bezrukav

35:06

what’s n in E_n?

Sam Raskin

35:15

2

bezrukav

35:27

thanks!

Tony Feng

39:03

In “factorization algebras = E_n algebras” does the curve also need to be A^1

Lin Chen

39:16

R^n

Sam Raskin

39:41

The statement in topology is that translation-invariant factorization cosheaves on R^n are the same as E_n-algebras.

Alexander Braverman

46:42

Does anybody know if Lurie's theorem is still true if you replace Rep_q(T) by some other braided monoidal category?

Lin Chen

50:16

Lurie’s theorem is the combination of two things: (1) E_2 vs factorization on R^2 (2) Drinfeld center vs E_2. The second part can be generalized to any ambient presentable E_2-category.

Alexander Braverman

51:15

So the answer is yes, right?

Sam Raskin

51:16

Sasha, in a sense, morally yes, but the point of using that category is that you have a good notion of positivity. Essentially, you want to use positivity to get simple Koszul duality statements (this is where Hopf algebras appear: you Koszul dualize the coalgebra structure to get an E_2-algebra). So it wouldn’t work as beautifully.

gurbir

52:27

(t-exact at negative level)

Alexander Braverman

53:34

I have a particular example in mind - in that case Rep_q(T) is replaced by Rep_q(GL(n)\times GL(m)) and some particular Hopf algebra there

Sam Raskin

01:11:57

That distinction can be absorbed into the definitions and is a little more subtle.

Dennis Gaitsgory

01:15:17

casselman-shalika: Frenkel-G-Vilonen

Roman Travkin

01:24:46

The convolution in the coherent RHS should, I guess, correspond to some kind of fusion…

Dennis Gaitsgory

01:25:48

let’s discuss this!

Dennis Gaitsgory

01:27:22

in fact, if you think of LocSys, this convolution has no meaning

Sam Raskin

01:27:51

Convolution doesn’t preserve the support condition….

Roman Travkin

01:30:30

Sam, yeah, maybe restrict to support at 1…

Roman Travkin

01:33:32

Dennis, why—doesn’t the factorization str give us the fusion over C?

Roman Travkin

01:34:43

On LocSys(D^\circ)

Justin

01:38:04

Isn't it true that under the iso G^/G = LS^, convolution in QCoh goes over to fusion?

Roman Travkin

01:42:43

that’s what I’d think…

Dennis Gaitsgory

01:43:18

I don’t think so, but maybe am wrong

Justin

01:50:17

If we use Betti local systems, then we have LS = Map(S^1,pt/G) = G/G and I thought the E_2 structure on the LHS corresponds to convolution on the RHS