An old question of Poincaré concerns creating periodic orbits
via perturbations of a flow/diffeomorphism. While pseudoholomorphic
methods have successfully addressed this question in dimensions
2-3, the higher-dimensional case remains less...
We will describe emerging understanding of the structures
related to the arithmetic of Zeta and Multizeta values for function
fields through various results and conjectures.
In a 3-𝖷𝖮𝖱 game , the verifier samples a challenge (x,y,z)∼μ
where μ is a probability distribution over Σ×Γ×Φ, and a map
t:Σ×Γ×Φ→ for a finite Abelian group defining a constraint.
The verifier sends the questions x, y and z to the
players...
A sparsification of a structure, with respect to a class of
queries, produces a compressed representation of the structure
while answering every query in the class approximately correctly.
The seminal example of sparsification is "graph...
I will describe a problem of unlikely intersections in a product
of modular curves, tracing the problem itself and the tools for
some results through the work of Enrico.
Most effective results for integral points on affine curves use
the works of Baker or Bombieri on Diophantine approximation by
S-units. Still, no completely general result is known already in
genus 2. I will briefly present some recent work with...
