AIM: p-DG Theory

There is an AIM research community on categorifcation and link homology.

You Qi and I are leading a section on p-DG theory.

We will meet every Tuesday at 1:00PM EST on zoom.

Meeting ID: 982 5626 7299

Passcode: p-dg

One tap mobile

+16468769923,,98256267299# US (New York)

+13126266799,,98256267299# US (Chicago)

Problem List:

problemlist.pdf

Schedule:

6/29/21: Organizational meeting

7/6/21: Introduction to hopfological algebra (Qi You) Video Slides

7/13/21: p-DG link homology (Josh Sussan) Video Slides

7/20/21: Infinite twists and Soergel bimodules (Ben Cooper) Video Slides

7/27/21: Infinite twists and Soergel bimodules II (Ben Cooper) Video Slides

8/3/21: Tensor product categorification at roots of unity (Qi You) Video Slides

8/10/21: Categorification of cyclotomic rings (Robert Laugwitz) Video Slides

8/17/21: Categorified projectors (Oscar Kivinen) Video Slides

8/24/21: Cell 2-representations & categorification at prime roots of unity (Vanessa Miemietz) Video Slides

8/31/21: Torus link homology (Nicolle Gonzalez) Video Slides

p-DG References:

Hopfological algebra and categorification at a root of unity: the first steps. Mikhail Khovanov. https://arxiv.org/abs/math/0509083
Hopfological algebra. You Qi. https://arxiv.org/abs/1205.1814
An approach to categorication of some small quantum groups. Mikhail Khovanov, You Qi. https://arxiv.org/abs/1208.0616
An approach to categorication of some small quantum groups II. You Qi, Ben Elias. https://arxiv.org/abs/1302.5478
A categorification of quantum sl(2) at prime roots of unity. You Qi, Ben Elias. https://arxiv.org/abs/1503.05114
p-DG cyclotomic nilHecke algebras. Mikhail Khovanov, You Qi, Joshua Sussan. arXiv:1711.07159
p-DG cyclotomic nilHecke algebras II. You Qi, Joshua Sussan. arXiv:1811.04372
On some p-differential graded link homologies. You Qi, Joshua Sussan. arXiv:2009.06498

Torus link references:

Categorified Young symmetrizers and stable homology of torus links. Matthew Hogancamp https://arxiv.org/abs/1505.08148
On the computation of torus link homology. Ben Elias, Matthew Hogancamp. https://arxiv.org/abs/1603.00407
Khovanov-Rozansky homology and higher Catalan sequences. Matthew Hogancamp. https://arxiv.org/abs/1704.01562
Homology of torus knots. Anton Mellit. https://arxiv.org/abs/1704.07630
Torus link homology. Matthew Hogancamp, Anton Mellit. https://arxiv.org/abs/1909.00418