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Institute of Mathematics, Statistics and Scientific Computing
Research lines
1.
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Computational Optimization Methods. Development and analysis of optimization algorithms, with special interest in large-scale problems. (Approved by the Department/Scientific Council in 1978). Line linked to the DEPARTMENT OF APPLIED MATHEMATICS.
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2.
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Applied Analysis. Theoretical and numerical aspects associated with partial differential equations, mainly those that model problems in thermomechanics and biology. (Approved by the Department/Scientific Council in 1992). Line linked to the DEPARTMENT OF APPLIED MATHEMATICS.
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3.
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Biomathematics. Application of dynamic systems theory to biology and the development of numerical procedures for processes in medicine (Approved by the Department/Scientific Council in 1985). Line linked to the DEPARTMENT OF APPLIED MATHEMATICS.
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4.
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Field Arithmetic and Galois Theory. Spaces of Orders, Sums of Squares, Invariants of the Theory of Quadratic Forms. Galois Group of Bodies. (Approved by the Department/Scientific Council in 1985). Line connected to the MATHEMATICS DEPARTMENT.
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5.
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Algebra theory. Study of various aspects of algebras. (Approved by the Department/Scientific Council in 1985). Line connected to the MATHEMATICS DEPARTMENT.
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6.
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Geometric Group Theory. Study of various aspects of Group Theory. (Approved by the Department/Scientific Council in 1985). Line connected to the MATHEMATICS DEPARTMENT.
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7.
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Inverse Problems. Inverse problems associated with prospecting geophysics (identification of parameters) and also with image processing. (Approved by the Department/Scientific Council in 1987). Line linked to the DEPARTMENT OF APPLIED MATHEMATICS.
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8.
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Operational Research and Mathematical Economics. It proposes the study, development, implementation and computational analysis of operational research methods applied to diverse areas, such as energy and economic planning, etc. Studies of algorithms for determining economic equilibria, simplex methods in piecewise linear networks, traveling salesman problems, algorithm for the set representation problem, statistics of the support problem two-dimensional. Economic plan-market tension. (Approved by the Department/Scientific Council in 1977). Line linked to the DEPARTMENT OF APPLIED MATHEMATICS.
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9.
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Mathematical Physics. Applications of modern mathematical methods to problems in Theoretical Physics. Studies of the foundations of the theories of special and general relativity and quantum mechanics. (Approved by the Department/Scientific Council in 1977). Line linked to the DEPARTMENT OF APPLIED MATHEMATICS.
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10
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Non-Linear Analysis, Differential Equations and Applications. Study of theoretical and applied aspects of mathematical problems involving differential equations. (Approved by the Department/Scientific Council in 1985). Line connected to the MATHEMATICS DEPARTMENT.
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11
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Riemannian Geometry. Relations between Local Invariants of Riemannian Varieties (Esp.Curvature) and Global and Topological Properties (Approved by the Department/Scientific Council in 1985). Line connected to the MATHEMATICS DEPARTMENT.
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12
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Applications of Geometry and Topology. Applications of Geometry and Topology results in various areas, in particular
Theoretical Physics. (Approved by the Department/Scientific Council in 1989). Line connected to the MATHEMATICS DEPARTMENT.
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13
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Dynamic Systems. Study of various aspects of finite-dimensional Dynamic Systems, including
its qualitative properties and bifurcations. (Approved by the Department/Scientific Council in 1985). Line connected to the MATHEMATICS DEPARTMENT.
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14
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Functional Analysis. Study of various aspects of Functional Analysis, including Approximation Theory,
Holomorphy and others. (Approved by the Department/Scientific Council in 1985). Line connected to the MATHEMATICS DEPARTMENT.
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15
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Combinatorics and Number Theory. Study problems in Additive Number Theory with an interest in combinatorial aspects using Hypergeometric Series and symbolic algebra packages. (Approved by the Department/Scientific Council in 1989). Line linked to the DEPARTMENT OF APPLIED MATHEMATICS.
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16
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Linear Models and Experiment Planning. Description of continuous variable as a linear function of parameters, with or without covariates, dependence between observations, etc... (Approved by the Department/Scientific Council I'm in 1989). Line connected to the STATISTICS DEPARTMENT.
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17
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Harmonic Analysis. Singular integral operators, maximal operators, multiplier operators and Sobolev and Besov spaces over homogeneous spaces. Muckenhoupt class weights. Harmonic analysis of vector functions defined over homogeneous spaces and with values in Banach spaces with the UMD property (Approved by the Department/Scientific Council in 1984). Line connected to the MATHEMATICS DEPARTMENT.
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18
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Mathematical Statistics. Research in the area of Statistical Inference (Approved by the Department/Scientific Council in 1985). Line connected to the STATISTICS DEPARTMENT.
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19
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Biostatistics. Statistics applied to biological sciences including the areas of categorical data, linear models, generalized linear models and survival analysis. (Approved by the Department/Scientific Council in 1998). Line connected to the STATISTICS DEPARTMENT.
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Lie theory. Study of various aspects of Lie Theory and applications. (Approved by the Department/Scientific Council in 1985). Line connected to the MATHEMATICS DEPARTMENT.
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Probability and Stochastic Processes. Theoretical studies of random processes subject to variations. (Approved by the Department/Scientific Council in 1985). Line connected to the STATISTICS DEPARTMENT.
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22
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Computational Statistics. When the exact calculation of certain statistical quantities cannot be obtained for some reason, computational methods are used to obtain approximations of these quantities. Methods of Interest: Monte Carlo, *Monte Carlo Markov Chain*, *Gibbs Sampling*, *Bootshap* and cross validation. (Approved by the Department/Scientific Council in 1996). Line connected to the STATISTICS DEPARTMENT.
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23
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Computational Geophysics. Development and application of numerical algorithms for processing seismic data associated with oil prospecting. (Approved by the Department/Scientific Council in 1996). Line linked to the DEPARTMENT OF APPLIED MATHEMATICS.
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Numerical Analysis. Numerical analysis and simulation of problems of interest to Engineering areas. (Approved by the Department/Scientific Council in 1977). Line linked to the DEPARTMENT OF APPLIED MATHEMATICS.
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25
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Genetic Statistics. Research in the area of DNA sequence modeling assuming dependence between positions, genetic distance measurements, analysis of DNA sequence variability, phylogeny trees, an Statistical analysis for family data. (Approved by the Department/Scientific Council in 1998). Line connected to the STATISTICS DEPARTMENT.
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26
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Statistical Methods. Research in the development and application of statistical models (Approved by the Department/Scientific Council in 1985).
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27
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Teaching Mathematics. The work is based on a pedagogical proposal in continuous evolution, which is based on the tripod: teaching through projects, incorporation of new technologies in the classroom, and at work team reflection. (Approved by the Department/Scientific Council in 2000).
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28
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Algebraic Geometry. No information (Approved by the Department/Scientific Council in 1993).
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