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Peter Smillie

Harry Bateman Instructor in Mathematics
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B.S., Stanford University, 2011; Ph.D., Harvard University, 2018. Caltech 2019-21.
Research Areas: Mathematics
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Research Interests

My research is in differential geometry, Teichmuller theory, and geometric structures. I am also interested in general relativity and other connections to physics.

Courses

Ma 157 abc. Riemannian Geometry. 9 units (3-0-6): second, third terms. Part a: basic Riemannian geometry: geometry of Riemannian manifolds, connections, curvature, Bianchi identities, completeness, geodesics, exponential map, Gauss's lemma, Jacobi fields, Lie groups, principal bundles, and characteristic classes. Part b: basic topics may vary from year to year and may include elements of Morse theory and the calculus of variations, locally symmetric spaces, special geometry, comparison theorems, relation between curvature and topology, metric functionals and flows, geometry in low dimensions. Part c not offered in 2018-2019. Instructor: Smillie.

Selected Publications

  1. The Minkowski problem in regular domains. (with F. Bonsante and A. Seppi). Math. Ann. (to appear)
  2. On the bordification of outer space. (with K.-U. Bux and K. Vogtmann). J. London Math Soc. 98, Issue 1 (2018), 12-34.
  3. The number of convex triangulations of the sphere by triangles, squares, or hexagons. (with P. Engel). Geom. Topology. 22, No. 5 (2018), 2839-2864.