Hodge theory just beyond geometry
speaker: Geordie Williamson (University of Sidney)abstract: Classical Hodge theory is a crucial part of a parcel of remarkable statements (Hodge decomposition, the weak and hard Lefschetz theorem, the Hodge-Riemann relations) concerning the cohomology of projective complex algebraic varieties (or more generally Kähler manifolds). Over the last decades, it has been discovered that there are several settings where structures similar to the cohomology groups of classical Hodge theory show up, but where the underlying variety is "missing". Typically, the existence of Hodge like structures on such spaces provides deep results in combinatorics. Examples include the bounds on the face numbers of polytopes, and the positivity of Kazhdan-Lusztig polynomials coming from the theory of Soergel modules. Another example (where my knowledge is scarce) occurs in the theory of matroids. I will try to introduce this web of ideas. If I get my act together, I should be able to highlight the general principles present in the known examples.
timetable:
Mon 19 Sep, 14:00 - 15:00, Aula Dini
Tue 20 Sep, 11:00 - 12:00, Aula Dini
Thu 22 Sep, 9:30 - 10:30, Aula Dini
Fri 23 Sep, 11:00 - 12:00, Aula Dini
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