2nd Section

Algebra and Geometry

The Algebra and Geometry Section includes the following fields of Mathematics: Abstract Algebra, Differential Geometry, Number Theory, Mathematical Logic, Differential and Algebraic Topology, Algebraic Geometry, etc.

An invaluable contribution of Mathematical Analysis is the supply of creative and effective tools to other fields of Mathematics, from purely theoretical to completely applied fields. Some of the basic and interdependent directions of Mathematical Analysis are the Theory of Real Functions, the Theory of Complex Functions, Topology, Differential Equations, the Theory of Measure and Integration, Functional Analysis, etc.

Algebra developed mainly in the 19th and 20th centuries and its aim was the solution of specific problems in Geometry, Number Theory and the Theory of Algebraic Equations. It also contributed to a better understanding of the existing solutions to such problems. Today, Algebra's contribution to other sciences, such as that of Computer Science, is invaluable.

Differential Geometry constitutes one of the main branches of mathematics and deals with the study of metric concepts on manifolds, such as metrics and curvature. The classic period of Differential Geometry was the 19th century, during which the local theory of curves and surfaces - now known as elementary Differential Geometry - developed as an application of Infinitesimal Calculus. In the 20th century the field developed rapidly, based on the recent achievements of the theory of Partial Differential Equations, Algebraic Topology and Algebraic Geometry. The dynamics and fruitfulness of Differential Geometry is also a result of its interaction with other sciences, such as Physics (Theory of Relativity), etc.

Personnel of the Algebra and Geometry Section and their scientific interests:

Name | Title | Scientific Interests |
---|---|---|

Beligiannis Apostolos | Professor | Algebra (Representation Theory - Homological Algebra). |

Kechagias Epaminondas | Professor | Algebraic Topology - Invariant Theory. |

Thoma Apostolos | Professor | Algebraic Geometry, Anticommutative Algebra. |

Vlachos Theodoros | Professor | Differential Geometry (Riemann Geometry, Submanifold Theory, Minimal Submanifolds). |

Papadakis Stavros | Assistant Professor | Algebraic Geometry, Commutative Algebra, Algebraic Combinatorics, Algebraic Transformation Groups. |

Savas-Halilaj Andreas | Assistant Professor | Riemannian Geometry, Geometric PDEs, Minimal Submanifolds, Geometric Flows, Soliton Solutions of the Mean Curvature Flow. |