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Feb 11

11 Feb (CLIM) Golhke, Floods, Heat and Health

Feb 11, 2026, 1:30 PM - Mar 11, 2026, 2:30 PM

Feb 12

12 Feb (GEOL) Allen Gellis, Geomorphology

Feb 12, 2026, 4:30 - 5:30 PM

Feb 13

13 Feb (CLIM) Burls, Modeling Pliocene Warmth

Feb 13, 2026, 11:00 AM - 12:00 PM

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Geometry MMA Seminar: A hyperbolic geometry proof of Lagrange's theorem for continued fractions

Feb 13, 2026, 1:30 - 2:30 PM

 

Speaker:  Anton Lukyanenko, GMU

Title:  A hyperbolic geometry proof of Lagrange's theorem for continued fractions

 

Abstract:  A base-10 expansion of a rational number is eventually-periodic. Famously, similar results hold for continued fraction representations: a number is rational if and only if it has a finite continued fraction (CF) expansion, and is the root of a non-degenerate quadratic equation over the integers if and only if it has an eventually-periodic CF expansion. Our new geometric proof of these classical results generalizes readily to higher-dimensional settings including complex CFs, 3D CFs, quaternionic CFs, and Heisenberg CFs, but we will mostly focus on the story in the Poincare upper half-plane. Everyone is welcome to attend!

 

Time:  Friday, February 13, 2026 – 1:30pm-2:30pm

Place: Exploratory Hall, Room 4208

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