Written Geometry: Commutative Algebra
Géométrie écrite : algèbre commutative

Tuesday 3 –  Saturday 7 January, 2023

Scientific Committee & Organizing Committee
Comité scientifique & Comité d’organisation

Marc Chardin (CNRS – Sorbonne Université)
David Eisenbud (MSRI Berkeley)
Claudia Polini (University of Notre Dame)
Bernd Ulrich (Purdue University)


  Commutative algebra has had great success in the last two years with the resolution of a number of important conjectures: the homological conjectures, open since the 1970s, have been proved by Yves André using the theory of preterite spaces; other long open questions, such as the Eisenbud-Goto conjecture on Castelnuovo-Mumford regularity, the Stillman conjecture on projective dimension and a version of the Buchsbaum-Eisenbud-Horrocks conjecture on Betti numbers have also been solved.
   The answers to these problems have brought to light new questions which will be themes of the conference. One aim is to bring together participants with expertise in various areas of commutative algebra as well as in the most relevant areas of recent developments, such as algebraic geometry, singularity theory, K-theory and the theory of preterite spaces.

L’algèbre commutative a connu de grands succès ces deux dernières années avec résolution de nombre de conjectures importantes : les conjectures homologiques, ouvertes depuis les années 1970, ont été démontrées par Yves André en utilisant la théorie des espaces perfectoïdes ; d’autres questions ouvertes depuis longtemps, comme la conjecture de Eisenbud-Goto sur la régularité de Castelnuovo-Mumford, la conjecture de Stillman sur la dimension projective et une version de la conjecture de Buchsbaum-Eisenbud-Horrocks sur les nombres de Betti ont aussi été résolues.
   Les réponses à ces problèmes ont mis en lumière des questions nouvelles qui seront des thèmes de la conférence. Un objectif est ainsi de rassembler des participants experts dans des domaines divers de l’algèbre commutative ainsi que dans les domaines les plus pertinents liés aux développements récents, comme la géométrie algébrique, la théorie des singularités, la K-théorie et la théorie des espaces perfectoïdes.



Manuel Blickle (JGU Mainz)      Applications of perverse sheaves in commutative algebra
Benjamin Briggs (University of Copenhagen)  Syzygies of the cotangent complex
Yairon Cid-Ruiz (KU Leuven)    K-polynomials of multiplicity-free varieties
Aldo Conca (University of Genova)  Ideals associated to subspace arrangements
Alessandra Costantini (Oklahoma State University)      The powers of a symmetric strongly shifted ideal
Dale Cutkosky (University of Missouri)      The analytic spread of a filtration
Alessandro De Stefani (University of Genova) Bounds on the number of generators of prime ideals
Luis Duarte (University of Genova)    Ideals in a local ring under small perturbations
Daniel Erman (University of Wisconsin-Madison)   Matrix factorizations of generic polynomials
Eleonore Faber (University of Leeds)   Line singularities and Grassmannian cluster structures
Hamid Hassanzadeh (Federal University of Rio de Janeiro)  The structure of residual intersections
Linquan Ma (Purdue University)    Perfectoid Hilbert-Kunz multiplicity
Luis Nunez-Betancourt (CIMAT, Laudun)    Blowup algebras of determinantal ideals 
Claudiu Raicu (University of Notre Dame)  Cohomology of line bundles on flag varieties
Maria Evelina Rossi (University of Genova)   Marilina Rossi: On the rate of generic Gorenstein k-algebras
Alessio Sammartano (Milan Polytechnic)       Rees algebras of determinantal ideals
Hal Schenk (Auburn University)      Gorenstein rings in codimension four
Alexandra Seceleanu (University of Nebraska-Lincoln)     Duality of asymptotic invariants
Anurag Singh (University of Utah)    When are the natural embeddings of classical invariant rings pure?
Bernard Teissier (Sorbonne Université)   Examples of toric degenerations with infinitely generated semigroups
Kevin Tucker (University of Illinois at Chicago)  Perfectoid signature and an application to étale fundamental groups
Matteo Varbaro (University of Genova)    Determinantal facet ideals
Jerzy Weyman (Jagiellonian University)     Higher structure maps for resolutions of length 3 and linkage