AIM: p-DG Theory

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