# MAT572: “Online seminar diagrammatic algebra: a prototypical example”

The theory of Soergel bimodules emerged in the work of Wolfgang Soergel in the 1990s and 2000s. Soergel bimodules are certain algebraic objects, and the collection of these forms a monoidal category under tensor product. Soergel bimodules are fairly elementary objects, yet they have deep links to representation theory, topology and geometry, and have a remarkably rich internal structure.
The purpose of this seminar is to provide a comprehensive introduction to the theory of Soergel bimodules, in particular, using diagrammatic methods. Indeed, it is not an exaggeration to say that the computational power afforded by diagrammatics was the key breakthrough that allowed many recent advances on the one hand, but is beautiful in its own right on the other hand.

### Contact

Daniel Tubbenhauer email

Please put [Seminar diagrams] as the subject.

### Online System of the UZH

This website is up to date, and not the ones from the UZH.

However, please still register yourself online.

### Why online?

• Short-term. Easy to record lectures $\Rightarrow$ Rewatch the talks anytime, or even from anywhere around the world e.g. other universities.
• Short-term. Improve everyone's technical skills $\Rightarrow$ This can only be positive, right? ;-)
• Short-term. No need for e.g. classrooms $\Rightarrow$ Lower total costs.
• Short-term. No need to commute $\Rightarrow$ Safe time and the environment.
• Long-run. We can take online courses while working, while in-between jobs, or while raising a family $\Rightarrow$ More flexibility.
• Long-run. The society is slowly shifting towards online events and e.g. your next job interview might be online $\Rightarrow$ Online seminars before will prepare you for your future career.
• Long-run. In the near future it might be possible to study at the, say, University of Zurich, but attend online lectures from, say, the University of Sydney $\Rightarrow$ More choices for everyone.

### Who?

• BSC or MSC or PhD students in Mathematics interested in a mixture of linear algebra and combinatorics, but everyone is welcome.

### Where and when?

• This is a online seminar. All talks will be given using zoom Click.
• Usual session:
• Every Monday from 13:00-14:45
• Zoom links will be sent to participants shortly before the seminar starts
• First meeting: 21.Sep.2020
• Last meeting: 23.Nov.2020
• Preliminary meeting:
• There is no preliminary meeting. Please write me an email in case you are interested.
• Summary:
• Mini presentation:

### Schedule

• 21.Sep.2020, Speaker: Daniel, Topic: The classical theory I - Coxeter groups, the beginnings, Video: Click
• 28.Sep.2020, Speaker: Rizacan, Topic: The classical theory II - Coxeter groups and reflection groups, Video: Click, Slides: Click
• 05.Oct.2020, Speaker: Daniel, Topic: The classical theory III - Kazhdan-Lusztig theory, Video: Click, Slides: Click
• 12.Oct.2020, Speaker: Anna, Topic: The classical theory IV - Soergel bimodules, the beginnings, Video: Click, Slides: Click
• 19.Oct.2020, Speaker: Najma, Topic: The classical theory V - Soergel bimodules, the feast, Video: Click, Slides: Click
• 26.Oct.2020, Speaker: Katja, Topic: The diagrammatic theory I - drawing monoidal categories, Video: Click, Slides: Click
• 02.Nov.2020, Speaker: Aurelia, Topic: The diagrammatic theory II - Frobenius extensions, Video: Click, Slides: Click
• 09.Nov.2020, Speaker: Daniel, Topic: The diagrammatic theory III - the dihedral cathedral, Video: Click, Slides: Click
• 16.Nov.2020, Speaker: Li, Topic: The diagrammatic theory IV - the diagrammatic Hecke category, Video: Click, Slides: Click
• 23.Nov.2020, Speaker: Hussein, Topic: The diagrammatic theory V - Soergel's categorification theorem, Video: Click, Slides: Click

### Goals of the talks

Here is the detailed plan. Click