Modularity of Calabi-Yau Kinds

Speaker(s) Noriko Yui Queen’s University, Canada
Date 20 July 2022 – 16:00 to 17:00
Venue INI Seminar Space 1
Session Title Modularity of Calabi-Yau Kinds
Chair James Lewis
Function [KA2W03] Mathematical physics: algebraic cycles, strings and amplitudes
Summary
Enable X be a Calabi-Yau assortment of dimension d. We will confine ourselves to Calabi-Yau
versions of tiny dimensions, e.g., d ≤ 3. Dimension one Calabi–Yaus are elliptic curves, people of dimension
two are K3 surfaces, and dimension a few types are Calabi-Yau threefolds. Geometry and physics are equally
very a lot in proof in Calabi-Yau types more than the industry of complex numbers.

These days I will target on Calabi-Yau versions defined over the discipline Q of rational quantities (or variety fields),
and will explore the modularity/automorphy of Calabi-Yau varieties in the framework of the Langlands
Philosophy. In the last 30 years or so, we have witnessed incredible innovations on the modularity
queries for Calabi-Yau versions. iMost of these outcomes relaxation on the modularity of the two-dimensional
Galois representations involved to them.

In the first part of the lecture, I will current these fascinating modularity success for Calabi–Yau versions
around Q of dimension ≤ 3, as perfectly as conjectures.

Then I will focus on the current exploration in progess on the rank 4 bodyweight 3 Calabi–Yau motives in excess of Q
and their Siegel modularity.

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