Markus J. Pflaum (Department of Mathematics, CU Boulder) Classical variational calculus

Jan. 25, 2023 4:40pm (MATH 3…

Grad Student Seminar

Dan Lyness (CU Boulder)

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Galois Connections are something that arise in many different areas of Maths. We normally see them for the first time in Galois Theory, while studying the connection between field extensions and automorphism groups. In this talk I will consider this example, and some more examples of Galois Connections including the connection between prime ideals and varieties in Algebraic Geometry, and between kernels and cokernels in Category Theory. We will see how Galois Connections lead to a closure operator, that in some cases can be used to define a topology on our spaces. I intend to keep the talk accessible, and hopefully approach some familiar concepts from a new perspective.