Project Grant 2516831

CONFERENCE: JORDAN TYPES OF ARTINIAN ALGEBRAS AND GEOMETRY OF PUNCTUAL HILBERT SCHEMES -THIS AWARD SUPPORTS THE PARTICIPATION OF US-BASED MATHEMATICIANS AT THE CONFERENCE ?JORDAN TYPES OF ARTINIAN ALGEBRAS AND GEOMETRY OF HILBERT SCHEMES,? TO BE HELD JUNE 23-27, 2025, AT UNIVERSIT? C?TE D?AZUR IN NICE, FRANCE. THE CONFERENCE WILL BRING TOGETHER MATHEMATICAL RESEARCHERS FROM AROUND THE WORLD TO DISCUSS RECENT ADVANCES IN THE THEORY OF DEFORMATIONS OF ARTINIAN ALGEBRAS. IT WILL PROVIDE AN OPPORTUNITY FOR RESEARCHERS--PARTICULARLY THOSE IN THE EARLY STAGES OF THEIR CAREERS--TO EXCHANGE IDEAS IN A FOCUSED AND COLLABORATIVE SETTING. THE CONFERENCE PROGRAM WILL FEATURE LECTURES ON FOUR SPECIALIZED TOPICS: (1) THE GEOMETRY OF PUNCTUAL HILBERT SCHEMES, (2) HILBERT FUNCTIONS OF ARTINIAN GORENSTEIN ALGEBRAS, (3) COMMUTING NILPOTENT MATRICES, AND (4) JORDAN TYPES OF ARTINIAN ALGEBRAS. THE UNIFYING SCIENTIFIC THEME IS ON DEFORMATIONS OF ARTINIAN ALGEBRAS, A CENTRAL TOPIC IN COMMUTATIVE ALGEBRA THAT HAS APPLICATIONS AND CONNECTIONS TO COMBINATORICS, GEOMETRY, AND OTHER MATHEMATICAL FIELDS OF STUDY. IN ADDITION TO THE LECTURES, TIME WILL BE ALLOCATED FOR DISCUSSIONS AND COLLABORATIVE WORK ON OPEN PROBLEMS. IN PARTICULAR, RESEARCHERS ACROSS THE FOUR SPECIALIZED TOPICS OF FOCUS WILL HAVE THE OPPORTUNITY TO SHARE THEIR DIFFERENT PERSPECTIVES. MORE INFORMATION IS AVAILABLE ON THE CONFERENCE WEBSITE: HTTPS://JTAG-LJAD.SCIENCESCONF.ORG/. THIS AWARD REFLECTS NSF'S STATUTORY MISSION AND HAS BEEN DEEMED WORTHY OF SUPPORT THROUGH EVALUATION USING THE FOUNDATION'S INTELLECTUAL MERIT AND BROADER IMPACTS REVIEW CRITERIA.- SUBAWARDS ARE NOT PLANNED FOR THIS AWARD.