Julien Paupert
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School of Mathematical & Statistical Sciences PSA 431 PO Box 871804 Tempe, AZ 85287-1804
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Mail code: 1804Campus: Tempe
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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
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.
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, 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.
-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.
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 |
- 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).
- 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)