Research Groups - 2012
- ALGEBRA GROUP
- GEOMETRY GROUP
- ADDITIONAL MATHEMATICS GROUP
- MATHEMATICAL ANALYSIS GROUP
- PROBABILITY AND MATHEMATICAL STATISTICS GROUP
- MATHEMATICAL PHYSICS GROUP
- NUMERICAL ANALYSIS GROUP
- COMPUTER SCIENCE GROUP
Further information is available of the web pages of individual teachers
Members: Andrea Bandini, Giordano Gallina, Fiorenza Morini
AMS Subject Classification: 16Y30, 16Y76, 05B05, 05B30, 11R23, 11G05, 11G07, 11G40
Iwasawa theory for global fields (in any characteristic): class groups, p-adic L-functions, Main Conjectures.
Iwasawa theory for elliptic curves defined over global fields (in any characteristic): Selmer groups, Tate-Shafarevich groups, L-functions, p-adic L-functions, Main Conjectures.
Orbits of irreducible polynomial respect to an automorphism group of polynomial domain.
Construction of nearrings which are extension of nilpotent ideals.
Construction of combinatorial structures ( for example designs, codes) from circular planar nearrings.
p-singular nearrings with simple additive groups.
Members: Lucia Alessandrini,
AMS Subject Classification: : 32C30, 32C17, 58J50, 32J27, 32V05, 53C15, 32Q26, 32M10,
53C25, 32J27, 53C43, 68T45, 53D12
Positive currents on complex manifolds and special metrics on Hermitian manifolds.
Construction of Steiner Systems S(2,k,v) from a planar Frobenius group G and analyse the dimension dm when G is imprimitive and when G is primitive.
Colourability of hypergraphs and Steiner systems.
Ricci-flow on complex manifolds:
twisted Kahler-Einstein equation; Ricci-flow on Fano varieties;
functionals for deformation of complex manifolds (K-energy of Mabuchi and Chen-Tian functionals E_k);
existence of Kaehler-Ricci solitons and smooth/singular Einstein metrics.
Surgery of Calabi-Yau manifolds with cylindrical ends and resolution of conical singularities.
Existence of Calabi-Yau metrics on resolutions of singularities of Calabi-Yau varieties.
Lie group acting on manifolds; isometric and Hamiltinonian actions.
Riemannian and Sub-Riemannian geometry: existence, uniqueness and molteplicity of closed geodesics.
Fibrations of 3-Sasakian manifolds on quaternion Kδhler manifolds and submanifolds.
Invariant special structure (in particular CR) on Lie groups and their quotients.
Applications of exterior differential systems and of the method of moving frame to
submanifold geometry in homogeneous spaces, geometric variational problems,
and integrable systems.
Convex properties of domains in $C^n$ (convexity, C-convexity, strictly and strongly
pseudoconvexity): extension of functions and analytic objects;
relation between the notion of Hilbert and Kobayashi hyperbolicity.
Deformations of complex structures. Hermitian metrics with torsion.
Calibrations. Symplectic structures. Cohomological properties of almost-complex manifolds.
ADDITIONAL MATHEMATICS GROUP
Members: Carlo Marchini,
Daniela Medici, Maria Gabriella Rinaldi, Paola Vighi
Focusing on the obstacles and failures of the algebraic language through the analysis of the procedures to solve problems.
Geometrical transformation and their contribution to knowledge.
Geometry in macro and meso space.
Assessment of the pre-university learning of mathematics.
Beliefs and behavior of pre and in-service teachers.
Research on logical and mathematical thinking in 4 6 years old pupils.
MATHEMATICAL ANALYSIS GROUP
Members: Emilio Acerbi,
Domenico Mucci, Stefano Panizzi,
Elliptic and parabolic PDE's:
- mathematical models in combustion theory, cavitation, nonlinear elasticity, fluid dynamics;
- optimal regularity issues in linear and nonlinear problems;
- nonlinear potential theory and pointwise estimates for solutions via linear and nonlinear potentials;
- singular sets;
- mappings between manifolds;
- markovian systems, invariant measures, infinite dimensional elliptic and parabolic
AMS Subject Classification: 35J, 35K
Calculus of variations:
- variational problems in phase transitions, optimal transport, shape optimization, geometric measure theory; problems related to the
first eigenvalue and the first eigenfunction of the infinity laplacian.
AMS Subject Classification: 49
- conservation laws, asymptotic behavior in nonlinear wave equations and Kirchhoff equations.
AMS Subject Classification: 35L
Analytic number theory:
- additive Golbach type problems, distribution of primes.
AMS Subject Classification: 11N, 11P
PROBABILITY AND MATHEMATICAL STATISTICS GROUP
Members: Francesco Morandin
Dyadic shell models in fluid mechanics. In particular, anomalous
dissipation for nonlinear models (both deterministic and stochastic)
derived from the 3-dimensional Euler and Navier-Stokes equations.
AMS Subject Classification: 35Q35, 35R60, 60H15, 35B44, 35B65, 35C06
Urn processes. In particular, large deviations principles in
generalized urn models.
AMS Subject Classification: 60J10, 60F10
Branchig processes. In particular applied to the construction of
explicit solutions of nonlinear ODE's.
