Dr. Natalia Budarina

Postdoctoral Researcher

Working with Dr. Detta Dickinson

Room: 212 Top Logic

Phone: +353 1 708 3991

Fax: +353 1 708 3913

E-mail: Natalia.Budarina@maths.nuim.ie

Research Interests

Natalia Budarina is interested in the metric theory of Diophantine approximation, Khintchine-Type theorems and simultaneous Diophantine approximation.

Recently, she became interested in Diophantine approximation. Natalia considers the classical problem of arithmetic theory of the quadratic forms on integer representations by another form of lower dimension. The increase of the dimension of the problem allows us to apply the deformation method of the quadratic systems. Using local methods (Venkov, Mordell, Witt, Hasse, Kneser, Kitaoka, Watson, Niemeier, Conway, Sloane, Zhuravlev) Natalia considers special kinds of specialization of quadratic systems, when their global and local arithmetic properties are transformed by rational methods. The deformation method of quadratic systems through non-homogeneous specialization allows us to connect the space of quadratic forms with the important theoretic-numerical problem: the number of solutions for equations of the highest degrees and prime twins.