Guillem Blanco

I am an Assistant Professor at the Department of Mathematics of the Universitat Politècnica de Catalunya (UPC).

Contact

Departament de Matemàtiques
Universitat Politècnica de Catalunya
Diagonal 647
08028 Barcelona
Email: guillem (dot) blanco (at) upc (dot) es

Research interests

I am interested in Algebraic Geometry and the study of Algebraic and Analytical Singularities. My research centers around the interaction between the birational study of singularities and the D-module theoretic approach. In this context, I am mainly focused on the theory of Bernstein-Sato polynomials and related invariants such as multiplier/Hodge ideals, jumping numbers, the complex zeta funtion, the Gauss-Manin connection and the theory of V-filtrations.

Publications

• The Gauss-Manin system of an ICIS, pdf
  Preprint.
• Topological roots of the Bernstein-Sato polynomial of plane curves, pdf
  Preprint.
• Monodromy conjecture for semi-quasihomogeneous hypersurfaces, pdf
  with N. Budur and R. van der Veer.
  Math. Nachr, 296 (2023), no. 4, 1394–1403
• An algorithm for Hodge ideals, pdf
  Math. Comp., 91 (2022), no. 4, 2955–2967
• Yano's conjecture, pdf
  Invent. Math., 226 (2021), 421-465
• The minimal Tjurina number of irreducible germs of plane curve singularities, pdf
  with M. Alberich-Carramiñana, P. Almirón and A. Melle-Hernández.
  Indiana Univ. Math. J., 70 (2021), 1211-1220
• Monomial generators of complete planar ideals, pdf
  with M. Alberich-Carramiñana and J. Àlvarez Montaner.
  J. Algebra Appl., 20 (2021), no. 3, 2150032
• A note on a question of Dimca and Greuel, pdf
  with P. Almirón.
  C. R. Math. Acad. Sci. Paris, 357 (2019), no. 2, 205–208
  
• Poles of the complex zeta function of a plane curve, pdf
  Adv. Math., 350 (2019), 396–439
• Effective computation of base points of ideals in two-dimensional local rings, pdf
  with M. Alberich-Carramiñana and J. Àlvarez Montaner.
  J. Symbolic Comput. , 92 (2019), 93–109.
• Computing multiplier ideals in smooth surfaces,
  with F. Dachs-Cadefau.
  Extended Abstracts February 2016. Positivity and Valuations.
  Research Perspectives CRM Barcelona. Trends in Mathematics. vol. 9. Birkhäuser, Basel, 2018.

Software

• GamBa: a fast program for computing Groebner bases, github.com/gblanco92/gamba .
• Hodge.lib: a Singular library to compute Hodge ideals, hodge.lib .
• SingularitiesDim2: algorithms to study singularities in dimension 2, github.com/gblanco92/SingularitiesDim2 .

Service

• Elected member of the European Mathematical Society Young Academy (EMYA) for the period 2023-2026.