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\textbf{SPEAKER}:
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Nick Arsenault, University of Kentucky
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{\bf TITLE}:
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Propagation of Singularities for the Wave Operator
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{\bf ABSTRACT:}\\ 
H\"ormander’s propagation of singularities theorem says the following: if a function has a certain level of regularity in a known region, then the function maintains this regularity at certain end regions. The catch, however, is that we have to propagate along the correct ``paths'' to conclude regularity in the end regions. In this talk, I’ll introduce concepts from microlocal analysis, which is a paradigm that will allow us to analyze the singularities of distributions.  We will then use a positive commutator argument and tools from microlocal analysis to prove propagation of singularities for the wave operator.






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