### Divye Kapoor

Shared publicly -Loved this song. Bought it too. Enjoy a free listen. :)

2

Add a comment...

Divye Kapoor

Works at Google

Attended Indian Institute of Technology, Roorkee

1,959 followers|265,043 views

AboutPostsPhotosYouTubeReviews

Loved this song. Bought it too. Enjoy a free listen. :)

2

Add a comment...

Grothendieck's inequality ( http://en.wikipedia.org/wiki/Grothendieck_inequality ) asserts that a certain discrete optimisation problem (optimising a quadratic form over inputs that are +1 or -1) is equivalent up to constants to a continuous optimisation problem (optimising the same quadratic form over unit vectors in a Hilbert space). This is important for theoretical computer science, because the former problem essentially contains NP-hard problems such as MAX-CUT, whereas the latter can be rephrased as a semidefinite program (by writing the problem in terms of the Gram matrix of the unit vectors) and can be solved in polynomial time by algorithms such as the ellipsoid method. So there are certain NP-hard problems which one can solve "up to constants" in polynomial time: in some sense, the "ratio" between NP and P is bounded! Furthermore, in a certain technical sense, one cannot achieve a better approximation to such problems by *any* polynomial-time algorithm than through the Grothendieck inequality, at least if one assumes the Unique Games Conjecture (a result of Raghavendra).

Grothendieck's inequality also has a very cute connection to Bell's inequality in quantum mechanics, as observed by Tsirelson; roughly speaking, the ability of quantum mechanics to violate Bell's inequality is logically equivalent to the constant in Grothendieck's inequality being greater than one (basically because the discrete optimisation problem describes the envelope of all possible measurement outcomes of a classical hidden-variable system, and the vector-valued optimisation problem describes the envelope of all possible measurement outcomes of a quantum system). Or to put it another way, Grothendieck's inequality asserts (in some sense) that Bell's inequality can only be violated "up to a constant", at least when there are only two measurements made. (For three or more measurements the violation can be much more dramatic, a result of Junge, Navascues, Palazuelos, Perez-Garca, Scholz, and Werner.)

[All this I learned today from a very nice lecture by Pisier on these topics, largely based on his survey article linked to here.]

#spnetwork #recommend arXiv:1101.4195

Grothendieck's inequality also has a very cute connection to Bell's inequality in quantum mechanics, as observed by Tsirelson; roughly speaking, the ability of quantum mechanics to violate Bell's inequality is logically equivalent to the constant in Grothendieck's inequality being greater than one (basically because the discrete optimisation problem describes the envelope of all possible measurement outcomes of a classical hidden-variable system, and the vector-valued optimisation problem describes the envelope of all possible measurement outcomes of a quantum system). Or to put it another way, Grothendieck's inequality asserts (in some sense) that Bell's inequality can only be violated "up to a constant", at least when there are only two measurements made. (For three or more measurements the violation can be much more dramatic, a result of Junge, Navascues, Palazuelos, Perez-Garca, Scholz, and Werner.)

[All this I learned today from a very nice lecture by Pisier on these topics, largely based on his survey article linked to here.]

#spnetwork #recommend arXiv:1101.4195

Selected Papers Network

Probably the most famous of Grothendieck's contributions to Banach space theory is the result that he himself described as "the fundamental theorem in the metric theory of tensor products". That is now commonly referred to as "Grothendieck's theorem" (GT in short), or sometimes as ...

1

Add a comment...

2

2 comments

marriage wo laddu h jise kha k v regret karna padta h aur na khye to v regret karna padta h

Add a comment...

The stuff that powers our online lives...

8

3 comments

+Shilpi Sinha that's strawberry jam... or if you want to make a scandal out of it, lipstick. :P

Add a comment...

It is important to let people know how much they have done for you. Here are my 2 words of gratitude for a teacher who's had a monumental impact in shaping my life and career...

10

2 comments

Thank you Divye, I am one of those silent souls who will shy away from writing it. But I feel you and your wishes none the less.

Add a comment...

In his circles

2,414 people

Awww...

"NYC subways have a strange rule. We took advantage of it."

"NYC subways have a strange rule. We took advantage of it."

5

1

Add a comment...

Interesting...

The +The New York Times reports as of last week +Mitt Romney had almost $62 million more cash on hand than +Barack Obama.

While the race to raise the most money continues and we head into two weeks of conventions, the +Google Politics & Elections team took a look at which candidate is garnering more "donate" +Google search interest.

Take a look!

2

Add a comment...

People

In his circles

2,414 people

Work

Occupation

Rockstar Software Developer at Google

Employment

- GoogleSoftware Engineer, 2011 - present
- ZigndogChief Technical Architect, 2009 - 2011
- QualcommIntern (Corp R&D division), 2009 - 2009
- MicrosoftIntern, 2009 - 2009

Basic Information

Gender

Male

Story

Tagline

Googler. Ex-Startup Guy. I work on stuff that you're using right now.

Introduction

Ubergeek, stellar student, harcore developer, occasionally belligerent, loves family and makes friends with care.

Bragging rights

Played chess with the Chess World Champion. Silver medallist, IIT Roorkee.

Education

- Indian Institute of Technology, RoorkeeComputer Science and Engineering, 2006 - 2011
- Indian Institute of Technology RoorkeeInformation Technology, 2006 - 2011
- Loyola High School2006

Links

YouTube

Contributor to

- Buzz (current)
- DeeKaying - Geekiness @ IIT Roorkee (current)

Public - 2 years ago

reviewed 2 years ago

I went for their Saturday dinner buffet. A little on the expensive side but lots of options and quite tasty "authentic" Indian food. I especially liked the basmati rice that day.

Public - 2 years ago

reviewed 2 years ago