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## Julien Paupert

Associate Professor

Faculty

TEMPE Campus

Mailcode

1804

## Biography

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.

## CV

## Education

Ph.D. Universit� Paris 6, France 2005

## Publications

- J. Paupert. A simple method to compute volumes of even-dimensional Coxeter polyhedra. AMS Contemporary Mathematics (2013).
- J. Paupert. Non-discrete hybrids in SU(2,1). Geometriae Dedicata (2012).
- M. Deraux, J. Parker, J. Paupert. Census of the complex hyperbolic sporadic triangle groups. Experimental Mathematics (2011).

## Research Activity

- Paupert,Julien Henri*. Complex hyperbolic discrete groups and lattices (ASUF 30006173). ASU FDN(9/1/2014 - 8/31/2019).
- Paupert,Julien Henri*. Complex hyperbolic reflection groups and lattices. NSF-MPS-DMS(5/7/2012 - 6/30/2014).

## Teaching Website

## Courses

Spring 2019 | |
---|---|

Course Number | Course Title |

MAT 590 | Reading and Conference |

MAT 591 | Seminar |

MAT 598 | Special Topics |

MAT 599 | Thesis |

MAT 792 | Research |

Fall 2018 | |
---|---|

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 | |
---|---|

Course Number | Course Title |

MAT 792 | Research |

Spring 2018 | |
---|---|

Course Number | Course Title |

MAT 590 | Reading and Conference |

MAT 591 | Seminar |

MAT 599 | Thesis |

MAT 792 | Research |

Fall 2017 | |
---|---|

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 |

Summer 2017 | |
---|---|

Course Number | Course Title |

MAT 792 | Research |

Spring 2017 | |
---|---|

Course Number | Course Title |

MAT 371 | Advanced Calculus I |

MAT 494 | Special Topics |

MAT 590 | Reading and Conference |

MAT 591 | Seminar |

MAT 792 | Research |

Fall 2016 | |
---|---|

Course Number | Course Title |

MAT 501 | Geomtry/Topolgy of Manifolds I |

MAT 590 | Reading and Conference |

MAT 591 | Seminar |

MAT 792 | Research |

Summer 2016 | |
---|---|

Course Number | Course Title |

MAT 792 | Research |

Spring 2016 | |
---|---|

Course Number | Course Title |

MAT 590 | Reading and Conference |

MAT 591 | Seminar |

MAT 598 | Special Topics |

MAT 599 | Thesis |

MAT 792 | Research |

Fall 2015 | |
---|---|

Course Number | Course Title |

MAT 440 | Group Theory |

MAT 590 | Reading and Conference |

MAT 591 | Seminar |

MAT 598 | Special Topics |

MAT 792 | Research |

Summer 2015 | |
---|---|

Course Number | Course Title |

MAT 792 | Research |

Spring 2015 | |
---|---|

Course Number | Course Title |

MAT 444 | Intermediate Abstract Algebra |

MAT 591 | Seminar |

MAT 599 | Thesis |

MAT 792 | Research |

Fall 2014 | |
---|---|

Course Number | Course Title |

MAT 310 | Introduction to Geometry |

MAT 499 | Individualized Instruction |

MAT 590 | Reading and Conference |

MAT 591 | Seminar |

MAT 598 | Special Topics |

MAT 792 | Research |

Summer 2014 | |
---|---|

Course Number | Course Title |

MAT 595 | Continuing Registration |

MAT 792 | Research |

## Presentations

- J. Paupert. Complex hyperbolic lattices. Advanced Training in Mathematics Workshop on "Lattices: Geometry and Dynamics", IISER Mohali, India (Dec 2014).
- J. Paupert. Real reflections, commutators and cross-ratios in complex hyperbolic space. Ahlfors-Bers Colloquium (parallel session on Geometry), Yale University (Oct 2014).
- J. Paupert. Bianchi groups generated by reflections; Picard modular groups generated by real reflectioons (2 talks). ASU Differential Geometry Seminar (Sep 2014).
- J. Paupert. New non-arithmetic lattices in SU(2,1). Borel Seminar 2014 "Discrete group actions in Geometry and Topology", Les Diablerets, Switzerland (Jun 2014).
- J. Paupert. Real reflections, commutators and cross-ratios in complex hyperbolic space. Second GEAR Network Junior Retreat, University of Michigan (May 2014).
- J. Paupert. New non-arithmetic lattices in SU(2,1). Geometry and Topology seminar at the California Institute of Technology (Feb 2014).
- J. Paupert. Constructing hyperbolic lattices. Colloquium at UNR (Dec 2013).
- J. Paupert. Real reflections, commutators and cross-ratios in complex hyperbolic space. Topology Seminar at UCSB (Nov 2013).
- J. Paupert. New non-arithmetic lattices in SU(2,1). Workshop on "Exotic Geometric Structures" at ICERM/Brown (Sep 2013).
- J. Paupert. Volumes of Coxeter polyhedra. ASU Differential Geometry Seminar (Sep 2013).
- J. Paupert. New non-arithmetic lattices in SU(2,1). "Algebraic Geometry and Hyperbolic Geometry - New Connections", IMPA/Cabo Frio, Brazil (Jun 2013).
- Julien Paupert. Real reflections, commutators and cross-ratios in complex hyperbolic space. University of Indiana (Bloomington), Geometry Seminar (Oct 2012).
- Julien Paupert. New examples of non-arithmetic lattices in PU(2,1). Universite Grenoble 1, Seminaire de Theorie Spectrale et Geometrie (Jun 2012).
- J. Paupert. Topology of Surfaces and Euler characteristic; Hyperbolic Structures on Surfaces and 3-manifolds; Geodesics in the Modular Surface H2/SL(2,Z) (3 talks). ASU Differential Geometry Seminar (Jan 2012).
- J. Paupert. Hyperbolic volumes and arithmetic functions. ASU Number Theory Seminar (Oct 2011).
- J. Paupert. Hyperbolic Surfaces; Hyperbolic Manifolds; Hyperbolic Reflection Groups (3 talks). ASU Differential Geometry Seminar (Oct 2011).
- J. Paupert. Non-arithmetic lattices in complex hyperbolic geometry, part 2. London Mathematical Society EPSRC Durham Symposium GEOMETRY AND ARITHMETIC OF LATTICES (Jul 2011).

## Service

- Differential Geometry Seminar, Organizer; speaker (2 talks) (2014 - 2014)
- Math Circle, Speaker (2 talks) (2014 - 2014)
- Math Circle, Speaker (2 talks) (2014 - 2014)
- Differential Geometry Seminar, Organizer; speaker (1 talk) (2013 - 2013)
- Math Circle, Speaker (2013 - 2013)
- Math Circle, Speaker (2013 - 2013)
- Math Circle, Speaker (2012 - 2012)
- Math Circle, Speaker (2012 - 2012)
- Differential Geometry Seminar, Organizer; speaker (3 talks) (2012 - 2012)
- Special Session on "Hyperbolic Geometry" at AMS 2012 Fall Western Sectional Meeting, Main organizer (2012 - 2012)
- First Year Seminar, Speaker (2012 - 2012)
- Differential Geometry Seminar, Organizer; speaker (3 talks) (2011 - 2011)
- Math Circle, Speaker (2011 - 2011)
- Math Circle, Speaker (2011 - 2011)
- First Year Seminar, Speaker (2011 - 2011)