Due to the COVID-19 Pandemic, the University has instruction to cancel all in-person events through the Spring semester to adhere to city and state orders limiting public gatherings. Events still running must now take place Online— listed events will include a link in which one may access the Online webspace:

To view Mr. Buck’s defense, enter his Online chatroom via Blackboard Collaborate— it will open at 12:30 pm on Thursday, April 23, 2020.

Asymptotic Probability of Incidence Relations over Finite Fields

Mr. Adam Buck
University of Wisconsin-Milwaukee
PhD Graduate Student – Dissertator

“Given four generic lines in projective 3-space over a field F, we ask, “How many lines meet the four?” The answer depends on the field. When F is the complex numbers, the answer is two. When F is the real numbers, the answer is either zero or two.
If we work over a finite field with q elements, there are only finitely many projective lines. We compute the probability four lines are met by two. The main result is that as q approaches infinity, this probability approaches 1/2. Asymptotically, the other half of the time zero lines will meet the four.”

Committee Members:
Profs. Jeb Willenbring (Advisor); Allen Bell, Craig Guilbault, Kevin McLeod & Yi Ming Zou

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