MATH 408
L-Functions and Sphere Packing Fall 2024
Division III Q Quantitative/Formal Reasoning

Class Details

Optimal packing problems arise in many important problems, and have been a source of excellent mathematics for centuries. The Kepler Problem (what is the most efficient way to pack balls in three-space) is a good example. The original formulation has been used in such diverse areas as stacking cannonballs on battleships to grocers preparing fruit displays, and its generalizations allow the creation of powerful error detection and correction codes. While the solution of the Kepler Problem is now known, the higher dimensional version is very much open. There has been remarkable progress in the last few years, with number theory playing a key role in these results. We will develop sufficient background material to understand many of these problems and the current state of the field. Pre-requisites are real analysis.
The Class: Format: lecture
Limit: 40
Expected: 20
Class#: 1454
Grading: yes pass/fail option, yes fifth course option
Requirements/Evaluation: Class participation, homework, exams.
Prerequisites: Math 350 or 351
Enrollment Preferences: Senior math majors, students planning on graduate study in a STEM field
Distributions: Divison III Quantitative/Formal Reasoning
QFR Notes: This is a 400 level math class

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