Topic | People | Description | |
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Associative rings and algebras standard compliant MSC | |||
Rings and algebras arising under various constructions |
Lidia Angeleri Francesca Mantese |
Localization of rings. Ring epimorphisms. Endomorphism rings of tilting and cotilting modules. | |
Modules, bimodules and ideals |
Lidia Angeleri Francesca Mantese |
Indecomposable decompositions. Approximations. Purity. Endoproperties of modules. | |
Representation theory of rings and algebras |
Lidia Angeleri Alessandro Rapa |
Infinite dimensional modules over finite dimensional algebras. Classification of tilting objects in module categories and in associated geometric categories. | |
Category theory; homological algebra standard compliant MSC | |||
Homological algebra |
Lidia Angeleri Francesca Mantese Alessandro Rapa |
Tilting theory. Homological Conjectures. Localization in abelian and triangulated categories. | |
Abelian categories |
Lidia Angeleri Francesca Mantese Alessandro Rapa |
Torsion pairs and cotorsion pairs in abelian categories. Approximations in abelian categories. Heart of t-structures associated to torsion pairs. | |
General theory of categories and functors |
Enrico Gregorio |
Adjoint functors. Equivalence and dualities between module categories. Triangulated and derived functors. Equivalence and dualities between triangulated and derived categories. | |
Graph theory standard compliant MSC | |||
Graph Theory |
Giuseppe Mazzuoccolo Romeo Rizzi |
Graphs are a flexible model for core combinatorial problems as arising in various applications. In particular, graphs are encountered in various fields of mathematics, computer science, science in general, and technology. With this, graph theory is not only fun, but it is also a well established and central area of discrete mathematics of topmost interdisciplinarity. Some topics we are interested in: matching, factoring, edge-coloring, flows, cycle basis, packing, covering and partitioning, graph classes, algorithmic graph theory. | |
Computer science standard compliant MSC | |||
Combinatorial Algorithms and algorithmic graph theory |
Romeo Rizzi |
When we say that our approach to graph theory and combinatorics is algorithmic we not only want to underline the fact that we are most often interested in the obtaining effective algorithms for the problems investigated but also that we indulge unraveling the mathematical problems down till the bottom most level to achieve a most elementary comprehension. Also, we rest on computational complexity as the methodological lighthouse of our research approaches and investigations. This depth and awareness characterizes the strength of the research by our department in Verona. | |
Discrete mathematics in relation to computer science |
Romeo Rizzi |
Discrete mathematics has a privileged link to computer science, and the converse is also true. As algorithmists, we tangle discrete mathematics in order to give our contribution to computer science. Discrete mathematics in relation to computer science is a huge factory all over the world, and our computer science department here in Verona is well present in all this. | |
Theory of computing |
Romeo Rizzi |
The theory of computation is the branch of mathematics and computer science that deals with whether and how efficiently problems can be solved on a model of computation, using an algorithm. In more than one way, this fascinating field has affected our perception of the world and of mathematics itself. In mathematics, it is an eye opener and a source of methodology and philosophical inspiration. This is particularly true for its two main branches of computability theory and computational complexity. | |
Polytopes and polyhedra standard compliant MSC | |||
Polytopes and Polihedra |
Giuseppe Mazzuoccolo Romeo Rizzi |
Polytopes and polyhedra are objects of study in topology, computational geometry, mathematical programming, and combinatorial optimization. The last two perspectives offer tools of operations research which find employment in some of the applied mathematics research lines in Verona. | |
Mathematical logic and foundations standard compliant MSC | |||
Hilbert's Programme for Abstract Mathematics |
Peter Michael Schuster |
Extracting the computational content of classical proofs in conceptual mathematics. Particular attention is paid to invocations of logical completeness in mathematical form, typically as variants of Zorn's Lemma. | |
Philosophical aspects of logic and foundations |
Ruggero Ferro |
Several results in mathematical logic point out and explain the limitations, possibilities and advantages of formalization (the use of formal languages). An increasing precision in determining of the role of formal languages is basic to a critical attitude in philosophy of mathematics, spotting untenable positions and supporting others. An empiricist point of view is being developed that overcomes the vagueness and difficulties of know presentations. This type of research has developed, and will continue to support, competences on the following themes: Mathematical logic; Understanding, acquiring, and constructing basic mathematical notion, in particular the primitive ones; The role of logic in the construction and acquisition of mathematical notions; The role of the language in mathematics; The role of formalism in mathematics; Mathematics teacher’s initial and life long education; Mathematical motivations for the teaching of mathematics. | |
Proof theory and constructive mathematics |
Peter Michael Schuster |
Proof theory at large studies mathematical proofs, which thus become themselves objects of mathematics. In a nutshell, the goal is to understand "what can be proved with what" and to gain computational information from proofs. Constructive mathematics aims at direct proofs from which one can read off algorithms; any such algorithm comes with a certificate of correctness for free, which just is the original proof. | |
Operations research, mathematical programming standard compliant MSC | |||
Operations research and management science |
Romeo Rizzi |
Operations research is a discipline that deals with the application of advanced analytical methods to help make better decisions. The terms management science and decision science are sometimes used as more modern-sounding synonyms. Employing techniques from other mathematical sciences, such as mathematical modeling, statistical analysis, and mathematical optimization, operations research arrives at optimal or near-optimal solutions to complex decision-making problems. Operations Research is often concerned with determining the maximum (of profit, performance, or yield) or minimum (of loss, risk, or cost) of some real-world objective. Originating in military efforts before World War II, its techniques have grown to concern problems in a variety of industries. Besides its applications in industry and in management, Operations Research is at the very junction of mathematics and economics. Operations research embodies lots of deep results and theory but, at the same time, it is the archetype of applied mathematics. | |
Mathematical programming |
Romeo Rizzi |
In mathematics, statistics, empirical sciences, computer science, or management science, mathematical optimization (alternatively, mathematical programming) is the selection of a best element (with regard to some criteria) from some set of available alternatives. Here, optimization includes finding "best available" values of some objective function given a defined domain, including a variety of different types of objective functions and different types of domains. Optimization theory, techniques, and algorithms, comprises a large area of applied mathematics. Among the many sectors of mathematical programming, some of those represented in Verona are the following: linear programming, integer linear programming, combinatorial optimization, multiobjective optimization. |
Name | Description | URL |
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Algebra | Il gruppo lavora in teoria delle rappresentazioni di algebre e teoria dei moduli. | http://profs.sci.univr.it/~angeleri/RT%20Verona.html |
INdAM - Unità di Ricerca dell'Università di Verona | Questa pagina è dedicata all'unità di ricerca INdAM dell'Università di Verona. | |
Logica | Logica in matematica ed informatica. | https://www.logicverona.it/ |