ESyMath

Why physicists love kagome lattices

Kagome lattices do not just make nice pictures for TRR proposals, they also constitute a paradigmatic example of frustrated quantum magnetism. In my presentation I will qualitatively explain what the fascinating magnetic properties are by contrasting them with the usual (boring) properties of bipartite antiferromagnets.

Explained with as much mathematics as I can.

12:00h - TRR Multimedia Room, UHG M4-122/126

tba

10:30h - Lecture Hall H5
A joint RCM² Colloquium

The cost of cyclic permutations

16:15h - Lecture Hall H10
A joint RCM² Colloquium

Inplace rotation of an array involves nothing but moving data around in computer memory. As modern computer architectures involve several layers of caching, it is a surprisingly non-trivial problem. We describe a competitively fast algorithm (as indicated by measurements) and asymptotically count the number of data moves in the best, worst, and average case. It turns out that this task is equivalent to determining the expected sum of remainders encountered in a run of the Euclidean algorithm, which in turn can be estimated using tools from analytic number theory.
I shall motivate, describe and discuss this algorithm in detail an also compare it to several other reasonable choices.
(Joint work with Valentin Blomer)