Feb 26, 2019 · Just a word to end the post: as long as the characteristic of the field is not 2, it is possible to generalise this construction (and thus equivalence) to *-algebras. This is related to epsilon-quadratic form.

I’m a fourth year mathmo at Cambridge. Inspired by some of my great predecessors, I started to live-LaTeX notes during lectures and made them available online. Please send any corrections or advice to me as I certainly will make a lot of mistakes. That aside, feel free to contribute to/fork this project on Github.

Links in grey indicate incomplete notes. Michaelmas Algebra Algebraic Geometry Algebraic Number Theory Algebraic Topology Category Theory Combinatorics Differential Geometry Elliptic Curves Lent 3-manifolds Analytic Number Theory Complex Manifolds Introduction to Approximate Groups Profinite Groups Symplectic Topology

Links in grey indicate incomplete notes. Michaelmas Galois Theory Riemann Surfaces Graph Theory Linear Analysis Number Theory Probability and Measure Algebraic Topology Lent Differential Geometry Number Fields Logic and Set …

Links in grey indicate incomplete notes. Michaelmas Methods Linear Algebra Analysis II Markov Chains Quantum Mechanics Lent Geometry Groups, Rings and Modules Numerical Analysis Complex Analysis Complex Methods

May 6, 2018 · Just a word to end the post: as long as the characteristic of the field is not 2, it is possible to generalise this construction (and thus equivalence) to *-algebras. This is related to epsilon-quadratic form.

Dec 14, 2017 · The post is also available as pdf.. Cayley-Hamilton theorem is usually presented in a linear algebra context, which says that an -vector space endomorphism (and its matrix representation) satisfies its own characteristic polynomial.Actually, this result can be generalised a little bit to all modules over commutative rings (which are certainly required to be finitely generated for determinant ...

This is a temporary homepage for a derived algebraic geometry reading group in SISSA in spring 2022. We group every Wednesday in room A136 and online. The first session is on 23/03/2022 at 16:30. If you have any questions please contact me at qkuang at sissa dot it. Schedule Date Content Speaker 23/03/2022 Introduction, DAG … Continue reading "DAG reading group"

I’ve just finished reading Timothy Chow’s A beginner’s guide to forcing and what a nice read! I recommend all readers, particularly those interested in model and set theory, to take a look. I’m particularly fond of the exposition at the beginning addressing the validity of ZFC as the foundation of maths, which I had had qualms about at some point:

An illustrated summary of IID Number Fields using quadratic fields is available here.Therein the following concepts/results are stated, usually accompanied by a worked example in quadratic field: