Math Colloquium, Han Li (University of Texas at Austin): 'Horospherical orbits, Farey fractions and the Frobenius numbers'

Thursday, October 9, 2014
4:15 PM - 5:15 PM (ET)
ESC 638
Event Type
Academic Calendar
Cameron Hill
Math/CS Colloquium

Abstract: The study of horospherical orbits in homogeneous spaces has found numerous applications in number theory and geometry. A remarkable example is Zagier's reformulation of the Riemann hypothesis in terms of the quantitative equidistribution of long closed horocycles in the modular surface. Around 2010 Marklof observed that the distribution of the Farey fractions on the horospherical orbits predicts the averaging behavior of the Frobenius numbers (also known as the coin exchange problem). The plan of this talk is to explain the connections between these research topics, and discuss our recent quantitative refinement of Marklof?s work. Our method involves harmonic analysis in combination with ergodic theory and the geometry of numbers.

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