The Commonwealth of the Northern Marianas Islands.
*Prayers for you and your family, Arrendajo.
Woah, sorry to hear that man. 
Dang, some of these sound really interesting. Now I’m going to have to think. There might be other topics, but definitely -
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Overgrowth of bluegreen algae in the downtown Stockton Channel, causes and prevention.
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Science with Shit
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Medieval (European) cooking, general.
Been thinking about this, and I’m rather underwhelmed at myself for the lack of things I could do an hour about with no prep:
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The works of JRR Tolkien
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My thesis about how the first three Velvet Underground albums chart the journey of addiction (lasts more than an hour because I’d play some tracks and Sister Ray is really quite long)
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Some stuff about my job
I could do:
Instructional Systems Design (or Systems Approaches to Training);
Vehicular bicycling and bike safety; and, on a superficial level
Urban design
Especially if I was armed with a good sized whiteboard and a few dry-erase markers.
And Arrendajo, I am sincerely sorry to hear about that.
I can easily cover forty five minutes and more regarding operation, installation maintenance and testing of commercial fire alarm systems. It is admittedly boring stuff, and all of you would probably snooze off in the first ten minutes or so.
I would find it fascinating, unless you’re way too monotone and inexpressive! 
I am very passionate about what I do.
Basic intro to German
Raising monarch butterflies
Native plants
Starting and maintaining a school garden
Growing vegetables and cooking the results
Not to bump the thread, but to those of you who expressed sympathy with my last response, thank you very kindly. I would like to report that, though it was a horrific experience, my son made a remarkable recovery, and graduated with a degree in German from Oregon State last spring. And the fact is, while I could talk about it for an hour, I really don’t want to.
Handwashing and the Chain of infection–I actually had an impromptu “make up a lesson and teach it to us” question on a job interview and did this one.
Differences in dementia vs delirium.
How injury or lesions on different parts of the brain affect behaviour.
(I am a nurse, and a health care educator but I have never actually taught those subjects)
A brief history of the Finnish people in the Thunder Bay Ontario region.
History of the United Church of Canada.
Writing for children. I can do 45 minutes each on short stories, poems, and picture books.
(Missed edit window) Also: Amusing anecdotes from my years as a substitute teacher.
Total Solar Eclipses!
Child support laws in Minnesota
How to find people that so do not want to be found
Things to consider before filing contempt
Polycystic Kidney Disease: What it is and why is sucks
Renal diets
Edmund Spenser’s “The Faerie Queene”
Shakespeare’s Sonnets
Cross Stitch 101
Dealing with a Mentally Ill Feline
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Arthurian stuff, with special emphasis on the foundational works - I don’t talk about King Arthur much because it triggers my obsessiveness. But man, I can go on.
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Egyptian mythology - ditto.
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War of the Roses
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English history in general
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The history of ladies’ underwear
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Dogs
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Greek/Roman mythology
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Norse/Germanic mythology
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Any number of genre authors
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The history of the English Language and etymology of Latin loan words
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The History of Pants
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Horses
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The time I worked in a Zoo
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The time I worked in a Vet’s
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The time I worked in a Theater
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All kinds of Theater stuff, generally
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Van Morrison’s songwriting
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Poetry, with particular emphasis on the Romantics
…
…
…
I’m beginning to see the problem.
I essentially did this once with the life of Abraham Lincoln. I was teaching English Language Learners in central Illinois, and the program director was going to take the class on a field trip to some Lincoln sites. She asked if I could talk about Lincoln for a while. The next thing I knew, it was about an hour later.
Crapping my pants? The methods and haste thereof?
I could probably give a pretty decent 45 (or more) minute speech about the evolution of the american animation industry (once I finished panicking), but I couldn’t give an impromptu presentation. Presentations require visual aids, even when they aren’t about a visual medium.
How to teach a child the art of playing baseball. Actually, I could do (and have done) 45 minutes each on hitting, fielding, catching, throwing, and practice setup/safety. It would include lecture, demonstration and audience participation in roughly equal measure. So if you ever need someone to fill 4 hours on your agenda, call me!
My current research.
For a general audience, perhaps an elementary explanation of what calculus is about and why it is important. I could go on for hours.