## Profile

## Stream

### prabhu shankar

Shared publicly -Chrome24

Firefox14

Chrome23

Firefox18

IE9

Mozilla

Safari6

Firefox19

IE8

Unknown

Firefox3

IE7

Safari5

IE10

Chrome26

Safari4

IE6

Firefox16

Safari

Chrome10

Firefox12

Firefox20

Chrome22

Opera9

Firefox15

Firefox10

Chrome16

Firefox17

Firefox6

Chrome18

Chrome27

Firefox13

Firefox4

IEMobile9

Firefox9

Firefox1

Chrome8

IE5

Chrome5

Chrome20

Firefox11

BlackBerry4

Chrome9

Chrome21

Chrome11

Chrome12

Chrome4

Safari7

Chrome15

Chrome7

Chrome6

Firefox7

IEMobile6

### prabhu shankar

Shared publicly -**and**

*weight***, the gas behaves like a liquid. #ScienceSunday**

*density*An adorable Rosie & Anna perform this experiment and more in this video Magic Floating Boat - Sulfur Hexafluoride

via +Carlos MuZzLeBoY Escanlar and +Ross Dmochowski and Reddit :)

### prabhu shankar

Shared publicly -**topos theory**as an approach to unifying mathematics. She was a student of one of the best topos theorists in the world, now she's a research fellow at Cambridge University, and she lives and breathes math. I always enjoy meeting brilliant young mathematicians who are eager to explore mind-blowing new realms and confident in their power to do it. They can be scary, but they're fun to see - sort of like a lion or tiger.

I'm not going to tell you what a topos is; I'll just say some stuff about them. They were invented by Grothendieck in the 1960's as part of his quest to prove some conjectures in number theory. The solutions of a bunch of polynomial equations give, indirectly, a topos, and he thought of this topos as a generalization of a

*space*, hence the name 'topos'. Later he and other realized that a topos is like a

*mathematical universe*, since the world of set theory is one topos, but there are many more. So, you can think of topos theory as a grand generalization of set theory.

But then people realized that a topos is also like a

*theory*. For many familiar mathematical gadgets - groups, rings, etcetera - there is a topos called the

**classifying topos**of that gadget, which acts like an axiomatic theory of that gadget. In particular, any particular instance of that gadget in the world of sets - for example, any particular group - gives a map from the topos of sets to the classifying topos of that gadget, and conversely.

Olivia Caramello is deeply focused on classifying topoi and how they can be used as 'bridges' to relate seemingly different fields of math. She has an easy-to-read introduction to this idea here:

http://oliviacaramello.com/Unification/Unification.htm

My friend Colin McLarty, who also attended this conference, has written a nice history of topos theory that gives a good flavor of what it's about, without revealing the - somewhat terrifying, at first -

*definition*of a topos:

http://www.cwru.edu/artsci/phil/UsesandAbuses%20HistoryToposTheory.pdf

It's taken me a long time to learn what little I know about topos theory - in part because I'm interested in lots of other things, and in part because I found it a bit intimidating for the first few decades. A long time ago, I wrote this introduction:

http://math.ucr.edu/home/baez/topos.html

whose main virtue is that it points you to 2 free books on the subject: the easy one by Goldblatt, and the vastly more profound)book by Barr and Wells. But now I've reached the point where topos theory makes a lot more sense! So, I should probably expand this page a bit someday.

If you know topos theory and/or a fair amount of logic, you can get a good intro to Caramello's work here:

• Olivia Caramello, The unification of mathematics via topos theory, http://arxiv.org/abs/1006.3930.

However, this is not for the faint-hearted! Here's a sample, just so you can decide if this is for you:

"Now, the fundamental idea is the following: if we are able to express a

property of a given geometric theory as a property of its classifying topos then we can attempt to express this property in terms of any of the other theories having the same classifying topos, so to obtain a relation between the original property and a new property of a different theory which is Morita-equivalent to it. The classifying topos thus acts as a sort of ‘bridge’ connecting different mathematical theories that are Morita-equivalent to each other, which can be used to transfer information and results from one theory to another. The purpose of the present paper is to show that this idea of toposes as unifying spaces is technically very feasible; the great amount and variety of results in the Ph.D. thesis [2] give clear evidence for the fruitfulness of this point of view and, as we shall argue in the course of the paper, a huge number of new insights into any field of Mathematics can be obtained as a result of the application of these techniques."

