Lecture Announcement
Date: Wednesday, 17 September 2025
Time: 2:00 p.m.
Venue: Seminar Hall
Permanental ideals and $F$-singularities
Trung Chau
Chennai Mathematical Institute.
17-09-25

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Abstract

The permanent of a matrix is exactly its determinant, with all the signs being 1. In particular, in characteristic 2, the two concepts coincide. Given a generic matrix $X$ of indeterminates, let $P_t(X)$ denote the ideal of a polynomial ring $k[X]$ generated by all $t\times t$ subpermanents of $X$. The ideal $P_t(X)$ is called a permanental ideal. Similarly, one can also define determinantal ideal. Determinantal ideals have found applications across algebra and geometry, and yet their permanental counterparts have not enjoyed a similar level of popularity. In this talk, I will present the known algebraic properties of permanental ideals and their $F$-singularities in prime characteristic. Spoiler alert: The behavior of permanental ideals is dependent on the characteristic of the field. This is an extension of the speaker's Ph.D thesis.