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Hodge theory of matroids (Session 4)

Zoom

This 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 A

For 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.

Sebastian Wolf: Extending exodromy

Heidelberg, Mathematikon, SR A

For 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 $X$.

Hodge theory of matroids (Session 5)

Zoom

This 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)

Hodge theory of matroids (Session 6)

Zoom

This 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