đ About
I am an Associate Professor in mathematics at Université Paris Cité (Paris Diderot campus, formerly Paris 7).
I defended my HDR (Habilitation) Geometric Approaches to Resolution of Singularities and Integer Partitions in December 2020.
I defended my PhD thesis, On the geometry of jet schemes of some singular algebraic varieties, in June 2010 at the University of Versailles Saint-Quentin-en-Yvelines; my thesis advisor was Monique Lejeune-Jalabert.
đ My complete CV (PDF)
đ Featured in Quanta Magazine
Popular science article by Jordana Cepelewicz published in Quanta Magazine about a research topic I helped develop, linking singularities and number theory in the spirit of Ramanujan.
Research Area
My research area is at the intersection of algebraic geometry, commutative algebra, and combinatorics. Most of the problems I am interested in come from singularity theory.
Publications
Preprints
[1]
Partition identities associated with A_r-Surface singularities
with Pooneh Afsharijoo and Pedro D. GonzĂĄlez PĂ©rez
arXiv:2601.12048
arXiv:2601.12048
[2]
On the geometry of punctual Hilbert schemes on singular curves and their motivic zeta functions
with Mounir Hajli and Wenhao Zhu
arXiv:2509.06761
arXiv:2509.06761
[3]
Jet Schemes, Newton Polygons and Continued Fractions
with Ghadi Abdallah, Maximiliano Leyton-Alvarez and Bassam Mourad
arXiv:2509.06095
arXiv:2509.06095
Published Articles
[4]
Classification of singularities of cluster algebras of finite type II: coefficients
with Angélica Benito, Eleonore Faber and Bernd Schober
Journal of Combinatorial Algebra, to appear, DOI 10.4171/JCA/117
Link
Journal of Combinatorial Algebra, to appear, DOI 10.4171/JCA/117
Link
[5]
Teissier singularities
[6]
The Nash problem for torus actions of complexity one
[7]
Neighborly partitions, hypergraphs and Gordon's identities
with Pooneh Afsharijoo
J. Combin. Theory Ser. A 210 (2025), Paper No. 105963, 16 pp
arXiv:2309.13334
J. Combin. Theory Ser. A 210 (2025), Paper No. 105963, 16 pp
arXiv:2309.13334
[8]
Hilbert meets Ramanujan: singularity theory and integer partitions
Bull. Amer. Math. Soc. (N.S.) 62 (2025), no. 1, 93-111
PDF
I gave a talk on this topic at the Current Events Bulletin, Joint Mathematics Meetings, San Francisco 2024
đ„ Watch the video
I gave a talk on this topic at the Current Events Bulletin, Joint Mathematics Meetings, San Francisco 2024
đ„ Watch the video
[9]
Groebner fans and embedded resolutions of ideals on toric varieties
with Fuensanta Aroca and Mirna Gomez-Morales
Beitr. Algebra Geom. 65 (2024), no. 1, 217-228
DOI: 10.1007/s13366-023-00684-0
Beitr. Algebra Geom. 65 (2024), no. 1, 217-228
DOI: 10.1007/s13366-023-00684-0
[10]
New companions to the Andrews-Gordon Identities motivated by commutative algebra
with Pooneh Afsharijoo, Jehanne Dousse and Frédéric Jouhet
Adv. Math. 417 (2023), Paper No. 108946, 40 pp
arXiv:2104.09422
DOI: 10.1016/j.aim.2023.108946
Adv. Math. 417 (2023), Paper No. 108946, 40 pp
arXiv:2104.09422
DOI: 10.1016/j.aim.2023.108946
[11]
Resolving singularities of curves with one toric morphism
with Ana Belén de Felipe and Pedro D. Gonzålez Pérez
Mathematische Annalen, 387 (2023), no. 3-4, 1853-1902
Link
Mathematische Annalen, 387 (2023), no. 3-4, 1853-1902
Link
[12]
Jet schemes and their applications in singularities, toric resolutions and integer partitions
Handbook of geometry and topology of singularities IV, 211-249. Springer, Cham, 2023
PDF
[13]
Neighborly partitions and the numerators of Rogers-Ramanujan identities
with Zahraa Mohsen
Int. J. Number Theory 19 (2023), no. 4, 859-872
arXiv:2201.02481
DOI: 10.1142/S1793042123500434
Int. J. Number Theory 19 (2023), no. 4, 859-872
arXiv:2201.02481
