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Rigorous trivialities is a web log about mathematics, but especially geometry, broadly construed. Contributors will be Charles Siegel, Jim Stankewicz and occasionally Matt Deland. Charles specializes in algebraic geometry, topology and mathematical physics. Jim specializes in arithmetic algebraic geometry. Matt has transitioned from algebraic geometry to work in industry.

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# Category Archives: Hodge Theory

## ICTP Day 9

So, today a few lecture series finished up, and I’ve posted notes from some of the older ones in pdfs on my personal website. And here’s the notes, which I’ll admit are getting spottier, as Griffiths is lecturing from his … Continue reading

Posted in Conferences, Hodge Theory, ICTP Summer School
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## ICTP Day 8

Today was a half day, and we finished Carlson’s series. I think this afternoon I’ll clean some things up and maybe post notes from the finished series on my website, along with links from here. In any case, here are … Continue reading

Posted in Conferences, Hodge Theory, ICTP Summer School
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## ICTP Day 7

Today we kept going with the advanced topics, and started Shimura varieties, though that one went VERY fast. As always, comments and corrections are welcome!

Posted in Conferences, Hodge Theory, ICTP Summer School
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## ICTP Day 6

Today we started the third part of the summer school: Algebraic Cycles, Arithmetic aspects of Hodge Structures-Mumford-Tate Groups. There was actually quite a bit of review today, which surprised me, and instead of taking notes on the definition of Hodge … Continue reading

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## ICTP Day 5

Today was the last day of “basic Hodge theory”…so we talked about intersection cohomology and the decomposition theorem and the like. I admit to losing the thread of the lectures a couple of times (marked in the notes) and not … Continue reading

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## ICTP Day 4

And today, Hodge theory is in full swing. There were some commutative diagrams today, and wordpress is famous for not supporting xy, so I’ll do what I can.

Posted in Conferences, Hodge Theory, ICTP Summer School
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## ICTP Day 3 Part II

Here’s the second set of notes, the beginning of the crash course in Hodge theory before we get to advanced topics next week. My notes from the first day and a half are available here, please let me know if … Continue reading

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## ICTP Day 3 Part I

This is the end of the preliminary background lectures. This afternoon, we start Hodge Theory itself, with Hodge Structures, Variations, and Hodge Theory of Maps as the three lecture series. Tonight, when I post the notes for the next three … Continue reading

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## ICTP Day 2

More of the background stuff. Tomorrow I’ll be making two posts, one around lunchtime here, with the last background material and links to complete notes without having to deal with the vagaries of wordpress formatting (I’ve noticed that theorem, example, … Continue reading

Posted in Conferences, Hodge Theory, ICTP Summer School
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## ICTP Day 1

So, I’ve put the actual lecture notes below the fold. Today was a back-to-basics day, to make sure everyone has the same definitions (and I think to give people time to get used to the area before diving into the … Continue reading

Posted in Conferences, Hodge Theory, ICTP Summer School
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