic data. Bayesian econometric models of the regional population. Long experience in developing the theory and in applications of dynamical equations for quantum open systems and generators of quantum dynamical semigroups, the Schrödinger stochastic equation, quantum stochastic differential equations. Development of entropy techniques for information and uncertainty analysis in quantum systems that finds its natural application in the emerging field of quantum technologies.
|10||LADELLI Lucia Maria||PA|
The group activity is focused on statistical models and methods applied to industrial problems or arising in biomedical sciences, geosciences and social sciences. Beside an intense theoretical research, also along the Bayesian approach, applied research is pursued within the MOX laboratory (http://mox.polimi.it) in the area Statistics@MOX (https://statistics.mox.polimi.it). Specific domains are those related to the analysis of complex and high dimensional data and to health analytics. The research focus in Bayesian statistics is on modelling and computational aspects, in particular on mixture models for clustering
Big data, statistical learning, functional data analysis, Bayesian statistics, data mining, generalized linear models with mixed effects, urn models for adaptive design of experiment, geostatistics, health care management.
|5||PAGANONI Anna Maria||PO|
|6||SANGALLI Laura Maria||PA|