Previous Conferences & Workshops

I will introduce Apollonian circle packings, and describe the local-global conjecture, which predicts the set of curvatures of circles occurring in a packing. I will then describe reciprocity obstructions, a phenomenon rooted in reciprocity laws...

Cubic forms are homogeneous polynomials of degree 3 in several 
variables. Number theory is interested in their zeros over the rational 
numbers. Algebraic geometry studies the cubic hypersurfaces defined by 
them (e.g., the 27 lines on smooth cubic...

I will discuss escape of mass estimates for SL(d,ℝ)-horospheres embedded in the space of affine lattices, which depend on the Diophantine properties of the shortest affine lattice vector. These estimates can be used, in conjunction with Ratner's...

In this talk, I will present a computation of the image of the Hodge-Tate logarithm map (defined by Heuer) in the case of smooth Stein varieties. When the variety is the affine space, Heuer has proved that this image is equal to the group of closed...

Define the category of solid quasi-coherent sheaves $\mathcal{D}_\blacksquare(X)$ on a rigid-analytic varity $X$. Show that this assignment comes with a natural $6$-functor formalism. Finally, prove the Grothendieck--Serre duality in the rigid...

Agreement testing (aka direct product testing), checks if consistent local information reveals global structure. Beyond its theoretical connections to probabilistic checkable proofs (PCPs), constructing agreement testers is a fundamental...

We will discuss de Rham and Hyodo-Kato flip-flopping for dual towers of rigid analytic spaces. The main tools are comparison theorems expressing the two cohomologies as pro-étale cohomologies of corresponding relative period sheaves that, by...

A deep result of Furstenberg from 1967 states that if $\Gamma$ is a lattice in a semisimple Lie group $G$, then there exists a measure on $\Gamma$ with finite first moment such that the corresponding harmonic measure on the Furstenberg boundary of...