The Eighth Congress of Romanian Mathematicians

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I. Algebra and Number Theory

II. Algebraic, Complex and Differential Geometry and Topology

III. Real and Complex Analysis, Potential Theory

IV. Ordinary and Partial Differential Equations, Variational Methods, Optimal Control

V. Functional Analysis, Operator Theory and Operator Algebras, Mathematical Physics

VI. Probability, Stochastic Analysis, and Mathematical Statistics

VII. Mechanics, Numerical Analysis, Mathematical Models in Sciences

VIII. Theoretical Computer Science, Operations Research and Mathematical Programming

IX. History and Philosophy of Mathematics

Algebra and Number Theory 

(this list is in updating process)

Colegiul Național de Informatică Grigore Moisil din Brasov, Romania
Title: A Simple Proof of Fermat's Last Theorem for n=4 and n=6. (details)
We give a simple elementary and natural proof of Fermat's Last Theorem for the exponents n=4 and n=6.
University of Louisville and National Institute of Standards and Technology, United States of America
Title: Quantum-Resistant Public Key Cryptography (details)
Multivariate public key cryptosystems form a family of purported quantum-resistant cryptosystems, schemes which remain secure even if an adversary is assumed to have access to a large scale quantum computer. Such cryptosystems publish a public key consisting of a large collection of low degree polynomials in several variables over a finite field. Many cryptographic tasks can be accomplished if the system of equations is unfeasible to invert for an illegitimate user while being efficiently invertible to a legitimate user. We derive several new techniques for determining the security (or insecurity) of multivariate public key cryptosystems. The author presents new security criteria which are practical and are readily proven for a multitude of multivariate schemes. We further demonstrate an attack utilizing a subspace differential invariant illustrating a sharp contrast between cryptosystems which provably have a trivial differential structure and those for which an attack can be realized.
Islamic Azad University, Iran
Title: Ideal cimaximal graph and its application (details)
Let R be a commutative ring and G(R) be a graph with vertices as proper and non-trivial ideals of R. Two distinct vertices I and J are said to be adjacent if and only if I + J = R. In this paper we study a graph constructed from a subgraph of G(R) which consists of all ideals I of R such that contained in Jacobson radical of R. In this paper we study about the relation between the number of maximal ideal of R and the number of partite of this subgraph. Also we study on the structure of ring R by some properties of vertices of this subgraph. In another section, it is shown that under some conditions on the G(R), the ring R is Noetherian or Artinian. Finally we characterize clean rings and then study on diameter of this constructed graph.