This is my last post of 2008, so happy holidays to everyone!. This one shouldn’t take too long, it’s just applying the lessons of the last few posts to compute some numbers. We start by talking like physicists. We’ll write , the classical and quantum parts. The classical part has the terms. We don’t really care about them. The quantum part only actually appears in its third derivatives, and so we can modify things by quadratic terms.

### December 2008

December 23, 2008

## Kontsevich’s Formula

Posted by Charles Siegel under Algebraic Geometry, Big Theorems, Cohomology, Computational Methods, Curves, Enumerative Geometry[6] Comments

December 18, 2008

## Quantum Cohomology

Posted by Charles Siegel under Algebraic Geometry, Cohomology, Computational Methods, Curves, Enumerative Geometry[2] Comments

Now that we know what a Gromov-Witten invariant is (at least, for nice spaces…we’re avoiding stacks for this series, and assuming that everything behaves nicely and that these actually count things…), we can start talking about Quantum Cohomology, which organizes all these invariants together. In the next (and potentially last) post in the series, we’ll use quantum cohomology to compute the Gromov-Witten invariants of , and talk about what it means.

December 15, 2008

And now it’s time for the sixth edition of The Giant’s Shoulders! Without further ado: the posts

**1672 – Isaac Newton** experiments with light and prisms. These experiments ignited a controversy in physics: is light a particle or a wave? This wasn’t resolved until the 1900s with the quantum theory. More on the events surrounding Newton’s experiments at the relevantly named Ether Wave Propaganda blog.

**1800s** – Bayblab chronicles the rise and fall of Phrenology, and speculates on why it’s gone, but Astrology is still with us.

**1897 – Eduard Buchner** shows that fermentation has no requirement of living cells, as discussed at the Big Room.

**1897 – David Hilbert** writes a number theory book. In it, he gives many new proofs of theorems, and the book is influential enough that many theorems are still referred to by their number in it. In particular, there is Hilbert Theorem 90, and the blogger at A Mind for Madness took this name. He has both the history, and a modern proof up.

**1933-1945 -** Orac at Respectful Insolence asks the hard question: Was Nazi science good science? Not morally good, but rather, methodologically. The comment thread is rather long and interesting too, and he has a followup.

**1941 – Beedle and Tatum** demonstrate the one gene, one enzyme rule. The Evilutionary Biologist discusses the process: fruit flies were too hard, so they found something simpler. And eventually, this begins modern molecular biology and biochemical genetics.

**1954 – Hans Luhn** writes down an algorithm for error detection, which is currently used to construct credit card numbers. The details, along with warnings to not try this at home, over at Money Blue Book.

**1956 – DuBois, Botelho, and Comro** calculate airway resistance in people with respiratory disease. Or more precisely, measuring it. Details at Isis the Scientist.

**1960-1963 – Simmons and Baluffi** work out equilibrium vacancy concentrations in the solid state theory of metals, over at Entertaining Research.

**1972 – Mintz and Alpert** investigate hallucinations, psychosis, and it all ties to UFO abduction experiences over at Podblack.

**1977** **- Roberts et al** study the process of addiction and cocaine. Scicurious at Neurotopia discusses it in great detail.

And finally, GrrlScientist at Living the Scientific Life discusses a book on the history of the Natural History Museum in London, as well as what goes on behind the scenes at such a place.

Next edition up in a month at the Questionable Authority. And a reminder to people: papers need to be at least a decade old! I got submissions from 2008, and that’s just not this Carnival, as well as a bunch of things that just didn’t match this carnival. Good posts, but not science history.

December 12, 2008

## Gromov-Witten Invariants

Posted by Charles Siegel under Algebraic Geometry, Cohomology, Computational Methods, Curves, Enumerative Geometry[3] Comments

Ok, sorry this took so long, but I’m back. Hopefully will be more regular now. Anyway, last time we talked about Stable Maps, and in the meantime, there’s been a post at the Secret Blogging Seminar talking about Gromov-Witten invariants and TQFTs. We’re following a series of talks I gave here, so we’re not going in that direction at all. Instead, here I’m going to define G-W invariants for nice spaces, prove a couple of nice lemmas, and eventually get to using them to solve some actual enumerative problems (give me a few more posts before that happens, though.)