# neverendingbooks

• ## Witt and his Niemeier lattices

Sunday, January 28th 1940, Hamburg Ernst Witt wants to get two papers out of his system because he knows he’ll have to enter the Wehrmacht in February. The first one, “Spiegelungsgruppen und Aufzählung halbeinfacher Liescher Ringe”, contains his own treatment of the root systems of semisimple Lie algebras and their reflexion groups, following up on […]

• ## the bongcloud attack

In this neverending pandemic there’s a shortage of stories putting a lasting smile on my face. Here’s one. If you are at all interested in chess, you’ll know by now that some days ago IGMs (that is, international grandmasters for the rest of you) Magnus Carlsen and Hikaru Nakamura opened an official game with a…

• ## de Bruijn’s pentagrids (2)

Last time we’ve seen that de Bruijn’s pentagrids determined the vertices of Penrose’s P3-aperiodic tilings. These vertices can also be obtained by projecting a window of the standard hypercubic lattice $\mathbb{Z}^5$ by the cut-and-project-method. We’ll bring in representation theory by forcing this projection to be compatible with a $D_5$-subgroup of the symmetries of $\mathbb{Z}^5$, which…

• ## Kasha-eating dragons

This semester I’m teaching a first course in representation theory. On campus, IRL! It’s a bit strange, using a big lecture room for a handful of students, everyone wearing masks, keeping distances, etc. So far, this is their only course on campus, so it has primarily a social function. The breaks in between are infinitely…

• ## Teapot supremacy

No, this is not another timely post about the British Royal family. It’s about Richard Borcherds’ “teapot test” for quantum computers. A lot of money is being thrown at the quantum computing hype, causing people to leave academia for quantum computing firms. A recent example (hitting the press even in Belgium) being the move of…

• ## de Bruijn’s pentagrids

In a Rhombic tiling (aka a Penrose P3 tiling) we can identify five ribbons. Opposite sides of a rhomb are parallel. We may form a ribbon by attaching rhombs along opposite sides. There are five directions taken by sides, so there are five families of ribbons that do not intersect, determined by the side directions.…

• ## this one’s for M.

and for everyone else feeling a bit lost in these tiring times. Photo credit: @itoldmythe

• ## Penrose’s aperiodic tilings

Around 1975 Sir Roger Penrose discovered his aperiodic P2 tilings of the plane, using only two puzzle pieces: Kites (K) and Darts (D) The inner angles of these pieces are all multiples of $36^o = \tfrac{180^o}{5}$, the short edges have length $1$, and the long edges have length $\tau = \tfrac{1+\sqrt{5}}{2}$, the golden ratio. These…

• ## Lockdown reading : Penumbra

In this series I’ll mention some books I found entertaining, stimulating or comforting during these Corona times. Read them at your own risk. It’s difficult to admit, but Amazon’s blurb lured me into reading Mr. Penumbra’s 24-Hour Bookstore by Robin Sloan: “With irresistible brio and dazzling intelligence, Robin Sloan has crafted a literary adventure story…

• ## The strange logic of subways

“A subway is just a hole in the ground, and that hole is a maze.” “The map is the last vestige of the old system. If you can’t read the map, you can’t use the subway.” Eddie Jabbour in Can he get there from here? (NYT) Sometimes, lines between adjacent stations can be uni-directional (as…