I am a Mathematics PhD student at the Graduate Center of the City University of New York.

I previously studied at the University of Oxford, where I graduated with a BA in Mathematics and a MSc in Mathematics and Computer Science.

I worked on my MSc dissertation Transfinite game values in infinite games over the summer 2021, under the supervision of Prof. Joel David Hamkins, for which I was awarded a Distinction.

Jointly with my supervisor, we expanded on this work and published the results achieved for Infinite Draughts and for Infinite Hex, to appear in Integers.

dleonessi at gc.cuny.edu

Infinite Hex is a draw

In this second joint paper with Prof. Joel David Hamkins, we expand the results achieved for infinite Hex in chapter 2 of my MSc dissertation, and present new open questions. You can read this article at arXiv:2201.06475. Abstract We introduce the game of infinite Hex, extending the familiar finite game to natural play on the infinite hexagonal lattice. Whereas the finite game is a win for the first player, we prove in contrast that infinite Hex is a draw—both players have drawing strategies. Meanwhile, the transfinite game-value phenomenon, now abundantly exhibited in infinite chess and infinite draughts, regrettably does not…

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Transfinite game values in infinite draughts

In this joint paper with Prof. Joel David Hamkins, we prove that every countable ordinal is realised as the game value of a position in infinite draughts, simplifying further the constructions in chapter 3 of my MSc dissertation. Joel David Hamkins and Davide Leonessi. “Transfinite game values in infinite draughts” Integers 22 (2022), #G5. You can also read this article at arXiv:2111.02053. Abstract Infinite draughts, or checkers, is played just like the finite game, but on an infinite checkerboard extending without bound in all four directions. We prove that every countable ordinal arises as the game value of a position…

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Transfinite game values in infinite games

Over the summer 2021 I completed my master’s dissertation under the supervision of Prof. Joel David Hamkins, achieving a Distinction in my MSc in Mathematics and Foundations of Computer Science at Oxford.This work is presented and expanded in the papers co-authored with my supervisor on infinite Draughts and infinite Hex. You can read my dissertation here, and at arXiv:2111.01630. Abstract The object of this study are countably infinite games with perfect information that allow players to choose among arbitrarily many moves in a turn; in particular, we focus on the generalisations of the finite board games of Hex and Draughts.…

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