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, 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.


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 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. Finsler Geometry.
• 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

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 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, 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 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 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 non-conservative phenomena.

• 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.
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   -  Home Numerical Analysis

Members: Alessandra Aimi, Mauro Diligenti

AMS Subject Classification: 65R20, 65N38, 65F30

Research topics:

• 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   -  Home Computer Science

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 non-ground 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 non-deterministic programming in the context of object-oriented 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 multi-agent systems and experimental evaluation in Artificial Intelligence applications.
1998 ACM: 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.
1998 ACM: I.4.3 Enhancement; I.6.5 Model Development; F.2.1 Numerical Algorithms and Problems



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