Graduation Year
2023
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Science
Department
Mathematics
Reader 1
Lenny Fukshansky
Reader 2
Michael Orrison
Terms of Use & License Information
Rights Information
2023 Tanis Nielsen
Abstract
Lattices are discrete subgroups of Euclidean spaces. Analogously to vector spaces, they can be described as spans of collections of linearly independent vectors, but with integer (instead of real) coefficients. Lattices have many fascinating geometric properties and numerous applications, and lattice theory is a rich and active field of theoretical work. In this thesis, we present an introduction to the theory of Euclidean lattices, along with an overview of some major unsolved problems, such as sphere packing. We then describe several more specialized topics, including prior work on well-rounded ideal lattices and some preliminary results on the study of planar deep hole lattices.
Recommended Citation
Nielsen, Tanis, "Explorations in Well-Rounded Lattices" (2023). HMC Senior Theses. 273.
https://scholarship.claremont.edu/hmc_theses/273
