University of Cambridge > > Isaac Newton Institute Seminar Series > Modularity of Calabi-Yau Varieties

Modularity of Calabi-Yau Varieties

Add to your list(s) Download to your calendar using vCal

If you have a question about this talk, please contact nobody.

KA2W03 - Mathematical physics: algebraic cycles, strings and amplitudes

Let X be a Calabi-Yau variety of dimension d. We will confine ourselves to Calabi-Yauvarieties of small dimensions, e.g., d ≤ 3. Dimension one Calabi–Yaus are elliptic curves, those of dimensiontwo are K3 surfaces, and dimension three ones are Calabi-Yau threefolds. Geometry and physics are bothvery much in evidence in Calabi-Yau varieties over the field of complex numbers. Today I will focus on Calabi-Yau varieties defined over the field Q of rational numbers (or number fields),and will discuss the modularity/automorphy of Calabi-Yau varieties in the framework of the LanglandsPhilosophy. In the last thirty years or so, we have witnessed tremendous advances on the modularityquestions for Calabi-Yau varieties. iMost of these results rest on the modularity of the two-dimensionalGalois representations associated to them. In the first part of the lecture, I will present these fascinating modularity results for Calabi–Yau varietiesover Q of dimension ≤ 3, as well as conjectures. Then I will discuss the current research in progess on the rank 4 weight 3 Calabi–Yau motives over Qand their Siegel modularity.

This talk is part of the Isaac Newton Institute Seminar Series series.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.


© 2006-2024, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity