Research


Fresh preprints (mathematics)

Near ideal decompositions of ideal polygons
Modular systoles are extremal for the crossing number
With C. Burrin
Hyperbolic spaces not quasi-isometric to curve complexes
With J. Aramayona and R. Webb
Crossing numbers of dense graphs on surfaces
With A. Hubard and A. de Mesmay
Ordering curves on surfaces
With H. Vo and B. Xu
Flip-graphs of non-orientable filling surfaces
With P. Panda and L. Pournin
Crossing number inequalities for curves on surfaces
With A. Hubard
Crossing lemmas for k-systems of arcs
With A. Hubard
A topological viewpoint on curves via intersection
With B. Xu
Geodesic and orthogeodesic identities on hyperbolic surfaces
Quantifying the sparseness of simple geodesics on hyperbolic surfaces
With P. Buser

Journal publications

The coarse geometry of hexagon decomposition graphs
With F. Gültepe
Canad. J. Math., to appear.
Universal families of arcs and curves on surfaces
With N. Fuladi and A. de Mesmay
Israel Journal of Math., to appear.
Prime orthogeodesics, concave cores and families of identities on hyperbolic surfaces
With A. Basmajian and S. P. Tan
Adv. Math., 460, 2025, 42pp.
Counting geodesics between surface triangulations
With L. Pournin
Math. Proc. Camb. Philos. Soc., 178(1), 2025, 45--63.
Computing a Dirichlet domain for a hyperbolic surface
With V. Despré, B. Kolbe and M. Teillaud
J. Comput. Geom., 15, 2024, 40-56.
Quasisymmetric maps, shears, lambda lengths and flips
With D. Šarić
Math. Z., 306(3), 2024, Paper No. 21, 14 pp.
A shorter note on shorter pants
Bull. Lond. Math. Soc., 56(4), 2024, 1483--1487.
The shortest non-simple closed geodesics on hyperbolic surfaces
With A. Basmajian and H. Vo
Math. Z., 306(1), 2024, Paper No. 8, 19 pp.
Bounded geometry with no bounded pants decomposition
With A. Basmajian and N. Vlamis
Israel Journal of Math. 260(1), 2024, 235--260.
Measuring pants
With N. M. Doan and S. P. Tan
Trans. Amer. Math. Soc., 376 (8), 2023, 5281--5306.
Systoles and diameters of hyperbolic surfaces
With F. Balacheff and V. Despré
Kyoto J. Math., 63(1), 2023, 211--222.
Minimal Delaunay triangulations of hyperbolic surfaces
With M. Ebbens and G. Vegter
Discrete Comput. Geom., 69(2), 2023, 568--592.
Ideally, all surfaces of infinite type admit a triangulation
With Alan McLeay
Bull. Lond. Math. Soc., 54(5), 2022, 2032--2040.
The simple separating systole for hyperbolic surfaces of large genus
With Y. Wu and Y. Xue
J. Inst. Math. Jussieu, 21(6), 2022, 2205--2214.
Flip graphs for infinite type surfaces
With A. Fossas
Groups Geom. Dyn., 16(4), 2022, 1165--1178.
The minimal length product over homology bases of manifolds
With F. Balacheff and S. Karam
Math. Ann., 380(1-2), 2021, 825--854.
Short closed geodesics with self-intersections
With V. Erlandsson
Math. Proc. Camb. Philos. Soc., 169(3), 2020, 623--638.
Geometric simplicial embeddings of arc-type graphs
With A. Weber
J. Korean Math. Soc., 57(5), 2020, 1103--1118.
Counting curves and the stable length of currents
With V. Erlandsson and J. Souto
J. Eur. Math. Soc. (JEMS), 22(6), 2020, 1675-1702.
The maximum number of systoles for genus two Riemann surfaces with abelian differentials
With C. Judge
Comment. Math. Helv., 94(2), 2019, 399-437.
The geometry of flip graphs and mapping class groups
With V. Disarlo
Trans. Amer. Math. Soc., 372(6), 2019, 3809-3844.
Simultaneous flips on triangulated surfaces
With V. Disarlo
Michigan Math. J., 67(3), 2018, 451-464.
Interrogating surface length spectra and quantifying isospectrality
Math. Ann., 370(3-4), 2018, 1759-1787.
The genus of curve, pants and flip graphs
With B. Petri
Discrete Comput. Geom., 59(1), 2018, 1-30.
Modular flip-graphs of one holed surfaces
With L. Pournin
European J. Combin., 67, 2018, 158-173.
Once punctured disks, non-convex polygons, and pointihedra
With L. Pournin
Ann. Comb., 22(3), 2018, 619-640.
Geometric filling curves on surfaces
With A. Basmajian and J. Souto
Bull. Lond. Math. Soc., 49(4), 2017, 660-669.
