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Colloquium and Seminars


Hudson Colloquium

Please join us this Wednesday at 12:15 PM for our final Hudson Colloquium of the semester. Dr. Saeed Nasseh (Statesboro) will be speaking about “INTERACTIONS BETWEEN COMMUTATIVE ALGEBRA AND
OTHER AREAS: SOLUTIONS TO LONG-STANDING CONJECTURES.”

As this will be our last Hudson Colloquium of the semester, the first 15 minutes are reserved for short chitchat about the weather. The talk will begin at 12:30 PM.

We look forward to see y’all there!

Speaker: Dr. Saeed Nasseh

Title: INTERACTIONS BETWEEN COMMUTATIVE ALGEBRA AND OTHER AREAS: SOLUTIONS TO LONG-STANDING CONJECTURES

Abstract: Commutative algebra and algebraic geometry are inseparable fields and have a long history. In 1950’s, homological algebra (that originates from algebraic topology) also made its way into the commutative algebra toolbox in the works of Auslander-Buchbaum and Serre. Tight connections between commutative algebra, representation theory, and deformation theory appeared in the past century in numerous places including the works of Auslander as well. In this talk, I introduce two long-standing major conjectures in commutative algebra { namely, Vasconcelos’ Conjecture (1974) and the Auslander-Reiten Conjecture (1975) { that have been solved in my recent works (one of them completely and the other one partially) using techniques from the above-mentioned areas of mathematics plus linear algebra, group theory, invariant theory, and rational homotopy theory. I will describe, in down-to-earth terms, the cast of characters that play fundamental roles in the solutions of these conjectures. Finally, I will sketch a new method that uses partial di fferential equations and I will show evidences that it might be used in solving the Auslander-Reiten Conjecture in its full generality.

Zoom: https://georgiasouthern.zoom.us/j/89066894782

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Last updated: 11/16/2020