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Mathematics Department

Colloquium Series

Fall 2019

All talks are 3:45-4:45 p.m. in the Colloquium room (Chauvenet 110), unless otherwise specified.

Cookies will be served in the lecture room starting shortly before the talk.

  • Nov
    20
  • Why is lettuce so wrinkly?
    John Gemmer
    Wake Forest
    Time: 03:45 PM

    View Abstract

    Many patterns in Nature and industry arise from the system minimizing an appropriate energy. Examples range from the periodic rippling in hanging drapes to the six-fold symmetries observed in snowflakes. Torn plastic sheets and growing leaves provide striking examples of pattern forming systems which can transition from single wavelength geometries (leaves) to complex fractal like shapes (lettuce). These fractal like patterns seem to have many length scales - the same amount of extra detail can be seen when looking closer (“statistical self-similarity”). It is a mystery how such complex patterns could arise from energy minimization alone. In this talk I will address this puzzle by showing that such patterns naturally arise from the sheet adopting a hyperbolic non-Euclidean geometry. However, there are many different hyperbolic geometries that the growing leaf could select. I will show using techniques from analysis, differential geometry and numerical optimization that the fractal like patterns are indeed the natural minimizers for the system.
  • Oct
    30
  • Tommy Wright
    US Census Bureau
    Time: 03:45 PM
  • Oct
    23
  • Gretchen Matthews
    Virginia Tech
    Time: 03:45 PM
  • Oct
    16
  • Mark Levi
    Penn State
    Time: 03:45 PM
  • Sep
    18
  • On Geodesic Triangles in the Hyperbolic Plane
    Rita Gitik
    U. Michigan
    Time: 03:45 PM

    View Abstract

    Let M be an orientable hyperbolic surface without boundary and let c be a closed geodesic in M. We prove that any side of any triangle formed by distinct lifts of c in the hyperbolic plane is shorter than c.
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