# Francesc Planas

I graduate in Mathematics in 1987 from the University of Barcelona, and obtained a PhD in algebra, from the same university, in 1994. Since 1987 I have been working at the Technical University of Catalonia, Barcelona, first as an Assistant Professor, and later as an Associate Professor. I have taught several basic courses like Linear and Multilinear Algebra, Projective Geometry, Calculus, Vectorial Calculus, Topology, several mid level courses like Commutative Algebra, Financial Calculus, Functional Analysis and some Master and Doctorate courses in Commutative Algebra, always at the Faculty of Mathematics and Statistics (FME) as well as at the Technical Engineering School of Barcelona (ETSEIB), at the UPC.

### Research lines

My current research interests are centred in the Shimoda Conjecture, related to the Sally conjecture, on the equations of the blowing-up of affine irreducible curves, on free resolutions of binomial ideals linked to special matrices and on the integral degree of integral ring extensions, all of them in the area of Commutative Algebra.

### Selected publications

- Shiro Goto, Liam O’Carroll, Francesc Planas-Vilanova, Sally’s question and a conjecture of Shimoda. Nagoya Math. J. 211 (2013), 137-161.
- Ferran Muiños, Francesc Planas-Vilanova, The equations of Rees algebras of equimultiple ideals of deviation one, Proc. American Math. Soc. 141 (2013), 1241-1254.
- Liam O’Carroll, Francesc Planas-Vilanova, The primary components of positive critical binomial ideals. J. Algebra 373 (2013), 392-413.
- Francesc Planas-Vilanova, Normal transversality and uniform bounds, J. London Math. Soc (2) 62 (2000), 716-728.
- Francesc Planas-Vilanova, The strong uniform Artin-Rees property in codimension one, J. Reine angew. Math. 527 (2000), 185-201.