Julien Paupert

Julien Paupert

Associate Professor,
School of Mathematical and Statistical Sciences
Other ASU affiliations
Associate Professor, Mathematics
  • julien.paupert@asu.edu
  • School of Mathematical & Statistical Sciences PSA 431 PO Box 871804 Tempe, AZ 85287-1804
  • Mail code: 1804
    Campus: Tempe
  • ‌
Biography Research Teaching Public Work
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Long Bio

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.

Education

Ph.D. Université Paris 6, France 2005

CV
Curriculum Vitae
Research Website URL
https://math.la.asu.edu/~paupert/
Research Interests

My research interests lie in low-dimensional geometry and topology. More precisely, I study hyperbolic geometry (mostly complex), reflection groups, and lattices in rank 1 semisimple Lie groups.



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.

Research Group

Theoretical Mathematics, Geometry & Topology

Publications

-A. Mark, J. Paupert, D. Polletta; Picard modular groups generated by complex reflections, in Computational Aspects of Discrete Subgroups of Lie Groups, Contemporary Mathematics 783, Amer. Math. Soc., Providence RI, 2023, 127-133.

-A. Mark, J. Paupert; Presentations for cusped arithmetic hyperbolic lattices. Algebr. Geom. Topol. 22 (2022), 3577-3626.

-M. Deraux, J. Parker, J. Paupert; New non-arithmetic complex hyperbolic lattices II. Michigan Math. J. 70 (2021), 133-205.

-J. Paupert, J. Wells; Hybrid lattices and thin subgroups of Picard modular groups. Topol. Appl. 269 (2020), 1-15.

-J. Paupert, P. Will; Involution and commutator length for complex hyperbolic isometries. Michigan Math. J. 66 (2017), 699-744.

- J. Paupert, P. Will; Real reflections, commutators and cross-ratios in complex hyperbolic space. Groups Geom. Dyn. 11 (2017), 311-352.

-M. Deraux, J. Parker, J. Paupert; New non-arithmetic complex hyperbolic lattices. Invent. Math. 203 (2016), 681-771.

- J. Paupert; A simple method to compute volumes of even-dimensional Coxeter polyhedra, in In the Tradition of Ahlfors-Bers, VI, Contemporary Mathematics 590, Amer. Math. Soc., Providence RI, 2013, 167-175.

-J. Paupert; Non-discrete hybrids in SU(2,1). Geom. Dedicata 157 (2012), 259-268.

-M. Deraux, J. Parker, J. Paupert; Census of the complex hyperbolic sporadic triangle groups. Experiment. Math. 20 (2011), 467-486.

-J. Paupert; Unfaithful complex hyperbolic triangle groups III: arithmeticity and commensurability . Pacific J. Maths. 245 (2010), 359-372.

- J. Parker, J. Paupert; Unfaithful complex hyperbolic triangle groups II: Higher order reflections. Pacific J. Maths. 239 (2009), 357-389.

-J. Paupert; Applications moment, polygones de configuration et groupes discrets de réflexions complexes dans PU(2,1). Séminaire de théorie spectrale et géométrie, Grenoble. TSG 24 (2007), 45-60.

-J. Paupert; Elliptic triangle groups in PU(2,1), Lagrangian triples and momentum maps. Topology 46 (2007), 155-183.

-M. Deraux, E. Falbel, J. Paupert; New constructions of fundamental polyhedra in complex hyperbolic space. Acta Math. 194 (2005), 155-201.

-E. Falbel, J. Paupert; Fundamental domains for finite subgroups in U(2) and configurations of Lagrangians. Geom. Dedicata 109 (2004), 221-238.

 

Research Activity

 -National Science Foundation grant DMS 2225583 "Conference on Complex Hyperbolic Geometry and Related Topics'', 07/2022-06/2023, $ 35,000, Principal Investigator.



  

 -National Science Foundation grant DMS 1708463 "Discrete groups in complex hyperbolic geometry'', 08/2017-07/2021, $ 177,582, Principal Investigator.



 

-Simons Foundation Collaboration Grant for Mathematicians # 318124, 09/2014-08/2019 (terminated 08/2017 because of incoming NSF grant), $ 35,000, Principal Investigator.

 

-National Science Foundation grants DMS 1107452, 1107263, 1107367 "RNMS: GEometric structures And Representation varieties" (the GEAR Network), 2012-2017, $~5 M, Member.

 



-National Science Foundation grant DMS 1007340 "Complex hyperbolic reflection groups and lattices'', 07/2010-06/2013, $94,573, Principal Investigator. Transferred to ASU as DMS 1249147.

