Finding Linear Spaces in Quadratic Systems
Organizers
Speaker
Time
Thursday, October 22, 2026 3:00 PM - 4:00 PM
Venue
A7-201
Online
Zoom 293 812 9202
(BIMSA)
Abstract
In this talk, we will explain the cryptographic significance of these spaces and presents an algebraic approach to their recovery. Starting from the inclusion of the ideal generated by the quadratic equations in the linear ideal defining the hidden space, we show how recovery can be reduced, under suitable conditions, to computing and interpreting the kernel of a Macaulay matrix. We then discuss how divided power structures yield additional relations in positive characteristic and explain the connection with Schur modules. This is joint work with Siyong Tao.
Speaker Intro
Peigen Li received his bachelor's degree from the Harbin Institute of Technology and his Ph.D. from the Department of Mathematical Sciences at Tsinghua University. He subsequently worked as a postdoctoral researcher at the Beijing Institute of Mathematical Sciences and Applications (BIMSA) and Tsinghua University. In 2024, he joined BIMSA as an Assistant Professor. His current research interests include post-quantum cryptography, algebraic geometry, and number theory.