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"content": "<p>New preprint (with coauthors Taylor Dupuy, Colin Ingalls, and Adam Logan) is now out!</p><p>Maybe you've heard about the hyperbolic plane - a very weird example of non-Euclidean geometry where parallel lines diverge away from each other and where the sum of the angles of a triangle are less than 180 degrees. The attached picture is M.C. Escher's "Circle Limit III" depicting the hyperbolic plane.</p><p>The hyperbolic plane (in the form of the upper half-plane) is also home to important objects in number theory such as modular forms.</p><p>Now there are also higher-dimensional hyperbolic spaces - for instance if you consider space and time as one entity (Minkowski spacetime) it is a 4D hyperbolic space.</p><p>Can we also have a theory of modular forms in such higher-dimensional hyperbolic spaces? The answer is yes. In 3D hyperbolic space for instance we have "Bianchi modular forms", very notable for not being directly accessible by algebraic geometry! These were studied by mathematicians such as John Cremona and many others.</p><p>In our work we go even higher and lay down foundations for studying certain (I would say number-theoretic) aspects of higher-dimensional hyperbolic spaces such as modular forms, using the theory of Clifford algebras and spin. Please check it out if you are interested!</p><p><a href=\"https://arxiv.org/abs/2407.19122\" target=\"_blank\" rel=\"nofollow noopener noreferrer\" translate=\"no\"><span class=\"invisible\">https://</span><span class=\"\">arxiv.org/abs/2407.19122</span><span class=\"invisible\"></span></a></p><p><a href=\"https://mathstodon.xyz/tags/Math\" class=\"mention hashtag\" rel=\"tag\">#<span>Math</span></a> <a href=\"https://mathstodon.xyz/tags/Mathematics\" class=\"mention hashtag\" rel=\"tag\">#<span>Mathematics</span></a> <a href=\"https://mathstodon.xyz/tags/NumberTheory\" class=\"mention hashtag\" rel=\"tag\">#<span>NumberTheory</span></a> <a href=\"https://mathstodon.xyz/tags/Geometry\" class=\"mention hashtag\" rel=\"tag\">#<span>Geometry</span></a></p>",
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