In this public lecture, Thomas Piketty will present new findings and reflections on global inequality dynamics. In particular, he will stress the need to go beyond the Western-centered historical perspective on inequality regimes developed in his book, Capital in the 21st Century. Piketty will also address the relation between rising inequality and the changing structure of electoral conflict, from class-based to identity-based conflict.
The string topology coproduct is an intersection type operation, originally described by Goresky-Hingston and Sullivan, which considers transverse self-intersections on chains of loops in a smooth manifold and splits loops at these intersection points. The geometric chain level construction of string topology operations involves deforming chains to achieve certain transversality conditions and these deformations introduce higher homotopy terms for algebraic compatibilities and properties.
The Grothendieck-Katz $p$-curvature conjecture is an analogue of the Hasse Principle for differential equations. It states that a set of arithmetic differential equations on a variety has finite monodromy if its $p$-curvature vanishes modulo $p$, for almost all primes $p$. We prove that if the variety is a generic curve, then every simple closed loop has finite monodromy.