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
ALGEBRA GROUP
Members: Andrea Bandini, Giordano Gallina, Fiorenza Morini
AMS Subject Classification: 16Y30, 16Y76, 05B05, 05B30, 11R23, 11G05, 11G07, 11G40
Research topics:
Iwasawa theory for global fields (in any characteristic): class groups, padic Lfunctions, Main Conjectures.
Iwasawa theory for elliptic curves defined over global fields (in any characteristic): Selmer groups, TateShafarevich groups, Lfunctions, padic Lfunctions, 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.
psingular nearrings with simple additive groups.
GEOMETRY GROUP
Members: Lucia Alessandrini,
Claudio Arezzo,
Laura Bertani,
Leonardo Biliotti,
Stefania Donnini,
Vittorio Mangione,
Costantino Medori,
Lorenzo Nicolodi,
Alberto Saracco,
Adriano Tomassini
AMS Subject Classification: : 32C30, 32C17, 58J50, 32J27, 32V05, 53C15, 32Q26, 32M10,
53C25, 32J27, 53C43, 68T45, 53D12
Research topics:
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 d_{m} when G is imprimitive and when G is primitive.
Colourability of hypergraphs and Steiner systems.
Ricciflow on complex manifolds:
twisted KahlerEinstein equation; Ricciflow on Fano varieties;
functionals for deformation of complex manifolds (Kenergy of Mabuchi and ChenTian functionals E_k);
existence of KaehlerRicci solitons and smooth/singular Einstein metrics.
Surgery of CalabiYau manifolds with cylindrical ends and resolution of conical singularities.
Existence of CalabiYau metrics on resolutions of singularities of CalabiYau varieties.
Lie group acting on manifolds; isometric and Hamiltinonian actions.
Riemannian and SubRiemannian geometry: existence, uniqueness and molteplicity of closed geodesics.
Finsler Geometry.
Fibrations of 3Sasakian 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, Cconvexity, 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 almostcomplex manifolds.
ADDITIONAL MATHEMATICS GROUP
Members: Carlo Marchini,
Daniela Medici, Maria Gabriella Rinaldi, Paola Vighi
Research topics:
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 preuniversity learning of mathematics.
Beliefs and behavior of pre and inservice teachers.
Research on logical and mathematical thinking in 4 6 years old pupils.
MATHEMATICAL ANALYSIS GROUP
Members: Emilio Acerbi,
Alberto Arosio,
Marino Belloni,
Pietro Celada,
Alessandra Coscia,
Gianluca Crippa,
Luca Lorenzi,
Alessandra Lunardi,
Silvana Marchi,
Giuseppe Mingione,
Massimiliano Morini,
Domenico Mucci, Stefano Panizzi,
Alessandro Zaccagnini
Research topics:
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
problems.
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
Hyperbolic equations:
 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
Research topics:
Dyadic shell models in fluid mechanics. In particular, anomalous
dissipation for nonlinear models (both deterministic and stochastic)
derived from the 3dimensional Euler and NavierStokes 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
codes, turbocodes.
AMS Subject Classification: 94A24, 82D30, 82B44, 94B60, 68P30
MATHEMATICAL PHYSICS GROUP
Members: Marzia Bisi, Giancarlo Cantarelli,
Gianluca Caraffini
,
Maria Groppi, Marina Iori,
Stefano Pasquero,
Giampiero Spiga
Research topics:
A) Kinetic theory for nonconservative phenomena.
• Kinetic equations for gas mixtures undergoing chemical reactions of different types. Hydrodynamic limits in different regimes driven by some kind of resonant interactions, multivelocity and/or multitemperature 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 NavierStokes 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 fluiddynamic (Euler or NavierStokes) models for reactive flows. Shock structures, detonation and deflagration waves, RankineHugoniot and ChapmanJouguet 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.
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. Preypredator models, comparison of different functional responses and of different nonlogistic 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 multibody 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
Research topics:
Spacetime boundary integral equation formulations of elastic wave propagation problems in bounded and unbounded domains.
Analysis of an energetic weak formulations of spacetime boundary integral equations and of suitable regularization techniques. Theoretical and experimental study of stability and convergence of approximated solutions obtained with Galerkintype numerical methods.
Extension of the integral model to multidomain 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,
Federico Bergenti,
Alessandro Dal Palω,
Grazia Lotti,
Gianfranco Rossi,
Enea Zaffanella
Research topics:
• Study, design and implementation of solvers for the computation of
nonground stable models for Answer Set Programming.
1998 ACM:
D.1.6 Logic Programming
• Study, design and implementation of a package for mining relatioships
between genes, phylogenesis and biological networks.
1998 ACM:
D.1.6 Logic Programming; J.3 Life and Medical Sciences
• Study, design and implementation of tertiary structure predictors
based on constraint programming.
1998 ACM:
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.
1998 ACM:
D.2.4 Software/Program Verification; F.3.2 Semantics of Programming Languages
• Advanced tools for the verification, testing, debugging and measurement
of software.
1998 ACM:
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 nondeterministic programming in the context
of objectoriented languages.
1998 ACM:
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
constraint programming.
1998 ACM:
D.1.3 Concurrent Programming
• Design and implementation of planners and validation of conformant plans.
1998 ACM:
I.2.8 Problem Solving, Control Methods, and Search
• Study and formalization of programming languages for multiagent systems;
1998 ACM:
I.2.5 Programming Languages and Software
• Implementation of prototype tools supporting programming of
multiagent systems and experimental evaluation in Artificial
Intelligence applications.
1998 ACM:
I.2.11 Distributed Artificial Intelligence
• Analysis of algorithms for the nonnegative image deconvolution;
analysis and synthesis of algorithms for solving shiftinvariant
problems; study of stochastic models for texts.
1998 ACM:
I.4.3 Enhancement; I.6.5 Model Development; F.2.1 Numerical Algorithms
and Problems
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