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CONFERENCE

The Ubiquity of Commutative Algebra
Ubiquité de l’algèbre commutative

16 – 20 March, 2026

INTRANET FOR ORGANIZERS

Organizing Committee
Comité d’organisation

Marc Chardin (IMJ-PRG Paris)
Claudia Polini (University of Notre Dame)
Bernd Ulrich (Purdue University)

Time schedule
Abstracts
Participants
Audiovisual Mathematics Library (after the event)
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n the last few years, Commutative Algebra has seen remarkable developments with the solution of several important conjectures, such as Hochster’s direct summand conjecture, Stillman’s regularity conjecture, the Eisenbud-Goto conjecture, and the Buchsbaum-Eisenbud-Horrocks conjecture. New directions were developed and unexpected links to other parts of mathematics, from topology to combinatorics and from computer algebra to statistics, were discovered. The strongest and most fruitful interaction likely remains the one between commutative algebra and algebraic geometry.
The topics of the conference include:

(1) Representation theory theoretic methods in Commutative Algebra,
(2) Differential graded algebras and infinite free resolutions,
(3) Singularity theory with a focus on prime and mix-characteristics and applications of perfectoid spaces,
(4) Elimination theory and its interaction with geometric modeling,
(5) Groebner degeneration,
(6) Geometry of syzygies.

Ces dernières années, l’algèbre commutative a connu des avancées remarquables, avec la résolution de plusieurs conjectures importantes, comme la conjecture du facteur direct d’Hochster, la conjecture de Stillman concernant la régularité de Castelnuovo-Mumford, la conjecture de Eisenbud et Goto, et la conjecture de Buchsbaum-Eisenbud-Horrocks. De nouvelles directions se sont développées et des liens inattendus avec d’autres champs des mathématiques, de la topologie à la combinatoire et du calcul formel aux statistiques, ont été découverts. L’interaction la plus forte et féconde reste probablement celles entre l’algèbre commutative et la géométrie algébrique. 
 Nos principaux sujets d’intérêt incluent:

(1) Méthodes de théorie des représentations en algèbre commutative,
(2) Algèbres différentielles graduées et résolutions libres infinies,
(3) Théorie des singularités, notamment en caractéristique première ou mixte et applications des espaces pefectoïdes,
(4) Théorie de l’élimination et ses interactions avec la modélisation géométrique, 
(5) Dégénérescence des bases de Groebner,
(6) Géométrie des syzygies.

SPEAKERS

To be announced

SPONSORS