Julien Paupert

School of Mathematical & Statistical Sciences PSA 431 PO Box 871804 Tempe, AZ 852871804

Mail code: 1804Campus: Tempe

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 nonoverlapping tiles in a pattern that repeats infinitely often. A lattice is the symmetry group of a tessellation. For example, the Euclidean plane (or 3space, 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 nonintersecting lines diverge from each other in both directions. These spaces appear naturally in special relativity, as Lorentz and Minkowski spacetimes.
Ph.D. Université Paris 6, France 2005
My research interests lie in lowdimensional 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 nonoverlapping tiles in a pattern that repeats infinitely often. A lattice is the symmetry group of a tessellation. For example, the Euclidean plane (or 3space, 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 nonintersecting lines diverge from each other in both directions. These spaces appear naturally in special relativity, as Lorentz and Minkowski spacetimes.
Theoretical Mathematics, Geometry & Topology
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, 127133.
A. Mark, J. Paupert; Presentations for cusped arithmetic hyperbolic lattices. Algebr. Geom. Topol. 22 (2022), 35773626.
M. Deraux, J. Parker, J. Paupert; New nonarithmetic complex hyperbolic lattices II. Michigan Math. J. 70 (2021), 133205.
J. Paupert, J. Wells; Hybrid lattices and thin subgroups of Picard modular groups. Topol. Appl. 269 (2020), 115.
J. Paupert, P. Will; Involution and commutator length for complex hyperbolic isometries. Michigan Math. J. 66 (2017), 699744.
 J. Paupert, P. Will; Real reflections, commutators and crossratios in complex hyperbolic space. Groups Geom. Dyn. 11 (2017), 311352.
M. Deraux, J. Parker, J. Paupert; New nonarithmetic complex hyperbolic lattices. Invent. Math. 203 (2016), 681771.
 J. Paupert; A simple method to compute volumes of evendimensional Coxeter polyhedra, in In the Tradition of AhlforsBers, VI, Contemporary Mathematics 590, Amer. Math. Soc., Providence RI, 2013, 167175.
J. Paupert; Nondiscrete hybrids in SU(2,1). Geom. Dedicata 157 (2012), 259268.
M. Deraux, J. Parker, J. Paupert; Census of the complex hyperbolic sporadic triangle groups. Experiment. Math. 20 (2011), 467486.
J. Paupert; Unfaithful complex hyperbolic triangle groups III: arithmeticity and commensurability . Pacific J. Maths. 245 (2010), 359372.
 J. Parker, J. Paupert; Unfaithful complex hyperbolic triangle groups II: Higher order reflections. Pacific J. Maths. 239 (2009), 357389.
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), 4560.
J. Paupert; Elliptic triangle groups in PU(2,1), Lagrangian triples and momentum maps. Topology 46 (2007), 155183.
M. Deraux, E. Falbel, J. Paupert; New constructions of fundamental polyhedra in complex hyperbolic space. Acta Math. 194 (2005), 155201.
E. Falbel, J. Paupert; Fundamental domains for finite subgroups in U(2) and configurations of Lagrangians. Geom. Dedicata 109 (2004), 221238.
National Science Foundation grant DMS 2225583 "Conference on Complex Hyperbolic Geometry and Related Topics'', 07/202206/2023, $ 35,000, Principal Investigator.
National Science Foundation grant DMS 1708463 "Discrete groups in complex hyperbolic geometry'', 08/201707/2021, $ 177,582, Principal Investigator.
Simons Foundation Collaboration Grant for Mathematicians # 318124, 09/201408/2019 (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), 20122017, $~5 M, Member.
National Science Foundation grant DMS 1007340 "Complex hyperbolic reflection groups and lattices'', 07/201006/2013, $94,573, Principal Investigator. Transferred to ASU as DMS 1249147.
Courses
2024 Fall
Course Number  Course Title 

MAT 492  Honors Directed Study 
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 
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 
2019 Summer
Course Number  Course Title 

MAT 792  Research 
MAT 792  Research 
MAT 792  Research 
 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 crossratios in complex hyperbolic space. AhlforsBers 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 nonarithmetic 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 crossratios in complex hyperbolic space. Second GEAR Network Junior Retreat, University of Michigan (May 2014).
 J. Paupert. New nonarithmetic 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 crossratios in complex hyperbolic space. Topology Seminar at UCSB (Nov 2013).
 J. Paupert. New nonarithmetic 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 nonarithmetic lattices in SU(2,1). "Algebraic Geometry and Hyperbolic Geometry  New Connections", IMPA/Cabo Frio, Brazil (Jun 2013).
 Julien Paupert. Real reflections, commutators and crossratios in complex hyperbolic space. University of Indiana (Bloomington), Geometry Seminar (Oct 2012).
 Julien Paupert. New examples of nonarithmetic 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 3manifolds; 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. Nonarithmetic lattices in complex hyperbolic geometry, part 2. London Mathematical Society – EPSRC Durham Symposium GEOMETRY AND ARITHMETIC OF LATTICES (Jul 2011).
 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)