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BIMSA Integrable Systems Seminar
Commuting ring of differential operators with more than three generators
Commuting ring of differential operators with more than three generators
Organizers
Speaker
Yuancheng Xie
Time
Tuesday, November 18, 2025 4:00 PM - 5:00 PM
Venue
A6-101
Online
Zoom 873 9209 0711
(BIMSA)
Abstract
In 1920s, Burchnall and Chaundy studied when two ordinary differential operators commute, and this leads to deep connection with the theory of plane algebraic curves. This theory was later developed and used by Krichever to construct algebro-geometric solutions for KP hierarchy.
In this talk, I will associate a family of singular space curves indexed by the numerical semigroups $\langle l, lm+1, \dots, lm+k \rangle$ where $m \ge 1$ and $1 \le k \le l-1$ with a class of generalized KP solitons. Some of these curves can be deformed into smooth ``space curves", and they provide canonical models for the $l$-th generalized KdV hierarchies (KdV hierarchy corresponds to the case $l = 2$). We will see how to construct the space curves from a commutative ring of differential operators with more than three generators.
This talk is based on a joint work with Yuji Kodama.
In this talk, I will associate a family of singular space curves indexed by the numerical semigroups $\langle l, lm+1, \dots, lm+k \rangle$ where $m \ge 1$ and $1 \le k \le l-1$ with a class of generalized KP solitons. Some of these curves can be deformed into smooth ``space curves", and they provide canonical models for the $l$-th generalized KdV hierarchies (KdV hierarchy corresponds to the case $l = 2$). We will see how to construct the space curves from a commutative ring of differential operators with more than three generators.
This talk is based on a joint work with Yuji Kodama.