Rongmin Lu

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More clues to how an RNA base can be formed out of simpler chemical molecules.

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So everyone seems to be sharing the Feynman lectures video...

**Seven Brilliant Lectures by Richard Feynman**

*accessible to anyone*

Feynman makes physics easy to understand with his characteristic wit and style, the only problem with these is that there are only seven. Richard Feynman was obviously famous for his work as a physicist, but he's also easily regarded as one of the most lucid and effective lecturers to ever address an audience. The set is a phenomenal resource to anyone with even a passing interest in the physical world and the laws that govern it — but even these lectures cannot capture the essence of what it might have been like to attend a presentation given by Feynman himself. Feynman delivered a series of seven, hour-long lectures at Cornell University. Those lectures were recorded by the BBC, and in 2009, they were released to the public. You'll find all seven of them linked below, but you may want to check out the lectures on Microsoft's Project Tuva, where they have been carefully edited to include closed captioning and annotations.

Possibly someone could point Bill O'Rielly in the direction of these to help him out with basic physics. ;)

Here are the links to the uploads on YouTube.

Richard Feynman - The.Character of Physical Law - Part 1 The Law of Gravitation (full version)

Richard Feynman - The.Character.of.Physical.Law - Part 2 (full version)

Richard Feynman - The Character of Physical Law - 3 -The Great Conservation Principles

Richard Feynman - The Character of Physical Law - Part4 Symmetry in Physical Law (full version)

Richard Feynman - The Character of Physical Law - 5 -The Distinction of Past and Future

Richard Feynman - The Character of Physical Law - Part 6 Probability and Uncertainty (full version)

Richard Feynman - The Character of Physical Law - Part 7 Seeking New Laws (full version)

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This one just

*had*to be shared for the pun alone.Harmonic analysis on the adeles.

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A mathematician is giving classes on how to give talks! Rejoice!

The art of giving talks (Matilde Marcolli)

http://www.its.caltech.edu/~matilde/Ma10fall2011.html

via +lieven lebruyn 's blog.

http://www.its.caltech.edu/~matilde/Ma10fall2011.html

via +lieven lebruyn 's blog.

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Spending this semester at Columbia University as the Eilenberg Visiting Professor. Videos of my lectures are available on YouTube.

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A post of John Baez on the n-Category Café:

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I found the paper by Loday and Nikolov (http://arxiv.org/abs/1202.1206) very interesting, so since +Marco Gualtieri was asking for a summary on +David Roberts's post... here's a short exposition of the ideas in the paper, which is really an announcement of the authors' results in a future work.

It is helpful to start with a rough definition of the endomorphism operad End_V of a vector space V, which is the toy example of an operad. End_V is simply a collection of vector spaces {End_V(n)}, for n>=1, where End_V(n):= Hom(V^n,V), (V^n denotes the tensor product of n copies of V), and the operad is defined when you turn End_V into a monoid.

The functor G from the category of symmetric operads to the category of groups is given by sending P={P(n)} to {id} times an infinite product of P(n), for n>=2. Multiplication is given as in 5.1.13 (see also 5.1.20) of Algebraic Operads (http://math.unice.fr/~brunov/Operads.pdf). In other words, this takes the vector spaces in the operad and puts them into an infinite product, with the exception of P(1), which is sent to the identity. As an example, by applying the functor to End_V, we see from (8) that we get (10).

Section 4 sets up the notation to describe Feynman diagrams as decorated graphs. This is standard, except that they call half-edges "flags". All this is to define Dgm(n) in (15) and a commutative monoid M(n) in (16). Proposition 2 then shows that a bijection, defined in the paragraph after (17), gives an isomorphism between Dgm(n) and M(n)

The universal contraction operad is then defined in (18): R(n) is the vector space over the ground field spanned by Dgm(n) x Colv, at least if Colv, the set of colours for vertices, is finite, which they assume. Proposition 3 claims the universal contraction operad R={R(n)} is a symmetric operad, which can be deduced with the knowledge of (20)-(25).

The authors claim that QFT models can be considered as particular suboperads of the universal contraction operad. Proposition 4 claims that if we take a system of subsets F(n) of Dgm(n) x Colv, then R_{F(n)} is a suboperad of R if and only if F(n) satisfies condition (ii) of the Proposition. They then define a "physical theory" R_{E,V} to be the intersection of the operads given by 1PI graphs and two other operads defined, respectively, by admissible half-edges E and admissible vertices V.

The renormalization group appears in this way. Renormalization, as the authors explain in Section 7.1, may be viewed as a change of variables for formal power series. From previous work by Nikolov (http://arxiv.org/abs/0903.0187), it is known that there are additional ambiguities, described by the contraction maps, which are elements of R, the universal contraction operad.

The main result is that a morphism X of operads can be defined (see Sections 7.2-7.4) from the contraction operad of the particular physical theory to the endomorphism operad of the vector space spanned by the set of admissible vertices V. Applying the functor G induces a map between the corresponding groups and the authors claim this coincides with the renormalization group action from the renormalization theory.

It is helpful to start with a rough definition of the endomorphism operad End_V of a vector space V, which is the toy example of an operad. End_V is simply a collection of vector spaces {End_V(n)}, for n>=1, where End_V(n):= Hom(V^n,V), (V^n denotes the tensor product of n copies of V), and the operad is defined when you turn End_V into a monoid.

The functor G from the category of symmetric operads to the category of groups is given by sending P={P(n)} to {id} times an infinite product of P(n), for n>=2. Multiplication is given as in 5.1.13 (see also 5.1.20) of Algebraic Operads (http://math.unice.fr/~brunov/Operads.pdf). In other words, this takes the vector spaces in the operad and puts them into an infinite product, with the exception of P(1), which is sent to the identity. As an example, by applying the functor to End_V, we see from (8) that we get (10).

Section 4 sets up the notation to describe Feynman diagrams as decorated graphs. This is standard, except that they call half-edges "flags". All this is to define Dgm(n) in (15) and a commutative monoid M(n) in (16). Proposition 2 then shows that a bijection, defined in the paragraph after (17), gives an isomorphism between Dgm(n) and M(n)

The universal contraction operad is then defined in (18): R(n) is the vector space over the ground field spanned by Dgm(n) x Colv, at least if Colv, the set of colours for vertices, is finite, which they assume. Proposition 3 claims the universal contraction operad R={R(n)} is a symmetric operad, which can be deduced with the knowledge of (20)-(25).

The authors claim that QFT models can be considered as particular suboperads of the universal contraction operad. Proposition 4 claims that if we take a system of subsets F(n) of Dgm(n) x Colv, then R_{F(n)} is a suboperad of R if and only if F(n) satisfies condition (ii) of the Proposition. They then define a "physical theory" R_{E,V} to be the intersection of the operads given by 1PI graphs and two other operads defined, respectively, by admissible half-edges E and admissible vertices V.

The renormalization group appears in this way. Renormalization, as the authors explain in Section 7.1, may be viewed as a change of variables for formal power series. From previous work by Nikolov (http://arxiv.org/abs/0903.0187), it is known that there are additional ambiguities, described by the contraction maps, which are elements of R, the universal contraction operad.

The main result is that a morphism X of operads can be defined (see Sections 7.2-7.4) from the contraction operad of the particular physical theory to the endomorphism operad of the vector space spanned by the set of admissible vertices V. Applying the functor G induces a map between the corresponding groups and the authors claim this coincides with the renormalization group action from the renormalization theory.

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