Sheaves as a Data Structure (Part 2)

Abstract: We continue our discussion with an example of “Path-Optimization Sheaves” (https://arxiv.org/abs/2012.05974); an alternative approach to classical Dijkstra’s Algorithm, paths from a source vertex to sink vertex in a graph are revealed as Sections of the Path-finding Sheaf.

Tables, Arrays, and Matrices are useful in data storage and manipulation, employing operations and methods from Numerical Linear Algebra for computer algorithm development. Recent advances in computer hardware and high performance computing invite us to explore more advanced data structures, such as sheaves and the use of sheaf operations for more sophisticated computations. Abstractly, Mathematical Sheaves can be used to track data associated to the open sets of a topological space; practically, sheaves as an advanced data structure provide a framework for the manipulation and optimization of complex systems of interrelated information. Do we ever really get to see a concrete example? I will point to several recent examples of (1) the use of sheaves as a tool for data organization, and (2) the use of sheaves to gain additional information about a system.

mathematical physicsalgebraic topologycategory theory

Audience: researchers in the topic

Comments: Notice the nonstandard day (Thursday) and the nonstandard time slot (2 pm Central Time).

Continuation of the talk given on October 3 (https://researchseminars.org/talk/tandg/8/).

Recording of Part I is available here: dmitripavlov.org/2023-10-03.mp4

Topology and Geometry Seminar (Texas, Kansas)