👓 Vladimir Voevodsky, Fields Medalist, Dies at 51 | IAS

Vladimir Voevodsky, Fields Medalist, Dies at 51 (Institute for Advanced Study)
The Institute for Advanced Study is deeply saddened by the passing of Vladimir Voevodsky, Professor in the School of Mathematics. Voevodsky, a truly extraordinary and original mathematician, made many contributions to the field of mathematics, earning him numerous honors and awards, including the Fields Medal. Celebrated for tackling the most difficult problems in abstract algebraic geometry, Voevodsky focused on the homotopy theory of schemes, algebraic K-theory, and interrelations between algebraic geometry, and algebraic topology. He made one of the most outstanding advances in algebraic geometry in the past few decades by developing new cohomology theories for algebraic varieties. Among the consequences of his work are the solutions of the Milnor and Bloch-Kato Conjectures. More recently he became interested in type-theoretic formalizations of mathematics and automated proof verification. He was working on new foundations of mathematics based on homotopy-theoretic semantics of Martin-Löf type theories. His new "Univalence Axiom" has had a dramatic impact in both mathematics and computer science.

 

Sad to hear of Dr. Voevodsky’s passing just as I was starting into my studies of algebraic geometry…

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Algebraic Geometry Lecture 1

For those who are still on the fence about taking Algebraic Geometry this quarter (or the follow on course next quarter), here’s a downloadable copy of the written notes with linked audio that will allow you to sample the class:

Algebraic Geometry-Lecture 1 notes [.pdf file with embedded and linked audio]

I’ve previously written some notes about how to best access and use these types of notes in the past. Of particular note, one must download the .pdf file and open in a recent version of Adobe Acrobat to take advantage of the linked/embedded audio file. (Trust me, it’s worth doing as it will be like you were there with the 20 of us who showed up last night!)

For those who prefer just the audio files separately, they can be listened to here, or downloaded.

Lecture 1 – Part 1

Lecture 1 – Part 2

Again, the recommended text is Elementary Algebraic Geometry by Klaus Hulek (AMS, 2003) ISBN: 0-8218-2952-1.

For those new to Dr. Miller’s classes, I’ve written up some hints/tips about them in the past as well.

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🔖 Elementary Algebraic Geometry by Klaus Hulek

Elementary Algebraic Geometry (Student Mathematical Library, Vol. 20) by Klaus Hulek (American Mathematical Society)
This is a genuine introduction to algebraic geometry. The author makes no assumption that readers know more than can be expected of a good undergraduate. He introduces fundamental concepts in a way that enables students to move on to a more advanced book or course that relies more heavily on commutative algebra. The language is purposefully kept on an elementary level, avoiding sheaf theory and cohomology theory. The introduction of new algebraic concepts is always motivated by a discussion of the corresponding geometric ideas. The main point of the book is to illustrate the interplay between abstract theory and specific examples. The book contains numerous problems that illustrate the general theory. The text is suitable for advanced undergraduates and beginning graduate students. It contains sufficient material for a one-semester course. The reader should be familiar with the basic concepts of modern algebra. A course in one complex variable would be helpful, but is not necessary. It is also an excellent text for those working in neighboring fields (algebraic topology, algebra, Lie groups, etc.) who need to know the basics of algebraic geometry.

Dr. Miller emailed me yesterday to confirm that the textbook for his Fall UCLA Extension ‏course Introduction to Algebraic Geometry will be Elementary Algebraic Geometry by Klaus Hulek (AMS, 2003) ISBN: 0-8218-2952-1.

Sadly, I totally blew the prediction of which text he’d use. I was so far off that this book wasn’t even on my list to review! I must be slipping…

Elementary Algebraic Geometry by Kaus Hulek (AMS, 2003)

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