The Aztec diamond, under the uniform measure on domino tilings, is one of the classic examples of an exactly solvable model in probability and statistical mechanics. Its rich geometric features—such a...
This lecture will provide some background on the geometry of 8-dimensional Riemannian
manifolds with holonomy Spin(7).
The talk is part of a series of lectures on the geometry of Riemannian manifolds...
By the seminal work of Joyce on the construction of compact exceptional holonomy metrics, it is known that exceptional holonomy orbifolds naturally arise on the boundary of the corresponding moduli sp...
For a real quadratic field K and positive integer r, we prove
an asymptotic formula for the number of rational integers of bounded
absolute value that can be written as a sum of r units of the ring of...
The known results about the stable irrationality of very general smooth Fano complete intersections $X^n\subset\mathbb P^{n+c}$ of dimension $n\geq 3$ and fixed type $(d_1,\ldots, d_c)$ pose the nat...
