Summer School of mathematics 2022By a result of Church-Putman, the rational cohomology of $\operatorname{SL}_n(\mathbb{Z})$ vanishes in "codimension one", i.e. $H^{{n \choose 2} -1}(\operatorname{SL}_n(\mathbb{Z});\mathbb{Q}) = 0$ for $n \geq 3$, where ${n \choose 2}$ is the virtual cohomological dimension of $\operatorname{SL}_n(\mathbb{Z})$. I will talk about work in progress on two generalisations of this result: The first project is joint work with Miller-Patzt-Sroka-Wilson (see https://arxiv.org/abs/2204.11967). We show that the rational cohomology of $\operatorname{SL}_n(\mathbb{Z})$ vanishes in codimension two, i.e. $H^{{n \choose 2} -2}(\operatorname{SL}_n(\mathbb{Z});\mathbb{Q}) = 0$ for $n \geq 3$. The second project is joint with Patzt-Sroka. Its aim is to study whether the rational cohomology of the symplectic group $\operatorname{Sp}_{2n}(\mathbb{Z})$ vanishes in codimension one, i.e. whether $H^{n^2 -1}(\operatorname{Sp}_{2n}(\mathbb{Z});\mathbb{Q}) = 0$ for $n \geq 2$.
De Mehmet Haluk Sengun
De Mehmet Haluk Sengun
De Aurel Page
De Alexander Hulpke
De Alexander Hulpke
De Alexander Hulpke
De Paul Gunnells
De Aurel Page
De Peter Patzt
De Peter Patzt
De Peter Patzt
De Jennifer Wilson
De Jennifer Wilson
De Jennifer Wilson
De Haowen Zhang
De Renaud Coulangeon
De Renaud Coulangeon
De Bill Allombert
De Lewis Combes
De Alexander Hulpke
De Alexander Hulpke
De Paul Gunnells
De Paul Gunnells
De Paul Gunnells
De Paul Gunnells
De Graham Ellis
De Graham Ellis
De Graham Ellis
De Graham Ellis
De Graham Ellis
De Philippe Elbaz-Vincent
De Philippe Elbaz-Vincent
De Philippe Elbaz-Vincent
De Bettina Eick
De Petru Constantinescu
De Angelica Babei
De Alexander, D. Rahm
De Benjamin Brück
De Calista Bernard
De Philippe Elbaz-Vincent
De Bettina Eick
De Bettina Eick
De Bettina Eick
De Bettina Eick
De Herbert Gangl
De Zachary Himes
