It’s morning at TechCrunch40. As the crowds filter in to the ballroom from the coffee klatch area, Internet luminary Esther Dyson boots up her laptop in the front row. Sequoia Capital’s 30-something star Roelof Botha (of YouTube (GOOG) investing fame) rolls up with his bluetooth earbud blinking. We’re minutes away from Day Two here at TechCrunch40 in San Francisco, so it’s time for a Best of Day One recap….

As expected, host Michael Arrington and Mark Zuckerberg stole the show with their late afternoon “fireside chat.” What do you need to know? Zuck, the 23-year old founder of Facebook, is as young and self-assured as ever — and Arrington is as no-nonsense as you’d expect of a guy who blogs more than he sleeps.

Arrington attempted a “deep dive” into Facebook’s platform strategy, rattling off some impressive stats: Apparently FB now boasts 4,000 independent applications, and upwards of 80,000 developers. Covering this ground elicited some breaking news from Zuck: Facebook and its investors are launching a $10 million “grant” fund. The idea is that Facebook VCs Accel Partners and the Founders Fund will dole out $25,000 to $250,000 “grants” to developers with promising ideas for new Facebook apps.

The venture sharks won’t be taking an equity stake for that cash, but, not to fear, there is a string attached: they will get the right of first refusal on the actual first equity round of funding. Should you be interested in applying, simply email platform@facebook.com.

As for Day One’s crowd favorite companies? Take a look at the following:

Cake Financial - Think Quicken (INTU) meets Facebook meets PayPal (EBAY). This is a highly engineered web application that allows users to track all their investing accounts in one place, and it allows them to compare their aggregate investing performance to that of their friends.

Musicshake - this Korean company got the crowd going with a web app that allows users to compose songs on the fly, simply by dragging and dropping clips.

Tripit -Anyone who has ever planned a trip with a group of friends will appreciate Tripit, which allows friends to consolidate flight information, calendars, tourist attractions, etc., into a single set of shared pages.