Manuel Gonzalez Villa

Manuel González Villa

Investigador Titular A
Sistema Nacional de Investigadores, nivel I (2026-2030)
Matemática Básica
CIMAT, A.C.

Email: manuel dot gonzalez at cimat dot mx

Research

Publications...

• (with N. Budur and P.D. González-Pérez) Log canonical thresholds of quasi-ordinary hypersurface singularities. Proc. of the AMS. 140 (2012) 4075-4083. Preprint at arXiv.

• (with P.D. González-Pérez) Motivic Milnor fiber of a quasi-ordinary hypersurface. J. Reine Angew. Math. 687 (2014), 159-205. Preprint at arXiv

• Newton process and semigroups of irreducible quasi-ordinary power series. Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 108 (2014), no. 1, 259-279.

• Inner Jumping Numbers of Non Degenerate Polynomials. Math. Z. August 2013, Volume 274, Issue 3-4, pp 1113-1118.

• (with A. Lemahieu) The Monodromy Conjecture for Plane Meromorphic germs Bull. Lond. Math. Soc. 46 (2014), no. 3, 441-453. Preprint at arXiv.

• (with A. Libgober and L. Maxim) Motivic infinite cyclic covers. Adv. Math. 298 (2016), 413-447. Preprint at arXiv.

• (with A. Libgober and L. Maxim) Motivic zeta functions and infinite cyclic covers. Local and global methods in algebraic geometry, 117-141, Contemp. Math., 712, Amer. Math. Soc., Providence, RI, 2018. N. Budur, R. Docampo, T. de Fernex, and K. Tucker (eds.) Preprint at arXiv

• (with G. Kennedy and L. McEwan) A recursive formula for the motivic Milnor fiber of a plane curve. Singularities, algebraic geometry, commutative algebra, and related topics, 203-218, Springer, Cham, 2018. G.-M. Greuel, L. Narváez Macarro, S. Xambó-Descamps (Eds.) Preprint at arXiv

• (with E. Artal-Bartolo) On Maximal order poles of generalized topological zeta functions. p-adic analysis, arithmetics, and singularities, 225?230, Contemp. Math. 778, Amer. Math. Soc., Providence, RI, 2022. C. Galindo, A. Melle-Hernandez, J.J. Moyano and W.A. Zúñiga-Galindo (eds.) Preprint at arXiv

• (with D. Jaramillo-Vélez, L. Núñez-Betancourt) F-thresholds and test ideals of Thom-Sebastiani type polynomials. Proc AMS Volume 150, Number 9, September 2022, Pages 3739--3755. Preprint at arXiv

• (with L. Alanis López, E. Artal-Bartolo, C. Bonatti, X. Gómez-Mont, and P. Portilla-Cuadrado) On a quadratic form associated with a surface automorphism and its applications to Singularity Theory. Indagationes Mathematicae Volume 33, Issue 4, July 2022, Pages 816-843. Preprint at arXiv. Additional material.

• (with C.R. Guzmán Durán, P.D. González Pérez, and M. Robredo Bruces) Multiplier ideals of plane curve singularities via Newton polygons, Communications in Algebra, 52:3, (2024) 1142-1162,. Additional material. Preprint at arXiv

• (with J. Àlvarez Montaner, E. León Cardenal, L. Núñez-Betancourt) Bernstein-Sato polynomial and related invariants for meromorphic functions. Transactions of the AMS, published electronically: January 30, 2025. DOI: https://doi.org/10.1090/tran/9390

...and preprints

• (with E. Artal-Bartolo, P.D. Gonzalez Perez, and E. León Cardenal, Denef-Loeser zeta functions of suspensions and Lê-Yomdin singularities arXiv.2604.24523. This preprint superseeds arXiv:2502.05022.

• (with E. Artal-Bartolo, P.D. Gonzalez Perez, and E. León Cardenal, On the suspension formula for Denef-Loeser zeta functions, arXiv:2502.05022, superseeded by arXiv.2604.24523.

• (with E. León Cardenal, V. Levandowskyy, and J. Martin Morales, An algorithm for annihilator and Bernstein-Sato polynomial of a rational function, arXiv:2602.00280.

Outreach, and other writings

Students and postdocs

Ph.D.

• Carlos Rodrigo Guzmán Durán, Ideales Multiplicadores de Curvas Planas, CIMAT, 2018, (co-advisor: Xavier Gómez-Mont).

• Oscar Moreno Castañón, UNAM (co-advisor: Fuensanta Aroca).

• Victor Manuel Burgos Guerrero, CINVESTAV (co-advisor: Wilson Zuñiga Galindo)

• Lorena Montserrat Noh Canul, CIMAT.

M.Sc.

• Delio Jaramillo Vélez, On F-Pure Thresholds: Computations and Relations to Others Invariants, CIMAT, 2019, (co-advisor: Luis Núñez Betancourt).

• Emmanuel Fuentes Peña, Descomposiciones de Zariski de ideales multiplicadores de curvas planas, CIMAT, 2020.

Postdocs

• Otto Hector Romero German (Postdoc Conacyt 2021-2025).

Activities (past)

• Coloquio CIMAT DEMAT,.

• Seminario AC/AG CIMAT, (with G. Guzmán, O. Gómez Martínez, O. Romero, A. Zenteno).

• Comité Editorial del Boletín RSME (último número)

• Congreso iberoamericano de singularidades, Universidad Técnica Federico Santa María, en Valparaíso, Chile, 9 al 13 de diciembre de 2025.

• VIII International Workshop on Singularities in Geometry and Applications, ICMC-USP, São Carlos, Brazil, 29 June - 4 July, 2025.

• 6th Brazil-Chile-Mexico Meeting on Singularities, CMO, 26 august-1 september, Oaxaca, Mexico.

• AM115 Algebraic and topological interplay of algebraic varieties A Conference in Honor of the 60th Birthday of Enrique Artal and the 55th Birthday of Alejandro Melle, June 12-17 2022, Jaca, Spain. (with J.I. Cogolludo, F. Delgado, M. Izquierdos, M.A. Marco Buzunáriz, L. Maxim, j. Martín Morales, M. Pe Pereira, H. Tokunaga)

• Interacciones p-ádicas: Análisis, Geometría Algebraica y Física. Sesión especial del 55 Congreso Nacional de la SMM (with M. Bocardo Gaspar)

Forma parte del #55CNSMM ?? Entra a https://t.co/FUE2dyqbni e inscríbete! pic.twitter.com/EhRUvMX933
— Soc. Matemática Mex. (@smm_mx) August 27, 2022

• PASCA 2022 Pan-American School in Commutative Algebra, A graduate summer school in Guanajuato, Mexico, June 20 - July 1, 2022, (with Jack Jeffries, J. Montaño, and Y. Pitones). Recordings

• CIMPA-CIMAT Research School: p-Adic Numbers, Ultrametric Analysis, and Applications Guanajuato, CIMAT, May 23-31, 2022 (with W. Zuñiga Galindo, T. Digernes, E. León Cardenal, R. Pérez Buendía...).
Recordings: Day 1, Day 2, Day 3, Day 4, Day 5, Day 6, Day 7

• Sesion Especial Virtual Teoria de Singularidades, (con José Seade y Carlos Galindo; programa) Reunión Conjunta SMM-RSME, CIMAT, Guanjuato, GTO, June 14-18, 2021. Cartel.