• FU-Students should register via Campus Management.
• Non-FU-students should register via MyCampus/Whiteboard.

Winter Term 2026/2027

Lecturer: Marius Nielsen and Elmar Vogt

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Time and place:  Wednesdays,  2pm -- 4pm, SR 140 (rear building), Arnimallee 7.

Criteria for proof of performance:
Grade and credit points will be awarded based on a presentation and written summary.

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Prerequisites: Basic knowledge of topology as taught in Topology I and II is required. 

Content: Simplicial sets form a different category in which we can do “algebraic topology”, but they are also heavily intertwined with category theory and especially higher category theory. In this seminar, we will start by introducing the category of simplicial sets and study basic objects in this category and how one manipulates simplicial sets. We will then focus on singular homology in this setting and start our study of the interaction between algebraic topology and the simplicial homotopy theory. 
For the final part of the seminar, we will cover the Dold—Kan theorem and begin the study of quasi-categories a specific class of simplicial sets, which forms the most popular model for infinity-categories. 

Schedule

Date	Title	Speaker
14.10.	Organisatorial meeting: Overview and distribution of talks	Marius Nielsen
21.10.	Talk 1: TBA	N.N.
28.10.	Talk 2: TBA	N.N.
04.11.	Talk 3: TBA	N.N.
11.11.	Talk 4: TBA	N.N.
18.11.	Talk 5: TBA	N.N.
25.11.	Talk 6: TBA	N.N.
02.12.	Talk 7: TBA	N.N.
09.12.	Talk 8: TBA	N.N.
16.12.	Talk 5: TBA	N.N.
2027
06.01.	Talk 9: TBA	N.N.
13.01.	Talk 10: TBA	N.N.
20.01.	Talk 11: TBA	N.N.
27.01.	Talk 12: TBA	N.N.
03.02.	Talk 13: TBA	N.N.
10.02.	Talk 14: TBA

References:

• Goerss, Paul G., and John F. Jardine. Simplicial homotopy theory. Springer Science & Business Media, 2009.
• May, J. Peter. Simplicial objects