Flip-graph moduli spaces of filling surfaces
With L. Pournin
J. Eur. Math. Soc. (JEMS), 19(9), 2017, 2697-2737.
Distances in domino flip graphs
With S. Zappa
Amer. Math. Monthly, 124(8), 2017, 710-722.
Arc and curve graphs for infinite-type surfaces
With J. Aramayona and A. Fossas
Proc. Amer. Math. Soc., 145(11), 2017, 4995-5006.
On the homology length spectrum of surfaces
With D. Massart
Int. Math. Res. Not. IMRN, 8, 2017, 2367-2401.
Filling sets of curves on punctured surfaces
With F. Fanoni
New York J. Math., 22, 2016, 653-666.
Chromatic numbers of hyperbolic surfaces
With C. Petit
Indiana Univ. Math. J., 65(4), 2016, 1401-1423.
Relative shapes of thick subsets of moduli space
With J. Anderson and A. Pettet
Amer. J. Math, 138(2), 2016, 473-498.
Injective maps between flip graphs
With J. Aramayona and T. Koberda
Ann. Inst. Fourier (Grenoble), 65(5), 2015, 2037-2055.
Systoles and kissing numbers of finite area hyperbolic surfaces
With F. Fanoni
Algebr. Geom. Topol., 15(6), 2015, 3409-3433.
Curve graphs on surfaces of infinite type
With A. Fossas
Ann. Acad. Sci. Fenn. Math., 40 (2), 2015, 793-801.
Connecting p-gonal loci in the compactification of moduli space
With A. F. Costa and M. Izquierdo
Rev. Mat. Complut., 28(2), 2015, 469-486.
A short note on short pants
Canad. Math. Bull., 57(4), 2014, 870-876.
Systole growth for finite area hyperbolic surfaces
With F. Balacheff and E. Makover
Ann. Fac. Sci. Toulouse, Math., 23(6), 2014, 175-180.
Kissing numbers for surfaces
J. Topology, 6(3), 2013, 777-791.
Convexity of strata in diagonal pants graphs of surfaces
With J. Aramayona, C. Lecuire and K. Shackleton
Publ. Mat., 57, 2013, 219-237.
Constructing metrics on a 2-torus with a partially prescribed stable norm
With E. Makover and C. Sutton
Manuscripta Math., 139, 2012, 515-534.
Bers' constants for punctured spheres and hyperelliptic surfaces
With Florent Balacheff
J. Topol. Anal., 4(3), 2012, 271-296.
Short loop decompositions of surfaces and the geometry of Jacobians
With F. Balacheff and S. Sabourau
Geom. Funct. Anal., 22(1), 2012, 37-73.
Growth of the Weil-Petersson diameter of moduli space
With Will Cavendish
Duke Math. J., 161(1), 2012, 139-171.
The homology systole of hyperbolic Riemann surfaces
Geom. Dedicata, 157(1), 2012, 331-338.
Pants decompositions of random surfaces
With L. Guth and R. Young
Geom. Funct. Anal., 21(5), 2011, 1069-1090.
Small filling sets of curves on a surface
With J. Anderson and A. Pettet
Topology Appl., 158, 2011, 84-92.
Constructing convex planes in the pants complex
With J. Aramayona and K. Shackleton
Proc. Amer. Math. Soc., 137, 2009, 3523-3531.
Applications of a theorem of Singerman about Fuchsian groups
With Antonio F. Costa
Arch. Math. (Basel), 91(6), 2008, 536-543.
On Harnack's Theorem and extensions: a geometric proof and applications
With Antonio F. Costa
Conform. Geom. Dyn., 12, 2008, 174-186.
Fixed point free involutions on Riemann surfaces
Israel Journal of Math., 166, 2008, 297-311.
Multiplicities of simple closed geodesics and hypersurfaces in Teichmüller space
With Greg McShane
Geom. Topol., 12, 2008, 1883-1919.
On the angles formed by N points of the Euclidean and hyperbolic planes
With Ghislain Jaudon
Geombinatorics, 17(4), 2008, 157-165.
Totally geodesic subgraphs of the pants complex
With J. Aramayona and K. Shackleton
Math. Res. Lett., 15(2), 2008, 309-320.
A geometric characterization of orientation reversing involutions
With Antonio F. Costa
J. London Math. Soc. (2), 77(2), 2008, 287-298.
Collars and partitions of hyperbolic cone-surfaces
With Emily Dryden
Geom. Dedicata, 127(1), 2007, 139-149.
Minimal length of two intersecting simple closed geodesics
With Thomas Gauglhofer
Manuscripta Math., 122(3), 2007, 321-339.
Hyperbolic polygons and simple closed geodesics
Enseign. Math. (2), 52, 2006, 295-317.
Lengths of geodesics on Riemann surfaces with boundary
Ann. Acad. Sci. Fenn. Math., 30(2), 2005, 227-236.
A note on collars of simple closed geodesics
Geom. Dedicata, 112(1), 2005, 165-168.

