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Nathan stares back at his teacher. She's handing out the usual frayed school-copy books. A bland cover done in black and white: a man's profile in black, a woman's in white. Othello. Nathan didn't know it was a book: he only remembers it as a board game. He used to play it in primary school with his best friend, Andrew. You flip the white discs over to reveal the black. The game can change in an instant: white discs can dominate the board but then a careful placement from your opponent means they can all flip to black. They seemed to play it every weekend, Weekend afternoons were spent splayed out on Nathan's bedroom floor, playing game after game: best of three, best of five, champion tournament. Andrew would always win. He was a master of it, turning the tables with ease, transforming the whole board into rows and rows of black discs. Nathan's mother coming in and saying, Why don't you boys go outside? It's such a lovely day. Nathan watching Andrew's wrists flipping disc after disc.

Nathan stares back at his teacher. She's handing out the usual frayed school-copy books. A bland cover done in black and white: a man's profile in black, a woman's in white. Othello. Nathan didn't know it was a book: he only remembers it as a board game. He used to play it in primary school with his best friend, Andrew. You flip the white discs over to reveal the black. The game can change in an instant: white discs can dominate the board but then a careful placement from your opponent means they can all flip to black. They seemed to play it every weekend, Weekend afternoons were spent splayed out on Nathan's bedroom floor, playing game after game: best of three, best of five, champion tournament. Andrew would always win. He was a master of it, turning the tables with ease, transforming the whole board into rows and rows of black discs. Nathan's mother coming in and saying Why don't you boys go outside? It's such a lovely day. Nathan watching Andrew's wrists flipping disc after disc.

Nathan stares back at his teacher. She's handing out the usual frayed school-copy books. A bland cover done in black and white: a man's profile in black, a woman's in white. Othello. Nathan didn't know it was a book: he only remembers it as a board game. He used to play it in primary school with his best friend, Andrew. You flip the white discs over to reveal the black. The game can change in an instant: white discs can dominate the board but then a careful placement from your opponent means they can all flip to black. They seemed to play it every weekend, Weekend afternoons were spent splayed out on Nathan's bedroom floor, playing game after game: best of three, best of five, champion tournament. Andrew would always win. He was a master of it, turning the tables with ease, transforming the whole board into rows and rows of black discs. Nathan's mother coming in and saying Why don't you boys go outside? It's such a lovely day. Nathan watching Andrew's wrists flipping disc after disc.

Nathan stares back at his teacher. She's handing out the usual frayed school-copy books. A bland cover done in black and white: a man's profile in black, a woman's in white. Othello. Nathan didn't know it was a book: he only remembers it as a board game. He used to play it in primary school with his best friend, Andrew. You flip the white discs over to reveal the black. The game can change in an instant: white discs can dominate the board but then a careful placement from your opponent means they can all flip to black. They seemed to play it every weekend, Weekend afternoons were spent splayed out on Nathan's bedroom floor, playing game after game: best of three, best of five, champion tournament. Andrew would always win. He was a master of it, turning the tables with ease, transforming the whole board into rows and rows of black discs. Nathan's mother coming in and saying, Why don't you boys go outside? It's such a lovely day. Nathan watching Andrew's wrists flipping disc after disc.

You have ten seconds. The car rolls over for the last time; the birds have flown away. You only have time to turn to your lover and rasp: I'm sorry, I wish, I -. You have four minutes. You gather with your family in the living room. The sirens are deafening. You snatch the curtains shut, you shove the coffee table against the windows. Everyone is blanched with fear. Silent, clenched. You hide under cushions. You begin to mutter compulsively: everything will be all right, keep calm everybody, we're all together, we... The muttering subsides. The sirens cut out. You listen to the dog outside, howling. As you wait for the blinding flash, the flesh-tearing heat, you say: I wish, I'm sorry, I -...

For every smooth Jordan curve γ and cyclic quadrilateral Q in the Euclidean plane, we show that there exists an orientation-preserving similarity taking the vertices of Q to γ. The proof relies on the theorem of Polterovich and Viterbo that an embedded Lagrangian torus in C2 has minimum Maslov number 2.

We prove that for every smooth Jordan curve \\(\\gamma \\subset \\mathbb{C}\\) and for every set \\(Q \\subset \\mathbb{C}\\) of six concyclic points, there exists a non-constant quadratic polynomial \\(p \\in \\mathbb{C}[z]\\) such that \\(p(Q) \\subset \\gamma\\). The proof relies on a theorem of Fukaya and Irie. We also prove that if \\(Q\\) is the union of the vertex sets of two concyclic regular \\(n\\)-gons, there exists a non-constant polynomial \\(p \\in \\mathbb{C}[z]\\) of degree at most \\(n-1\\) such that \\(p(Q) \\subset \\gamma\\). The proof is based on a computation in Floer homology. These results support a conjecture about which point sets \\(Q \\subset \\mathbb{C}\\) admit a polynomial inscription of a given degree into every smooth Jordan curve \\(\\gamma\\).

We construct a version of Lagrangian Floer homology whose chain complex is generated by the inscriptions of a rectangle into a real analytic Jordan curve. By using its associated spectral invariants, we establish that a rectifiable Jordan curve admits inscriptions of a whole interval of rectangles. In particular, it inscribes a square if the area it encloses is more than half that of a circle of equal diameter.

We show that there always exists an inscribed square in a Jordan curve given as the union of two graphs of functions of Lipschitz constant less than \\(1 + \\sqrt{2}\\). We are motivated by Tao's result that there exists such a square in the case of Lipschitz constant less than \\(1\\). In the case of Lipschitz constant \\(1\\), we show that the Jordan curve inscribes rectangles of every similarity class. Our approach involves analysing the change in the spectral invariants of the Jordan Floer homology under perturbations of the Jordan curve.

For every smooth Jordan curve \\(\\gamma\\) and cyclic quadrilateral \\(Q\\) in the Euclidean plane, we show that there exists an orientation-preserving similarity taking the vertices of \\(Q\\) to \\(\\gamma\\). The proof relies on the theorem of Polterovich and Viterbo that an embedded Lagrangian torus in \\(\\mathbb{C}^2\\) has minimum Maslov number 2.