Mathematics

The idea of considering the motive of an algebraic varietygoes back to Grothendieck, who realized that all cohomologicalinvariants associated to a variety via different cohomology theoriesshould be connected by a "common pattern", of which they are justdifferent realizations. Since then, there has been a lot of study onthis subject, but it is far from being fully understood (some parts arestill conjectural).In this seminar, I will explain the philosophy underlying the theory ofmotives. I will discuss both pure and mixed motives, focusing mostly onthe first ones (for simplicity). If time allows, I will also talk aboutmotivic Galois groups.