Elliptic Curves

#1

Post by CarolineW » Sat, Jun 10, 2017, 8:43 AM UTC

Re: Elliptic Curves

#2

Post by ice109 » Sat, Jun 10, 2017, 2:27 PM UTC

the profusion of posted slides on the internet is a detriment to researchers everywhere. so many times i've googled something technical (CS, math, engineering) and what percolates to the top are lecture slides, which are almost useless for actual in depth learning.

edit: spoke too soon - only the first link is slides.

Re: Elliptic Curves

#3

Post by stablemap » Sat, Jun 10, 2017, 2:38 PM UTC

ice109 wrote: post #2

the profusion of posted slides on the internet is a detriment to researchers everywhere. so many times i've googled something technical (CS, math, engineering) and what percolates to the top are lecture slides, which are almost useless for actual in depth learning. edit: spoke too soon - only the first link is slides.

It believe mathematicians will continue to favor boards. Sitting in the audience I greatly prefer this; however, such lectures have less chance of being posted at all.

For this topic we are lucky to have Silverman's book [1], which everyone seems to like.

[1] https://www.math.brown.edu/~jhs/AECHome.html

Re: Elliptic Curves

#4

Post by ice109 » Sat, Jun 10, 2017, 2:45 PM UTC

stablemap wrote: post #3

ice109 wrote: post #2

the profusion of posted slides on the internet is a detriment to researchers everywhere. so many times i've googled something technical (CS, math, engineering) and what percolates to the top are lecture slides, which are almost useless for actual in depth learning. edit: spoke too soon - only the first link is slides.

It believe mathematicians will continue to favor boards. Sitting in the audience I greatly prefer this; however, such lectures have less chance of being posted at all. For this topic we are lucky to have Silverman's book [1], which everyone seems to like. [1] https://www.math.brown.edu/~jhs/AECHome.html

can you explain to me why an elliptic curve over C is a quotient manifold (like the torus on page 7 of the first set of slides)?

Re: Elliptic Curves

#5

Post by lukejduncan » Sat, Jun 10, 2017, 2:46 PM UTC

I've seen a few links to resources on elliptic curves on HN, but I don't understand their importance or why they're trending with folks here.

Can someone give me some context?

Re: Elliptic Curves

#6

Post by baobrien » Sat, Jun 10, 2017, 2:51 PM UTC

lukejduncan wrote: post #5

I've seen a few links to resources on elliptic curves on HN, but I don't understand their importance or why they're trending with folks here. Can someone give me some context?

Elliptic Curves are one of the core mathematical constructs behind most of the commonly used non-RSA asymmetric cryptographic algorithms (curve25519, ed25519, ECDH, ECDSA).

Re: Elliptic Curves

#7

Post by yequalsx » Sat, Jun 10, 2017, 3:08 PM UTC

ice109 wrote: post #4

stablemap wrote: post #3

Earlier quoted context omitted.

It believe mathematicians will continue to favor boards. Sitting in the audience I greatly prefer this; however, such lectures have less chance of being posted at all. For this topic we are lucky to have Silverman's book [1], which everyone seems to like. [1] https://www.math.brown.edu/~jhs/AECHome.html

can you explain to me why an elliptic curve over C is a quotient manifold (like the torus on page 7 of the first set of slides)?

The explanation is in lecture 15. It requires knowledge of some advanced mathematics. Abelian varieties over the complex numbers are analytically isomorphic to a torus.

Re: Elliptic Curves

#8

Post by v64 » Sat, Jun 10, 2017, 3:08 PM UTC

baobrien wrote: post #6

lukejduncan wrote: post #5

I've seen a few links to resources on elliptic curves on HN, but I don't understand their importance or why they're trending with folks here. Can someone give me some context?

Elliptic Curves are one of the core mathematical constructs behind most of the commonly used non-RSA asymmetric cryptographic algorithms (curve25519, ed25519, ECDH, ECDSA).

But is there a particular reason like a news event that they're trending right now?

Re: Elliptic Curves

#9

Post by sillysaurus3 » Sat, Jun 10, 2017, 3:11 PM UTC

v64 wrote: post #8

baobrien wrote: post #6

Earlier quoted context omitted.

Elliptic Curves are one of the core mathematical constructs behind most of the commonly used non-RSA asymmetric cryptographic algorithms (curve25519, ed25519, ECDH, ECDSA).

But is there a particular reason like a news event that they're trending right now?

Randomness doing its usual.

Re: Elliptic Curves

#10

Post by stablemap » Sat, Jun 10, 2017, 3:11 PM UTC

ice109 wrote: post #4

stablemap wrote: post #3

Earlier quoted context omitted.

It believe mathematicians will continue to favor boards. Sitting in the audience I greatly prefer this; however, such lectures have less chance of being posted at all. For this topic we are lucky to have Silverman's book [1], which everyone seems to like. [1] https://www.math.brown.edu/~jhs/AECHome.html

can you explain to me why an elliptic curve over C is a quotient manifold (like the torus on page 7 of the first set of slides)?

I would expect him to spell this out in lectures 15 and 16. It does take work. What is surprising is that despite their all looking the same -- certainly they are the same as real manifolds -- there are tons of elliptic curves. The difference is in the complex analytic structure.