The aim of this workshop is to investigate the interface between the arithmetic of the étale fundamental group and that of local systems, bringing together theories developed with independent vocabularies but governed by strikingly parallel mechanisms.

The workshop will be guided by a series of analogies: (a) Since wild ramification appears as inertia in the fundamental group and as a cycle on the cotangent bundle, what information passes between these two manifestations? (b) Since rank-one local systems are characters of the abelianised fundamental group, does bounded ramification admit equivalent descriptions through moduli and reciprocity? And (c) since monodromy is expressed through fundamental-group representations or Tannakian categories, what does each language retain?

These questions culminate in a reconstruction problem: can the linear shadows provided by Jacobians, Prym varieties, and ℓ-adic representations retain enough information to recover the underlying anabelian geometry?

The program will consist of survey lectures, research talks presenting recent advances, and expository presentations designed to expose common structures and possible bridges between the two approaches.

Keywords: étale fundamental group; local systems; wild ramification; Abbes–Saito theory; singular support and characteristic cycles; conductor formulas; fundamental groups with modulus; reciprocity sheaves; étale homotopy type and pro-étale refinements; higher-categorical monodromy; perverse sheaves and convolution; Tannaka formalism; Prym varieties; anabelian reconstruction.

※ This event is part of the special year ``Arithmetic, Homotopy, and Geometry 2027-28''.