Department members engage in cutting-edge research on a wide variety of topics in mathematics and its applications. Topics continually evolve to reflect emerging interests and developments, but can roughly grouped into the following areas.
Algebra, Combinatorics, and Geometry
Algebra, combinatorics, and geometry are areas of very active research at the University of Pittsburgh.
Analysis and Partial Differential Equations
The research of the analysis group covers functional analysis, harmonic analysis, several complex variables, partial differential equations, and analysis on metric and Carnot-Caratheodory spaces.
Applied Analysis
The department is a leader in the analysis of systems of nonlinear differential equations and dynamical systems that arise in modeling a variety of physical phenomena. They include problems in biology, chemistry, phase transitions, fluid flow, flame propagation, diffusion processes, and pattern formation in nonlinear stochastic partial differential equations.
Mathematical Biology
The biological world stands as the next great frontier for mathematical modeling and analysis. This group studies complex systems and dynamics arising in various biological phenomena.
Mathematical Finance
A rapidly growing area of mathematical finance is Quantitative Behavioral Finance. The high-tech boom and bust of the late 1990s followed by the housing and financial upheavals of 2008 have made a convincing case for the necessity of adopting broader assumptions in finance.
Numerical Analysis and Scientific Computing
The diversity of this group is reflected in its research interests: numerical analysis of partial differential equations, adaptive methods for scientific computing, computational methods of fluid dynamics and turbulence, numerical solution of nonlinear problems arising from porous media flow and transport, optimal control, and simulation of stochastic reaction diffusion systems.
Topology and Differential Geometry
Research in analytic topology continues in the broad area of generalized metric spaces. This group studies relativity theory and differential geometry, with emphasis on twistor methods, as well as geometric and topological aspects of quantum field theory, string theory, and M-theory.
This is a list of geometry topics, by Wikipedia page.
Retrieved from "//en.wikipedia.org/w/index.php?title=List_of_geometry_topics&oldid=1075231842"
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A 2D geometric model is a geometric model of an object as a two-dimensional figure, usually on the Euclidean or Cartesian plane.
Even though all material objects are three-dimensional, a 2D geometric model is often adequate for certain flat objects, such as paper cut-outs and machine parts made of sheet metal. Other examples include circles used as a model of thunderstorms, which can be considered flat when viewed from above.[1] 2D geometric models are also convenient for describing certain types of artificial images, such as technical diagrams, logos, the glyphs of a font, etc. They are an essential tool of 2D computer graphics and often used as components of 3D geometric models, e.g. to describe the decals to be applied to a car model. Modern architecture practice "digital rendering" which is a technique used to form a perception of a 2-D geometric model as of a 3-D geometric model designed through descriptive geometry and computerized equipment.[2]
- simple geometric shapes
- boundary representation
- Boolean operations on polygons
- 2D geometric primitive
- Computational geometry
- Digital image
- ^ Nissen, Silas Boye; Haerter, Jan O. [September 24, 2021]. "Circling in on Convective Self-Aggregation". JGR Atmospheres. 126. arXiv:1911.12849. doi:10.1029/2021JD035331.
- ^ Dresp, Birgitta; Silvestri, Chiara; Motro, René [2007]. "Which geometric model for the curvature of 2-D shape contours?". Spatial Vision. 20 [3]: 219–64. doi:10.1163/156856807780421165. PMID 17524256. S2CID 35702710.
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