Teaching Website URL
Teaching Website
Courses
2025 Spring
Course Number Course Title
MAT 300 Mathematical Structures
MAT 493 Honors Thesis
MAT 590 Reading and Conference
MAT 599 Thesis
MAT 591 Seminar
MAT 792 Research
MAT 799 Dissertation
MAT 795 Continuing Registration
MAT 412 Differential Geometry
MAT 599 Thesis
MAT 590 Reading and Conference
MAT 784 Internship
2024 Fall
Course Number Course Title
MAT 492 Honors Directed Study
MAT 493 Honors Thesis
MAT 590 Reading and Conference
MAT 792 Research
MAT 799 Dissertation
MAT 595 Continuing Registration
MAT 792 Research
MAT 590 Reading and Conference
MAT 599 Thesis
MAT 599 Thesis
MAT 584 Internship
2024 Summer
Course Number Course Title
MAT 792 Research
MAT 792 Research
MAT 792 Research
MAT 595 Continuing Registration
MAT 784 Internship
MAT 792 Research
MAT 795 Continuing Registration
MAT 799 Dissertation
MAT 799 Dissertation
MAT 599 Thesis
MAT 795 Continuing Registration
2024 Spring
Course Number Course Title
MAT 493 Honors Thesis
MAT 590 Reading and Conference
MAT 599 Thesis
MAT 444 Intermediate Abstract Algebra
MAT 591 Seminar
MAT 792 Research
MAT 799 Dissertation
MAT 795 Continuing Registration
MAT 599 Thesis
MAT 591 Seminar
MAT 590 Reading and Conference
MAT 784 Internship
2023 Fall
Course Number Course Title
MAT 492 Honors Directed Study
MAT 590 Reading and Conference
MAT 792 Research
MAT 799 Dissertation
MAT 591 Seminar
MAT 440 Group Theory
MAT 501 Geomtry/Topolgy of Manifolds I
MAT 595 Continuing Registration
MAT 792 Research
MAT 590 Reading and Conference
MAT 599 Thesis
2023 Summer
Course Number Course Title
MAT 792 Research
MAT 792 Research
MAT 792 Research
MAT 595 Continuing Registration
MAT 792 Research
MAT 795 Continuing Registration
MAT 799 Dissertation
2023 Spring
Course Number Course Title
MAT 493 Honors Thesis
MAT 590 Reading and Conference
MAT 599 Thesis
MAT 444 Intermediate Abstract Algebra
MAT 591 Seminar
MAT 792 Research
MAT 799 Dissertation
MAT 591 Seminar
2022 Fall
Course Number Course Title
MAT 492 Honors Directed Study
MAT 590 Reading and Conference
MAT 792 Research
MAT 799 Dissertation
MAT 591 Seminar
MAT 501 Geomtry/Topolgy of Manifolds I
MAT 595 Continuing Registration
MAT 792 Research
MAT 590 Reading and Conference
MAT 598 Special Topics
MAT 599 Thesis
2022 Summer
Course Number Course Title
MAT 792 Research
MAT 792 Research
MAT 792 Research
MAT 792 Research
MAT 795 Continuing Registration
2022 Spring
Course Number Course Title
MAT 493 Honors Thesis
MAT 590 Reading and Conference
MAT 599 Thesis
MAT 591 Seminar
MAT 792 Research
MAT 799 Dissertation
MAT 300 Mathematical Structures
MAT 441 Ring Theory
MAT 584 Internship
MAT 591 Seminar
2021 Fall
Course Number Course Title
MAT 492 Honors Directed Study
MAT 590 Reading and Conference
MAT 792 Research
MAT 799 Dissertation
MAT 591 Seminar
MAT 501 Geomtry/Topolgy of Manifolds I
MAT 595 Continuing Registration
MAT 590 Reading and Conference
2021 Summer
Course Number Course Title
MAT 792 Research
MAT 792 Research
MAT 792 Research
MAT 792 Research
2021 Spring
Course Number Course Title
MAT 590 Reading and Conference
MAT 599 Thesis
MAT 591 Seminar
MAT 792 Research
MAT 799 Dissertation
MAT 441 Ring Theory
MAT 591 Seminar
MAT 792 Research
2020 Fall
Course Number Course Title
MAT 590 Reading and Conference
MAT 572 Complex Analysis I
MAT 792 Research
MAT 799 Dissertation
MAT 591 Seminar
MAT 501 Geomtry/Topolgy of Manifolds I
MAT 595 Continuing Registration
MAT 590 Reading and Conference
2020 Summer
Course Number Course Title
MAT 792 Research
MAT 792 Research
MAT 792 Research
MAT 792 Research
2020 Spring
Course Number Course Title
MAT 590 Reading and Conference
MAT 599 Thesis
MAT 300 Mathematical Structures
MAT 591 Seminar
MAT 792 Research
MAT 799 Dissertation
2019 Fall
Course Number Course Title
MAT 590 Reading and Conference
MAT 792 Research
MAT 799 Dissertation
MAT 591 Seminar
MAT 501 Geomtry/Topolgy of Manifolds I
MAT 371 Advanced Calculus I
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)
Expertise Areas
Theoretical Mathematics
Geometry and Topology
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