| Résume | Abstract : One of the holy grails of symplectic geometry is understanding and classifying Lagrangians L in a symplectic manifold X. Mirror symmetry establishes a correspondence between these Lagrangians in X and algebraic cycles in a mirror algebraic variety Y. In this talk, I will explore what landmark results about algebraic cycles can teach us about Lagrangians. Although I will mention a correspondence between Chow groups and (cylindrical Lagrangian) cobordism groups, my focus will be to understand the Lagrangian mirror to Griffiths groups. For this, I will introduce an equivalence relation on Lagrangians “mirror” to algebraic equivalence of cycles, called algebraic (Lagrangian) cobordism. I will explain how to construct a Lagrangian version of the Ceresa cycle and prove a mirror to Ceresa’s Theoem that the Ceresa cycle is non-torsion in the Griffiths group. I will mention what other results about Griffiths groups - such as those due to Clemens, Bardelli, Voevodsky/Voisin, etc – could tell us about Lagrangians. No background in mirror symmetry or symplectic geometry will be assumed.
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