DOI: 10.1142/S1793042123500434
[14]
Newton non-degenerate Ό-constant deformations admit simultaneous embedded resolutions
with Maximiliano Leyton-Alvarez and Mark Spivakovsky
Compositio Mathematica, Volume 158, Issue 6, June 2022, pp. 1268-1297
arXiv:2001.10316
DOI: 10.1112/S0010437X22007576
Compositio Mathematica, Volume 158, Issue 6, June 2022, pp. 1268-1297
arXiv:2001.10316
DOI: 10.1112/S0010437X22007576
[15]
Classification of singularities of cluster algebras of finite type
with Angelica Benito, Eleonore Faber and Bernd Schober
Glasg. Math. J. 65 (2023), no. 1, 170-204
Link
DOI: 10.1017/S0017089522000209
Glasg. Math. J. 65 (2023), no. 1, 170-204
Link
DOI: 10.1017/S0017089522000209
[16]
New companions to Gordon identities from commutative algebra
with Pooneh Afsharijoo, Jehanne Dousse and Frédéric Jouhet
SĂ©minaire Lotharingien de Combinatoire 86B.48 (2022)
PDF
SĂ©minaire Lotharingien de Combinatoire 86B.48 (2022)
[17]
On the construction of valuations and generating sequences on hypersurface singularities
with Dale Cutkosky and Bernard Teissier
Algebraic Geometry 8 (6) (2021) 705-748
PDF
DOI: 10.14231/AG-2021-022
Algebraic Geometry 8 (6) (2021) 705-748
DOI: 10.14231/AG-2021-022
[18]
Jet schemes of quasi-ordinary surface singularities
[19]
The motivic Igusa zeta function of a space monomial curve with a plane semigroup
[20]
The embedded Nash problem of birational models of rational triple singularities
with Busra Karadeniz, Camille Plénat and Meral Tosun
Journal of Singularities volume 22 (2020), 337-372
PDF
Journal of Singularities volume 22 (2020), 337-372
[21]
Note on the monodromy conjecture for a space monomial curve with a plane semigroup
with Jorge Martin-Morales, Wim Veys and Lena Vos
C. R. Math. Acad. Sci. Paris 358 (2020), no. 2, 177-187
PDF
C. R. Math. Acad. Sci. Paris 358 (2020), no. 2, 177-187
[22]
Defect and Local Uniformization
with Dale Cutkosky
Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM 113 (2019), no. 4, 4211-4226
arXiv:1711.02726
Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM 113 (2019), no. 4, 4211-4226
arXiv:1711.02726
[23]
Partition Identities and Application to Infinite Dimensional Groebner Basis and Vice Versa
with Pooneh Afsharijoo
Arc Schemes and Singularities, World Scientific Publishing, pp. 145-161 (2020)
PDF
Arc Schemes and Singularities, World Scientific Publishing, pp. 145-161 (2020)
[24]
A polyhedral characterization of quasi-ordinary singularities
[25]
Mather discrepancy as an embedded dimension in the space of arcs
[26]
Jet schemes and minimal toric embedded resolutions of rational double point singularities
[28]
Jet schemes and generating sequences of divisorial valuations in dimension two
Michigan Math. J., Volume 66, Issue 1 (2017), 155-174
arXiv:1511.03907
arXiv:1511.03907
[29]
Jet schemes of rational double point surface singularities
Valuation Theory in Interaction, EMS Ser. Congr. Rep., Eur. Math. Soc., Sept. 2014, pp: 373-388
PDF
DOI: 10.4171/149-1/18
DOI: 10.4171/149-1/18
[30]
Jet schemes and minimal embedded desingularization of plane branches
with Monique Lejeune-Jalabert and Ana Reguera
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas: Volume 107, Issue 1 (2013), Page 145-157
Special issue dedicated to Professor H. Hironaka
PDF
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas: Volume 107, Issue 1 (2013), Page 145-157
Special issue dedicated to Professor H. Hironaka
[31]
Arc spaces and Rogers-Ramanujan Identities
with Clemens Bruschek and Jan Schepers
The Ramanujan Journal: Volume 30, Issue 1 (2013), Page 9-38
arXiv:1101.4950
The Ramanujan Journal: Volume 30, Issue 1 (2013), Page 9-38
arXiv:1101.4950
[32]
