Julien Paupert's research is in geometry and topology; more precisely he studies tessellations and their symmetry groups in hyperbolic geometry.
A tessellation is a way of filling space with non-overlapping tiles in a pattern that repeats infinitely often. A lattice is the symmetry group of a tessellation. For example, the Euclidean plane (or 3-space, or higher) can be tessellated by squares (or cubes, or hypercubes), and the corresponding lattice is a product of infinite cyclic groups. The full understanding of all crystallographic structures in 3 dimensions is crucial in Chemistry.
Analogous tessellations in hyperbolic spaces are much more abundant and much less understood. Hyperbolic spaces are spaces with negative curvature, which means loosely that non-intersecting lines diverge from each other in both directions. These spaces appear naturally in special relativity, as Lorentz and Minkowski space-times.
Ph.D. Université Paris 6, France 2005
Summer 2022 | |
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Course Number | Course Title |
MAT 792 | Research |
MAT 795 | Continuing Registration |
Spring 2022 | |
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Course Number | Course Title |
MAT 300 | Mathematical Structures |
MAT 441 | Ring Theory |
MAT 493 | Honors Thesis |
MAT 584 | Internship |
MAT 590 | Reading and Conference |
MAT 591 | Seminar |
MAT 599 | Thesis |
MAT 792 | Research |
MAT 799 | Dissertation |
Fall 2021 | |
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Course Number | Course Title |
MAT 492 | Honors Directed Study |
MAT 501 | Geomtry/Topolgy of Manifolds I |
MAT 590 | Reading and Conference |
MAT 591 | Seminar |
MAT 595 | Continuing Registration |
MAT 792 | Research |
MAT 799 | Dissertation |
Summer 2021 | |
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Course Number | Course Title |
MAT 792 | Research |
Spring 2021 | |
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Course Number | Course Title |
MAT 441 | Ring Theory |
MAT 590 | Reading and Conference |
MAT 591 | Seminar |
MAT 599 | Thesis |
MAT 792 | Research |
MAT 799 | Dissertation |
Fall 2020 | |
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Course Number | Course Title |
MAT 501 | Geomtry/Topolgy of Manifolds I |
MAT 572 | Complex Analysis I |
MAT 590 | Reading and Conference |
MAT 591 | Seminar |
MAT 595 | Continuing Registration |
MAT 792 | Research |
MAT 799 | Dissertation |
Summer 2020 | |
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Course Number | Course Title |
MAT 792 | Research |
Spring 2020 | |
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Course Number | Course Title |
MAT 300 | Mathematical Structures |
MAT 590 | Reading and Conference |
MAT 591 | Seminar |
MAT 599 | Thesis |
MAT 792 | Research |
MAT 799 | Dissertation |
Fall 2019 | |
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Course Number | Course Title |
MAT 371 | Advanced Calculus I |
MAT 501 | Geomtry/Topolgy of Manifolds I |
MAT 590 | Reading and Conference |
MAT 591 | Seminar |
MAT 792 | Research |
MAT 799 | Dissertation |
Summer 2019 | |
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Course Number | Course Title |
MAT 792 | Research |
Spring 2019 | |
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Course Number | Course Title |
MAT 590 | Reading and Conference |
MAT 591 | Seminar |
MAT 598 | Special Topics |
MAT 599 | Thesis |
MAT 792 | Research |
Fall 2018 | |
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Course Number | Course Title |
MAT 310 | Introduction to Geometry |
MAT 501 | Geomtry/Topolgy of Manifolds I |
MAT 590 | Reading and Conference |
MAT 591 | Seminar |
MAT 792 | Research |
Summer 2018 | |
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Course Number | Course Title |
MAT 792 | Research |
Spring 2018 | |
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Course Number | Course Title |
MAT 590 | Reading and Conference |
MAT 591 | Seminar |
MAT 599 | Thesis |
MAT 792 | Research |
Fall 2017 | |
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Course Number | Course Title |
MAT 410 | Intro to General Topology |
MAT 501 | Geomtry/Topolgy of Manifolds I |
MAT 590 | Reading and Conference |
MAT 591 | Seminar |
MAT 792 | Research |