分野別セミナー

I will talk about the mixed Hodge structures on the cohomology of locally symmetric varieties.
In the middle degree, I relate the weight filtration to the Siegel operators for certain modular forms.
This has application to a classical problem on the Siegel operators.
In the general degrees, I construct a spectral sequence which converges to the edge components in the Hodge
triangle, and whose E1 page is expressed by some simple geometric invariants associated to the cusps.
This already degenerates at E1 in a certain range.
MHS approach also has application to the restriction map to the Borel-Serre boundary.