Low-Depth Algebraic Circuit Lower Bounds Over Any Field

Explore groundbreaking developments in algebraic circuit complexity through this Computer Science seminar presentation where Michael A. Forbes from the University of Illinois at Urbana-Champaign discusses extending the Limaye, Srinivasan and Tavenas (LST) breakthrough in super-polynomial lower bounds against low-depth algebraic circuits to fields of small characteristic. Discover two distinct proofs demonstrating these bounds work over any field - first through a logical approach showing how characteristic zero results transfer to all fields, then through a constructive proof utilizing the Binet-Minc identity to achieve set-multilinearization independent of field characteristics. Gain insights into the implications for AC⁰[p]-Frege lower bounds and understand how these advances contribute to fundamental questions in computational complexity theory.