(A 'geometric theory' is not one about geometry; it's a technical term for an axiom system obeying certain properties,which Caramello explains. As I hinted, many different kinds of mathematical gadgets can be described using geometric theories. She also explains the concept of "Morita equivalence".)

### prabhu shankar

Shared publicly -- pokemon training schoolrearing pokemon, 1985 - present

- Pokémonpokemon trainer, 1985 - present

- Buzz (current)

TeamViewer para Remote Control market.android.com O TeamViewer fornece acesso remoto fácil, rápido e seguro para os sistemas Windows, Mac e Linux. O TeamViewer já está sendo usado em mais de |

Maps market.android.com Download the latest release of Google Maps, and never carry a paper map again. Google Maps for Android with Navigation (Beta) has:* Detailed |

250g –weight of your heart (a set of 9 rings) sakurakoshimizu.blogspot.com Year:1999, Material: silver 950, framed photographic image description: 250gram is the average weight of human heart. We usually don’t think |

Dasavatharam Song Copied from Vikram's Movie www.youtube.com "Kallai mattum kandal", it is the only listenable number from the entire album. Even this song is pathetic rip off from this song from Malay |

YouTube - Living Doll | My Fake Baby | Channel 4 www.youtube.com Create AccountSign In. Home. BrowseFilmsUpload. Hey there, this is not a commercial interruption. You're using an outdated browser, whic |

YouTube - Force-New Exclusive 2nd Latest Trailer 2011 ft John Abraham an... www.youtube.com Create AccountSign In. Home. BrowseUpload. Hey there, this is not a commercial interruption. You're using an outdated browser, which You |

YouTube - Boy Asks Obama, 'Why Do People Hate You?' www.youtube.com Create AccountSign In. Home. BrowseFilmsUpload. Hey there, this is not a commercial interruption. You're using an outdated browser, whic |

YouTube - Final Diner Scene-Pulp Fiction www.youtube.com Create AccountSign In. Home. BrowseFilmsUpload. Hey there, this is not a commercial interruption. You're using an outdated browser, whic |

YouTube - Funny Scene in RocknRolla :D www.youtube.com |

YouTube - RocknRolla Cigarettes www.youtube.com |

" Oy, to ne vecher ". Russian folk song. www.youtube.com " Oy, to ne vecher ". Russian folk song. Sings Kristina Vikhrova. Arrangement by Vladimir Sidorov. Concert in a sanatorium URAL; January, 20 |

Stick Cricket World T2 www.sticksports.com Click here to play Stick Cricket: World T2! Do you dream of playing for your country? Here's your chance to step up and win the World T2 in |

Yipman out Bruce Lee in - 2011 www.youtube.com after the yipman performance donnie yen become a new bruce lee |

The Dark Knight Rises (Main Theme) www.youtube.com The Dark Knight Rises (Main Theme) Hans Zimmer & James Newton Howard MaksFearless Version for Main Theme movie. |

GIRL DOING AN EYEBROW DANCE www.youtube.com SUBSCRIBE: http://www.youtube.com/subscription_center?add_user=LeBuzzDuBuzz Facebook: http://www.facebook.com/pages/Ecu/301217443228866 Twit |

Girl with a funny talent. (2 years ago) www.youtube.com Girl with a funny talent 2 years earlier. Original Video: http://www.youtube.com/watch?v=6Zx39v3JUUI Girl with a funny talent. Girl with a f |

Chalanam Chalanam HD Blu ray song - Urumi by 3r Mallu HD Ft HOT Vidya Ba... www.youtube.com http://www.facebook.com/pages/3r-entertainments/132418106827368?sk=app_167969729896883 website : http://www.3rentertainments.blogspot.com, h |