Topology, Geometry and Analysis

Dr. Yaé Ulrich Gaba, Email: yaegaba@acas-yde.org, phone: +229 95 87 22 69

Topology at ACAS touches on a wide range of highly active subdisciplines, benefiting from and capitalizing on strong overlap with the Algebra, Analysis, and Computer Science.
Our present research interests covers (a) symmetry topology, discrete mathematics and applications in theoretical computer science.

In topology, the objects we study are called topological spaces. The main tools for the study of topological spaces are algebra, geometry and combinatorics.

One class of spaces which plays a central role in mathematics, and whose topology has been recently extensively studied, due to its applications in computer science, are quasi-metric spaces.

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These are topological spaces equipped with geometrical structure, which gives meaning to concepts such as distance in an asymmetric setting. These spaces present many applications of areas like theoretical computer science, approximation theory and topological algebra.

In particular they are used to model quantitative computations. Moreover the study of a theory of completeness of quasi-uniform and quasi-metric spaces permits to obtain a common generalisation of dcpo’s and metric spaces as used in denotational semantics.

The partial metric spaces, and their equivalent weightable quasi-metric spaces, were introduced as a component in the study of the denotational semantics of data flow networks.

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One can study, domain properties as well as the complexity theory of algorithms with the help of partial metrics.

Research
Active areas of research in the group include:
– Partial quasi-metric properties of complexity spaces.
– Quasi-metric as a tool for Complexity Analysis of Algorithms.

– Fixed-point theory

Topology at ACAS is a new, young an emerging and promising group of your researchers. Broadly speaking, our research is concerned with the rich interaction and deep interconnections between algebra and geometry with a view to new applications and solutions to long-standing problems

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Members

Dr. Yae Gaba Ulrich, ACAS, Yaounde, Cameroon and IMSP, Benin

Dr. Yae Gaba Ulrich, email: yaegaba@acas-yde.org

Dr. Collins A. Agyingi
Email: caagyingi@acas-yde.org; collinsagyingi@nwu.ac.za

Prof. Binayak S. Choudhury
Email: scbinayak@acas-yde.org; binayak@math.iiests.ac.in

Publications