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Award ID contains: 2005444

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  1. ; ; (, Nonlinearity)
    Abstract A bicycle path is a pair of trajectories in R n , the ‘front’ and ‘back’ tracks, traced out by the endpoints of a moving line segment of fixed length (the ‘bicycle frame’) and tangent to the back track. Bicycle geodesics are bicycle paths whose front track’s length is critical among all bicycle paths connecting two given placements of the line segment. We write down and study the associated variational equations, showing that for n ⩾ 3 each such geodesic is contained in a 3-dimensional affine subspace and that the front tracks of these geodesics form a certain subfamily ofKirchhoff rods, a class of curves introduced in 1859 by Kirchhoff, generalizing the planar elastic curves of Bernoulli and Euler. 
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  2. ; (, Journal of Experimental Mathematics)
    In analogy with the well-known 2-linkage tractor-trailer problem, we define a 2-linkage problem in the plane with novel non-holonomic “no-slip” conditions. Using constructs from sub-Riemannian geometry, we look for geodesics corresponding to linkage motion with these constraints (“tricycle kinematics”). The paths of the three vertices turn out to be critical points for functionals which appear in the hierarchy of conserved quantities for the planar filament equation, a well known completely integrable evolution equation for planar curves. We show that the geodesic equations are completely integrable, and present a second connection to the planar filament equation. 
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    Free, publicly-accessible full text available February 28, 2026
  3. ; ; ; ; (, Journal of the Association for Mathematical Research)
    In this article, we study polygonal symplectic billiards. We provide new results, some of which are inspired by numerical investigations. In particular, we present several polygons for which all orbits are periodic. We demonstrate their properties and derive various conjectures using two numerical implementations. 
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    Free, publicly-accessible full text available February 28, 2026
  4. ; ; ; ; (, The Mathematical Intelligencer)
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  5. ; ; (, Annales de l'Institut Fourier)
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  6. ; (, Pacific Journal of Mathematics)
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  7. (, Moscow mathematical journal)
    Accepted Manuscript Full Text Available
  8. ; (, The American Mathematical Monthly)
    Full Text Available 
  9. ; (, European Journal of Mathematics)
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  10. ; ; (, European Journal of Mathematics)
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