New Mexico State University

Monday, March 31

• Algebra Seminar, "Non-Noetherian Cohen-Macaulayness in Directed Unions of Power Series Rings, Part 2". Richard Sayanagi, NMSU. 12:30PM – 1:30PM. SH 235 and Zoom Link: https://nmsu.zoom.us/j/89765494169.

Abstract: Power series rings over non-Noetherian rings can exhibit unexpected behavior, like possessing an infinite chain of prime ideals even when the base ring is local and 0-dimensional. We discuss a construction of directed unions of power series rings over non-Noetherian 0-dimensional rings that have properties seen in Noetherian Cohen-Macaulay rings, such as Krull's height theorem for finitely generated ideals and the unmixedness theorem. We make connections to several different notions of non-Noetherian Cohen-Macaulayness in the literature.

Tuesday, April 01

• No Events

Wednesday, April 02

• No Events

Tuesday, April 03

• No Probability Seminar for Graduate Students

Friday, April 04

• Faculty Meeting, John Harding. 11:00AM – 12:00PM. Zoom ONLY. Link: https://nmsu.zoom.us/j/85776616343.

• No Analysis Seminar

• Colloquium, "Behavior of Absorbing and Generating $p$-Robin Eigenvalues in Bounded and Exterior Domains". Robert Smits, NMSU. 12:00PM refreshments | 12:30PM – 1:20PM. SH 107 and Zoom. Link: https://nmsu.zoom.us/j/82146375616.

Abstract: We establish rigorous quantitative inequalities for the first eigenvalue of the generalized $p$-Robin problem, for both the classical diffusion absorption case, where the Robin boundary parameter $\alpha$ is positive, and the superconducting \textcolor{blue}{generation regime} (\(\alpha<0\)), where the boundary acts as a source. In bounded domains, we use a unified approach to derive a precise asymptotic behavior for all $p$ and all small real $\alpha$, improving existing results in various directions, including requiring weaker boundary regularity for the case of the classical 2-Robin problem, studied in the fundamental work by R. Sperb. In exterior domains, we characterize the existence of eigenvalues, establish general inequalities and asymptotics as \(\alpha\to 0\) for the first eigenvalue of the exterior of a ball, and obtain some sharp geometric inequalities for convex domains in two dimensions.

• No Geometry and Topology Seminar