Mathematics Colloquia and Seminars

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Similarly to the growth of Applied Topology, the uses and applications of Geometry are now expanding into scientific, computational, and engineering domains. First, we’ll review the recent history of this expanding Applied Geometry area.

I’ll then mention a couple of collaborations, developing and implementing algorithms inspired by the marked length spectrum that classifies complex networks (with Eliassi-Rad and Torres) and analyzes digital images using a variant of curve-shortening flow (with Velazquez Richards). As well as a definition I proposed of a global convolution on manifolds of arbitrary topology. 

Then, I’ll present joint work with Evangelista and Ruiz Pantaleón on computational Poisson geometry and showcase an application to learning symbolic expressions of Hamiltonian systems. We developed and released two Python packages that perform symbolic and numerical computation of objects in Poisson geometry, and work with NumPy, TensorFlow and PyTorch.  We then used them to train neural networks (hybrids with CNN and LSTM components) that learn symbolic expressions of Hamiltonian vector fields.

If time allows, I’ll present a brief tutorial of our computational Poisson Geometry modules