Both in academics and industry, computing is a fundamental tool that raises mathematic challenge in the acting and optimization of multidimensional geometric data. These studies require methods from several mathematic fields including: topology, geometry, combinatorics, functional analysis, algebra and numeric methods.
The Mathematical Physics occupies the space between Theoretical Physics and Pure Mathematics. Mathematically based physical theories, building models with the standard of rigor required of any mathematical area, and creates new mathematical structures.
Algebraic Geometry studies properties of spaces locally defined by polynomial equations. Particularly important are properties invariant by birational transformations, that is, invariant by isomorphims over dense open sets, and not necessarily over the whole variety: birational geometry gives rise to nice classifications of curves, surfaces, and higher dimensional varieties. Directly linked with birational geometry is the study of moduli spaces, that is, spaces (variety, schemes, stacks) that parametrize isomorphism (or birational) classes of objects, that can be varieties, vector bundles, sheaves.
Varieties endowed with different structures such as Riemannian metric or foliation, minimal surfaces or constant mean curvature, compact leaves and leaves curvature. The methods used are Geometric, Analytical and Topological.
The Theory of Stochastic Processes examines the evolution (temporal or special) of systems with random behavior. Its techniques allow extracting the collective behavior of systems composed by a large number of components.
The study of asymptotic behavior of orbits of endomorphism, diffeomorphism and flows, with emphasis on intrinsic properties. The focus is on the stability problems and ways in which this feature disappears.
Mathematics Department / PUC-Rio
Rua Marquês de São Vicente, 225 - Edifício Cardeal Leme, sala 862 - Gávea - Rio de Janeiro - CEP 22451-900
Telephones: (+55-21) 3527-1280, (+55-21) 3527-1281, Fax: (+55-21)3527-1282
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