Refereed proceedings

Computing a Dirichlet domain for a hyperbolic surface (conference proceedings version of the paper with the same title above).
With V. Despré, B. Kolbe and M. Teillaud
39th International Symposium on Computational Geometry (SoCG), Art. No. 27, 15 pp., LIPIcs. Leibniz Int. Proc. Inform., 258, Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, 2023.
Minimal Delaunay triangulations of hyperbolic surfaces (conference proceedings version of the paper with the same title above).
With M. Ebbens and G. Vegter
37th International Symposium on Computational Geometry (SoCG), Art. No. 31, 16 pp., LIPIcs. Leibniz Int. Proc. Inform., 189, Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, 2021.
The distribution of simple closed geodesics on surfaces
With Peter Buser
Proc. of the 15th ICFIDCAA (Osaka 2007), 2008, 3-10.
Determinants of Binary Circulant Matrices
With Gerard Maze
Proc. 2004 IEEE Int. Sym. on Information Theory, 2004.

Book chapters

The topological types of length bounded multicurves
Essays in Geometry, dedicated to Norbert A'Campo, 97-109, IRMA Lect. Math. Theor. Phys., 34, EMS Press, Berlin, 2023.
Simple closed geodesics and the study of Teichmüller spaces
Handbook of Teichmüller theory, vol. IV, IRMA Lect. Math. Theor. Phys., 2014, 113-134.
Simple closed geodesics of equal length on a torus
With G. McShane
Geometry of Riemann surfaces, LMS Lecture Notes 368, 2010, 268-282.

Outreach, games, art and culture

ReShape: a Collaborative Art Experience
With B. Teheux
Quadratis Puzzles
With M. Gutiérrez and P. Turner
Proceedings of Bridges 2022: Mathematics, Art, Music, Architecture, Culture, 2022, 49-56.
Mathema: a book-app
With P. Turner
Published by TomBooks, App Store, 2015-2020.

Appendices/other

An appendix to: Least dilatation of pure surface braids (by M. Loving)
With M. Loving
Algebr. Geom. Topol., 19(2), 2019, 941-964.
Illustrations for: Mirzakhani's Curve Counting and Geodesic Currents (by V. Erlandsson and J. Souto).
Birkhauser, 2023.

Older preprints:

Delaunay triangulations of points on circles
With V. Despré, O. Devillers and J.-M. Schlenker
Chromatic numbers for the hyperbolic plane and discrete analogs
With C. Petit
Separating simple closed geodesics and homology bases