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Non-commutative Freiman theorems, and model theory
This is an adaptation of a talk I gave recently for a program at IPAM. In this talk, I gave a (very informal and non-rigorous) overview of Hrushovski’s use of model-theoretic techniques to estab… more →
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Approximate bases, sunflowers, and nonstandard analysis
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Terence Tao wrote 1 week ago: One of the most basic theorems in linear algebra is that every finite-dimensional vector space has a … more →
Non-commutative Freiman theorems, and model theory
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Terence Tao wrote 2 weeks ago: This is an adaptation of a talk I gave recently for a program at IPAM. In this talk, I gave a (very … more →
Reading seminar 6: "Stable group theory and approximate subgroups", by Ehud Hrushovski
Terence Tao wrote 2 weeks ago: This is the last reading seminar of this quarter for the Hrushovski paper. Anush Tserunyan continued … more →
Reading seminar 5: "Stable group theory and approximate subgroups", by Ehud Hrushovski
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Terence Tao wrote 1 month ago: After a one-week hiatus, we are resuming our reading seminar of the Hrushovski paper. This week, we … more →
Nonstandard analogues of energy and density increment arguments
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Terence Tao wrote 1 month ago: In the course of the ongoing logic reading seminar at UCLA, I learned about the property of countabl … more →
Reading seminar 4: "Stable group theory and approximate subgroups", by Ehud Hrushovski
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Terence Tao wrote 1 month ago: This week, Henry Towsner concluded his portion of reading seminar of the Hrushovski paper, by discus … more →
The "no self-defeating object" argument
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Terence Tao wrote 1 month ago: A fundamental tool in any mathematician’s toolkit is that of reductio ad absurdum: showing tha … more →
Reading seminar 3: "Stable group theory and approximate subgroups", by Ehud Hrushovski
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Terence Tao wrote 1 month ago: This week, Henry Towsner continued some model-theoretic preliminaries for the reading seminar of the … more →
Reading seminar 2: "Stable group theory and approximate subgroups", by Ehud Hrushovski
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Terence Tao wrote 2 months ago: At UCLA we just concluded our third seminar in our reading of “Stable group theory and approxi … more →
Reading seminar: "Stable group theory and approximate subgroups", by Ehud Hrushovski
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Terence Tao wrote 2 months ago: One of my favorite open problems, which I have blogged about in the past, is that of establishing (o … more →
The completeness and compactness theorems of first-order logic
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Terence Tao wrote 8 months ago: The famous Gödel completeness theorem in logic (not to be confused with the even more famous G … more →
Infinite fields, finite fields, and the Ax-Grothendieck theorem
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Terence Tao wrote 9 months ago: Jean-Pierre Serre (whose papers are, of course, always worth reading) recently posted a lovely lectu … more →
245B, Notes 10: Compactness in topological spaces
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Terence Tao wrote 10 months ago: One of the most useful concepts for analysis that arise from topology and metric spaces is the conce … more →
245B, Notes 7: Well-ordered sets, ordinals, and Zorn's lemma (optional)
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Terence Tao wrote 10 months ago: Notational convention: As in Notes 2, I will colour a statement red in this post if it assumes the a … more →
245B, notes 2: Amenability, the ping-pong lemma, and the Banach-Tarski paradox (optional)
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Terence Tao wrote 11 months ago: Notational convention: In this post only, I will colour a statement red if it assumes the axiom of c … more →
Non-measurable sets via non-standard analysis
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Terence Tao wrote 1 year ago: Last year on this blog, I sketched out a non-rigorous probabilistic argument justifying the followin … more →
The blue-eyed islanders puzzle
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Terence Tao wrote 1 year ago: Given that there has recently been a lot of discussion on this blog about this logic puzzle, I thoug … more →
254A, Lecture 3: Minimal dynamical systems, recurrence, and the Stone-Čech compactification
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Terence Tao wrote 1 year ago: We now begin the study of recurrence in topological dynamical systems – how often a non-empty … more →
On Limits II
Pietro wrote 2 years ago: (This is a continuation of On Limits I.) Think of Pelé. When somebody asks “who is Pelé” … more →
