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Geometry of continued fractions (Prof. Oleg Karpenkov)
April 13, 2022 @ 4:15 pm - 5:30 pm
Title: Geometry of continued fractions
Speaker: Oleg Karpenkov, Department of Mathematical Sciences, University of Liverpool
Abstract: In this talk we introduce a geometrical model of continued fractions and discuss its appearance in rather different research areas:
— values of quadratic forms (Perron Identity for Markov spectrum)
— the 2nd Kepler law on planetary motion
— Global relation on singularities of toric varieties
Oleg Karpenkov is a mathematician at the University of Liverpool (UK), working in the general area of discrete geometry. Specifically, his interests include geometry of numbers, discrete and semi-discrete differential geometry and self-stressed configurations of graphs. He completed his Ph.D. at Moscow State University under the supervision of Vladimir Arnold in 2005. He held several postdoctoral positions in Paris (Fellowship of the Mairie de Paris), Leiden, and Graz (Lise Meitner Fellowship) before arriving in Liverpool in 2012. In 2013 he published a book “Geometry of Continued Fractions” (its extended second edition will be available soon). His Erdos number is 3.