### Comparison with Čech cohomology, algebraic version (Part 1)

Heidelberg, MATHEMATIKON, SR 4 INF 205, HeidelbergMarius Leonhardt

### Hodge theory of matroids (Session 4)

ZoomThis semester’s topic in our joint research seminar is Hodge theory of matroids. The meetings take place on Zoom on a bi-weekly basis during lecture time, Thursdays 15-18.

Talk 7: *A crash course on toric varieties* (Felix Goebler)

Talk 8: *Minkowski weights and the Chow ring of a toric variety* (Luca Battistella)

### Prof. Johannes Sprang: Towards integral p-adic cohomology theories for open and singular varieties

Heidelberg, Mathematikon, SR AFor primes $l≠p$, $l$-adic cohomology provides a good cohomology theory for varieties over a field of positive characteristic $p$. For $l=p$, there is a whole zoo of $p$-adic cohomology theories. While rigid cohomology provides a well-behaved $p$-adic cohomology theory for all varieties of characteristic $p$, it has the drawback of having only rational coefficients. On the other hand, crystalline cohomology provides a good integral $p$-adic cohomology theory for smooth and proper varieties. In this talk, we explain a joint work with Veronika Ertl and Atsushi Shiho towards the construction of a good integral $p$-adic cohomology theory beyond the smooth and proper case.

### Comparison with Čech cohomology, algebraic version (Part 2)

Marius Leonhardt

### Sebastian Wolf: Extending exodromy

Heidelberg, Mathematikon, SR AFor a scheme $X$, we will introduce the so called Galois category $\operatorname{Gal}(X)$ of $X$ due to Barwick, Glasman and Haine. Its objects are geometric points of $X$ and its morphisms are \'etale specializations of such. It is naturally equipped with a pro-finite topology and plays the role of an \'etale version of an exit-path category: Continuous representations of $\operatorname{Gal}(X)$ with values in finite sets are equivalent to constructible \'etale sheaves on $X$. After recalling the necessary ingredients, we will discuss how one can use the language of condensed/ pyknotic mathematics to generalize the exodromy equivalence to a much larger class of sheaves on $X$.

### Comparison with étale cohomology and finiteness in dimension

Christian Dahlhausen

### Dr. Baptiste Morin: tba

Heidelberg, Mathematikon, SR A### Joins of Henselian Huber pairs (Part 1)

Heidelberg, MATHEMATIKON, SR 4 INF 205, HeidelbergM. Amine Koubaa

### Hodge theory of matroids (Session 5)

ZoomThis semester’s topic in our joint research seminar is Hodge theory of matroids. The meetings take place on Zoom on a bi-weekly basis during lecture time, Thursdays 15-18.

Talk 9: *Bergman fans and the permutohedral variety* (Stefan Rettenmayr)

Talk 10: *Intersection theory on the permutohedral variety* (Andreas Gross)

### Joins of Henselian Huber pairs (Part 2)

Heidelberg, MATHEMATIKON, SR 4 INF 205, HeidelbergM. Amine Koubaa

### Comparison with Čech cohomology, adic version (Part 1)

Heidelberg, MATHEMATIKON, SR 4 INF 205, HeidelbergChristian Dahlhausen

### Hodge theory of matroids (Session 6)

ZoomThis semester’s topic in our joint research seminar is Hodge theory of matroids. The meetings take place on Zoom on a bi-weekly basis during lecture time, Thursdays 15-18.

Talk 11: *The Chow ring of a matroid* (Alex Küronya)

Talk 12 by June Huh (Princeton): *Kazhdan-Lusztig theory of matroids and its relationto Hodge theory*