Dr Oleg Karpenkov presents research at Westminster SET for Britain event

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Dr Oleg Karpenkov
Dr Oleg Karpenkov

Dr. Oleg Karpenkov, from the Department of Mathematical Sciences, represented the University of Liverpool at SET for Britain at the Houses of Parliament on March 9th.

Oleg was selected to display a poster regarding his recent discovery of lattice trigonometric functions.

From the school age we know complex formulae relating tan, sin, and cos of the same angle. In his poster Oleg describes a simpler version of trigonometry where tan(a)=sin(a)/cos(a)=7/5 implies that that sin(a)=7 and cos(a)=5. He figured out that the model of such trigonometry exists and it has deep relations to number theory and to algebraic geometry. It is not possible to realize such trigonometry in classical settings of Euclidean geometry. One should consider another geometry based on the lattice of points with integer coordinates. .

The notion of lattice trigonometric functions is closely related to continued fractions and hence various properties of geometry of numbers can be better understood via integer trigonometry. In addition lattice trigonometry helps to describe singularities of toric varieties (which already gave first results toward the solution of so-called "IKEA problem"), contributing to algebraic geometry.