String theory says we live in a ten-dimensional universe, but that only four are accessible to our everyday senses. According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds. The discoverer of these manifolds, Professor Yau Shing-Tung, will describe in general terms how geometry enables the understanding of space time and trace its historical development from the ancient Greeks through Einstein to modern string theory, analysing on the way the contributions of many great geometers and physicists.

Indeed some deep stuff, I was gonna study 5 year physics at university. But when I was faced with the option, I was to lazy school has a way for destoying ones passion. But watching vids like this is good enough for me hehe, so cheers intresting talk

You can do it on your own too. Letting school forbid you from such powerful knowledge? Come on man, you're better than that. Physics knowledge reaches into every single aspect of your life. It's as good as Taoist wisdom.

We study the cosmological implications of including angular motion in the Dirac–Born–Infeld brane inflation scenario. The non-canonical kinetic terms of the Dirac–Born–Infeld action give an interesting alternative to slow-roll inflation, and cycling branes can drive periods of accelerated expansion in the Universe. We present explicit numerical solutions demonstrating brane inflation in the Klebanov–Strassler throat. We find that demanding sufficient inflation takes place in the throat is in conflict with keeping the brane's total energy low enough that local gravitational back-reaction on the Calabi–Yau manifold can be safely ignored. We deduce that spinflation (brane inflation with angular momentum) can ease this tension by providing extra e-foldings at the start of inflation. Cosmological expansion rapidly damps the angular momentum causing an exit to a more conventional brane inflation scenario. Finally, we set up a general framework for cosmological perturbation theory in this scenario, where we have multi-field non-standard kinetic term inflation.

Haha, true maybe I start reading again when I got some free time. love science.

Don't you think that that pic of the Calabi-Yau form looks exactly like what you'd see on a high dose of spice? I distinctly remember similar shapes pulsing and waving hyperdimensionally through my vision everytime when I was on receptor saturating doses of mimosa. Same thing was observed on 2C-B and ketamine also.

..The one thing I vividly remember is closing my eyes, seeing these forms and "hearing" in my mind's ear this deep whoooom...
but this sound came from the visuals themselves. And yeah certainly they were imbued with some kind of consciousness, I guess they are the workings of our brain rendered using our brain itself.

I mean we do have a word for the more mundane 2D visuals on other hallucinogens: phosphenes or form constants. But what do you really call these things?

"There’s a chance, however, that the universe is ultimately curved and bounded. But even if it is, the allowable curvature is so slight that, according to some analyses, the Hubble volume we see is just one out of at least one thousand such volumes that must exist. And a recently launched space instrument, the Planck telescope, may reveal within a few years that there are at least one million Hubble volumes out there in the cosmos, only one of which we’ll ever have access to.
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At the other extreme, microscopes, particle accelerators, and various imaging devices continue to reveal the universe on a miniature scale…there may even be more dimensions, and possibly quite a few more than the three spatial dimensions we’re intimately acquainted with.
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My father died unexpectedly when I was fourteen, leaving our family not only grief-stricken but destitute, with a slew of debts to pay off and virtually no income. As I needed to earn some money to support the family, an uncle advised me to leave school and raise ducks instead. But I had a different idea: teaching mathematics to other stu dents. Given our financial circumstances, I knew there was just one chance for me to succeed and I placed my bets on math, double or nothing.
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So why did geometry, of all the areas of mathematics, come to occupy center stage for me, both in my waking thoughts and in my dreams? Primarily because it struck me as the field closest to nature and therefore closest to answering the kinds of questions I cared about most. Besides, I find it helpful to look at pictures when grappling with difficult concepts, and pictures are few and far between in the more abstruse realms of algebra and number theory. Then there was this fantastic group of people doing geometry at Berkeley ...

Dehn’s lemma, a geometric version of which was proven by William Meeks and the author (Yau), provides a mathematical technique for simplifying a surface that crosses, or intersects, itself into a surface with no crossings, folds, or other singularities. The lemma is typically framed in terms of topology, but the geometric approach taken by Meeks and Yau offers a more precise solution.
The argument is difficult to explain mainly because the Einstein field equation, which relates the physics in this situation to geometry, is a complicated, nonlinear formulation that is not intuitive. Basically, we started off by assuming that the mass of a particular space was not positive. Next we showed that you could construct an area-minimizing surface in such a space whose average curvature was non-negative. The surface, in other words, could have zero average curvature. That would be impossible, however, if the space in which the surface sat was our universe, where the observed matter density is positive. And assuming that general relativity is correct, a positive matter density implies positive curvature.
While this argument might seem circular, it actually is not. The matter density can be positive in a particular space, such as our universe, even though the total mass is not positive. That’s because there are two contributions to total mass—one coming from matter and the other coming from gravity."

The component that lies in the six compactified dimensions of the Calabi-Yau gives riseto the four-dimensional gauge fields of our world and hence to the strong, weak, and electromagnetic forces. In fact, it’s fair to say that those forces are generated by the internal structure of the Calabi-Yau, or so string theory maintains.

A two-dimensional torus, for example, is in many ways defined by two independent loops or cycles, one going around the hole and another going through. The moduli, by definition, measure the size of the cycles, which themselves govern both the size and shape of the manifold. If the cycle going through the donut hole is the smaller of the two, you’ll have a skinny donut; if it’s the larger, you’ll have a fat donut with a relatively small hole in the middle. A third modulus describes the degree to which the torus is twisted.

So much for the torus. A Calabi-Yau, which, as we’ve noted, can have upwards of five hundred holes, comes with many cycles of various dimensions and hence many more moduli—anywhere from dozens to hundreds. One way to picture them is as a field in four-dimensional spacetime. The field for the size moduli, for instance, assigns a number to every point in ordinary space corresponding to the size (or radius) of the unseen Calabi-Yau. A field of this sort—which is completely characterized by a single number at each point in space, with no direction or vector involved—is called a scalar field. One can imagine all sorts of scalar fields around us, such as those measuring the temperature at every point in space or the humidity, barometric pressure, and so forth.