### FACARD 2019

#### Frobenius Action in Commutative Algebra: Recent Developments

#### IMUB, Barcelona, 16 - 18 January 2019

#### Minicourses

Asymptotic properties of differential operators around a singularity - Holger Brenner (Universität Osnabrück)

Homological conjectures/theorems in commutative algebra - Linquan Ma (Purdue University)

#### Scientific Aim

####

Commutative algebra is the branch of pure mathematics which studies commutative rings, and their ideals and modules. Many fundamental problems and questions in commutative algebra originated from the neighbouring fields of algebraic geometry and algebraic number theory, and it still benefits from the mutual interactions with them. This is particularly evident when one studies rings of positive characteristic. For example, the geometric theory of vector bundles and their relations with the Frobenius homomorphism has been successfully applied to tight closure and Hilbert-Kunz problems in commutative algebra. More recently, the theory of perfectoid spaces developed by Peter Scholze in the context of arithmetic geometry has been used to tackle The Homological Conjectures in the case of mixed characteristic.

The focus of the workshop is on these recent developments and other related topics. It is addressed to Ph.D. students, postdocs and interested researchers in general. There will be two minicourses at graduate level and research talks given by international experts and young emerging scientists. The workshop will be hosted by the Institute of Mathematics of the University of Barcelona (IMUB), situated in the center of the city.

The workshop is an official event of Barcelona Graduate School of Mathematics (BGSMath). Here is the corresponding page.

#### Josep Àlvarez Montaner (Universitat Politècnica de Catalunya)

Angélica Benito (Universitad Autonoma de Madrid)

Javier Carvajal Rojas (EPFL)

Alberto F. Boix (Ben-Gurion University of the Negev)

Ricardo García López (Universitat de Barcelona)

Eloísa Grifo (University of Michigan)

Jack Jeffries (University of Michigan)

Jonathan Montaño (New Mexico State University)

#### Organizers

Alessio Caminata (Université de Neuchâtel)

Santiago Zarzuela Armengou (Universitat de Barcelona)

#### Julio José Moyano Fernández (Universitat Jaume I de Castelló)

Yusuke Nakajima (KAVLI IPMU)

Thomas Polstra (University of Utah)

Ilya Smirnov (Stockholm University)

Francesco Strazzanti (INdAM)

Naoki Taniguchi (Waseda University)