Hardness Results in Discrete Morse Theory for 2-Complexes

Explore hardness results in discrete Morse theory for 2-complexes in this 34-minute conference talk. Delve into the problem of minimizing critical simplices (Min-Morse Matching) from inapproximability and parameterized complexity perspectives. Learn about approximation factor limitations, WP-hardness with standard parameterization, and the absence of FPT-approximation algorithms. Discover an O(n/log n)-factor algorithm for Min-Morse Matching on 2-complexes, leveraging polynomial-time erasability determination. Gain insights into monotone circuits, reductions, and constructions related to this topic in applied algebraic topology.

Syllabus

Introduction
Outline
Discrete Morse theory
Motivation
Irritability
Complexity theory
Contributions
monotone circuits
reduction
construction
knife attempt
conclusion
questions