From exceptional collections to motivic decompositions via noncommutative motives

From HAG to DAG: derived moduli spaces

From Jacobians to one-motives: exposition of a conjecture of Deligne

From Klein to Painleve via Fourier, Laplace and Jimbo

From moment graphs to intersection cohomology

From monoids to hyperstructures: in search of an absolute arithmetic

From real affine geometry to complex geometry

From solitons to many-body systems

From WZW models to Modular Functors

Frontiers of Reality in Schubert Calculus

Fubini's Theorem in codimension two

Fuchsian equations of type DN

Fujiki relation on symplectic varieties

Fujita's Conjecture and Frobenius amplitude

Fujita's very ampleness conjecture for singular toric varieties

Fukaya category and Fourier transform

Full exceptional collections on the Lagrangian Grassmannians LG(4,8) and LG(5,10)

Full faithfulness for overconvergent F-isocrystals

Full faithfulness without Frobenius structure and partially overcoherent isocrystals

Full twists factorization formula for double number of strings