2026-09-19T16:00:34Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1599362025-07-08T03:04:20Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Guth, Lawrence
Portnoy, Elia
Massachusetts Institute of Technology. Department of Mathematics
2025-07-07T17:39:28Z
2025-07-07T17:39:28Z
2025-05
2025-05-13T13:31:25.439Z
https://hdl.handle.net/1721.1/159936
In this thesis, we discuss quantitative embeddings that generalize a theorem of Kolmogorov and Barzdin. The theorem says that any bounded degree graph with V vertices can be mapped into a 3-dimensional ball of radius sqrt(V), so that at most a constant number of edges intersect any unit ball. In one generalization we describe how much freedom we have in placing the vertices of the graph, and in the other we prove a similar result for simplicial complexes of any dimension. We also discuss applications of these quantitative embeddings to a problem in metric geometry related to the isoperimetric inequality and a problem about constructing local quantum error-correcting codes.
Ph.D.
Massachusetts Institute of Technology
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
Copyright retained by author(s)
https://creativecommons.org/licenses/by-nc-nd/4.0/
Quantitative embeddings with applications
Thesis
application/pdf
Doctoral
Doctor of Philosophy
Publication
unknown
unknown
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