Arithmetic and Diophantine Geometry, via Ergodic Theory and o-minimality

Session

Morning Chair: Martin Orr

10 sept. 2025, 09:00

Centre de conférences Marilyn et James Simons (Le Bois-Marie)

11. Determinant Values on Irrational Lattices

Hee Oh (Yale Univ.)

10/09/2025 09:30

We study the value-distribution problem of det on an irrational lattice $L < M_n(\mathbb R)$: how are the values of det on L distributed on $\mathbb R$? In a recent joint work in progress with Wooyeon Kim, we obtain quantitative results toward this question; for n=2, this amounts to a quantitative version of the Oppenheim conjecture for quadratic forms of signature (2,2), as studied by...

12. Higher Property T, Banach Representations and Applications

Uri Bader (Weizmann Inst. & Univ. of Maryland)

10/09/2025 10:50

Gromov conjectured that the $L^p$-cohomology of simple groups vanishes below the rank.
Farb conjectured a fixed point property for actions of lattices in such groups on CAT(0) cell complexes of dimension lower than the rank.
Both conjectures follow from a new cohomological vanishing result, which could be seen as a Banach version of higher property T.
In my talk I will survey the subject...

13. Convolution and Square on Abelian Groups

Yves Benoist (CNRS, Univ. Paris-Saclay)

10/09/2025 12:00

We will construct functions on finite abelian groups whose convolution square is proportional to their square. For that, we will interpret the abelian group as a subgroup of an abelian variety with complex multiplication, and use the modularity properties of their theta functions.