AMS Subject Classification: 60J80, 60J85, 34A34, 34A05
Statistical mechanics. In particular, spin glass models related to
error correcting codes: random energy model, random codes, LDPC
AMS Subject Classification: 94A24, 82D30, 82B44, 94B60, 68P30
MATHEMATICAL PHYSICS GROUP
Members: Marzia Bisi, Giancarlo Cantarelli,
Maria Groppi, Marina Iori,
• Kinetic equations for gas mixtures undergoing chemical reactions of different types. Hydrodynamic limits in different regimes driven by some kind of resonant interactions, multi-velocity and/or multi-temperature descriptions. Relaxation time approximations of reactive Boltzmann equations of statistical/ellipsoidal type, determination of transport coefficients in terms of relaxation parameters.
• Extension of the incompressible Navier-Stokes equations to a mixture of gases, formal derivation from the kinetic equations and mathematical study of the macroscopic system for a binary, possibly reactive, mixture.
• Kinetic (Boltzmann or BGK) and fluid-dynamic (Euler or Navier-Stokes) models for reactive flows. Shock structures, detonation and deflagration waves, Rankine-Hugoniot and Chapman-Jouguet relations, flame eigenvalue.
• Gaseous chemical aggression, deterioration of buildings by action of sulphite or general pollutants on limestones. Main mathematical problems, numerical simulations, comparison to heuristic models and experimental data.
• Granular flows and thin dust in the atmosphere. Simultaneous presence of linear and nonlinear collision operators, equilibrium induced by the thermal bath. Existence, uniqueness and regularity results for such a steady state, local and global stability.
A) Kinetic theory for non-conservative phenomena.
AMS Subject Classification: 76P05, 82C40, 80A32.
B) Dynamical system approaches in analytical mechanics.
• Sufficient conditions for strong stability of dynamical systems subject to Seibert perturbations. Applications to Lagrange equations for mechanical systems with time dependent /independent constraints.
AMS Subject Classification: 37N05.
C) Mathematical models in biomathematics.
• Mathematical models in population dynamics and in epidemiology. Prey-predator models, comparison of different functional responses and of different non-logistic growth rates. Global stability, Lyapunov functionals, bifurcations, biological interpretation. Epidemiological models in wildlife: optimal control theory applied to the determination of the optimal culling strategy for the eradication of wildlife diseases.
AMS Subject Classification: 92B05, 34C23.
D) Geometric theories for impulsive classical mechanics.
• Geometric approach to multiple impacts of rigid bodies and multi-body impacts with unilateral constraints. Historical and critical analysis on the fundamentals of Impulsive Mechanics.
AMS Subject Classification: 70G10.
NUMERICAL ANALYSIS GROUP
Members: Alessandra Aimi, Mauro Diligenti
AMS Subject Classification: 65R20, 65N38, 65F30
Space-time boundary integral equation formulations of elastic wave propagation problems in bounded and unbounded domains.
Analysis of an energetic weak formulations of space-time boundary integral equations and of suitable regularization techniques. Theoretical and experimental study of stability and convergence of approximated solutions obtained with Galerkin-type numerical methods.
Extension of the integral model to multi-domain problems in 2D and 3D.
Analysis of suitable algorithms for computational cost reduction in the construction and resolution of linear systems coming from the discretization phase.
Development of prototype specialized software for numerical testing.
COMPUTER SCIENCE GROUP
Members: Roberto Bagnara,
Alessandro Dal Palω,
• Study, design and implementation of solvers for the computation of
non-ground stable models for Answer Set Programming.
D.1.6 Logic Programming
• Study, design and implementation of a package for mining relatioships
between genes, phylogenesis and biological networks.
D.1.6 Logic Programming; J.3 Life and Medical Sciences
• Study, design and implementation of tertiary structure predictors
based on constraint programming.
D.1.6 Logic Programming; J.3 Life and Medical Sciences
• Design, development and implementation of (domains of) abstract
properties and approximation techniques for the automatic analysis and
verification of hardware and software systems.
D.2.4 Software/Program Verification; F.3.2 Semantics of Programming Languages
• Advanced tools for the verification, testing, debugging and measurement
F.3.1 Specifying and Verifying and Reasoning about Programs;
D.2.5 Testing and Debugging; D.2.8 Metrics
• Design, implementation, and development of a Java library supporting
declarative, constraint, and non-deterministic programming in the context
of object-oriented languages.
D.1.6 Logic Programming; D.3.3 Language Constructs and Features;
I.2.8 Problem Solving, Control Methods, and Search
• Design of parallel algorithms for GPGPU architectures applied to
D.1.3 Concurrent Programming
• Design and implementation of planners and validation of conformant plans.
I.2.8 Problem Solving, Control Methods, and Search
• Study and formalization of programming languages for multiagent systems;
I.2.5 Programming Languages and Software
• Implementation of prototype tools supporting programming of
multi-agent systems and experimental evaluation in Artificial
I.2.11 Distributed Artificial Intelligence
• Analysis of algorithms for the non-negative image deconvolution;
analysis and synthesis of algorithms for solving shift-invariant
problems; study of stochastic models for texts.
I.4.3 Enhancement; I.6.5 Model Development; F.2.1 Numerical Algorithms
Top Page -