Jet schemes of complex plane branches and equisingularity
Annales de l'Institut Fourier, Tome 61, numéro 6 (2011), p. 2313-2336
PDF
[33]
Computing Hironaka's invariants: ridge and directrix
with Jeremy Berthomieu and Pascal Hivert
Contemporary Mathematics, vol. 521, Amer. Math. Soc., Providence, RI, 2010, pp. 9-20
PDF
Contemporary Mathematics, vol. 521, Amer. Math. Soc., Providence, RI, 2010, pp. 9-20
[35]
Arc spaces and Rogers-Ramanujan Identities
with Clemens Bruschek and Jan Schepers
Discrete Mathematics & Theoretical Computer Science Proceedings, FPSAC (2011), 211-220
PDF
Discrete Mathematics & Theoretical Computer Science Proceedings, FPSAC (2011), 211-220
Book as Editor
Algebraic Geometry and Number Theory
Edited with Celal Cem Sarioglu, Christophe Soulé, Ayberk Zeytin
Lecture notes of a summer school in Istanbul
Progress in Mathematics, 321. Birkhauser/Springer, Cham, 2017
Cover PDF
Lecture notes of a summer school in Istanbul
Progress in Mathematics, 321. Birkhauser/Springer, Cham, 2017
Cover PDF
Conference Proceedings
Commutative Algebra and Integer Partitions
Oberwolfach Reports, proceedings of the conference Resolutions in Local Algebra and Singularity Theory (2023)
Teissier singularities: a viewpoint on quasi-ordinary singularities in positive characteristics
Oberwolfach Reports. Report 6 (2019)
đšâđ PhD Students
Ghadi Abdallah
Since September 2023 (co-supervised with Bassam Mourad)
Since September 2023 (co-supervised with Bassam Mourad)
Parian Khezerlo
Since September 2023 (co-supervised with Marc Chardin)
Since September 2023 (co-supervised with Marc Chardin)
Bilal Balo
Since November 2022 (co-supervised with Matteo Ruggiero)
Since November 2022 (co-supervised with Matteo Ruggiero)
Wenhao Zhu
Punctual Hilbert schemes of irreducible curve singularities
Co-supervised with Mounir Hajli from Jiao Tong University, Shanghai
December 2021 - November 2025
Punctual Hilbert schemes of irreducible curve singularities
Co-supervised with Mounir Hajli from Jiao Tong University, Shanghai
December 2021 - November 2025
Zahraa Mohsen
Cycles and paths in digraphs, monomial ideals and integer partitions
Co-supervised with Amine El Sahili from Lebanese University
2019-2022
Cycles and paths in digraphs, monomial ideals and integer partitions
Co-supervised with Amine El Sahili from Lebanese University
2019-2022
Andrei Bengus-Lasnier
Diskoids and extensions of valuations
2017-2021
Diskoids and extensions of valuations
2017-2021
Pooneh Afsharijoo
Looking for a new version of Gordon's identities, from algebraic geometry to combinatorics through partitions
2015-2019
Looking for a new version of Gordon's identities, from algebraic geometry to combinatorics through partitions
2015-2019
Teaching
Teaching in 2023-2024
Probability and Statistics, M1 MEEF
Galois Theory, M1
Elementary Algebra and Analysis, L1 Miashs
Mathematical Reasoning, L1
Mathematics, L1 Computer Science
Mock oral exams, Internal Agrégation
đ€ Seminars and Working Groups
Co-organized Conferences
AMS Special Session on Integer Partitions, Arc Spaces and Vertex Operators, I, II and III
January 3-6, 2024, at Joint Mathematical Meeting, San Francisco
Website
January 3-6, 2024, at Joint Mathematical Meeting, San Francisco
Website
Two approaches towards local uniformization and resolution of singularities in characteristic p > 0
May 23-27, Mittag-Leffler institute, Stockholm
Website
May 23-27, Mittag-Leffler institute, Stockholm
Website
Research Groups and Networks
Tropical Aspects of Singularities (SINTROP)
Website
Website
Lipschitz Geometry of Singularities (LISA)
Website
Website
More Invariants From Arc Schemes (MIAS)
Website
Website
Surface Singularities (SUSI)
Website
Website