Julien Paupert

School of Mathematical & Statistical Sciences
PSA 431
PO Box 871804
Tempe
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´┐Ż 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).

Courses

Summer 2019
Course Number Course Title
MAT 792 Research
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

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)