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We prove a generalisation of Elkies' theorem to nonunimodular definite forms (and lattices). Combined with inequalities of Froyshov and of Ozsvath and Szabo, this gives a simple test of whether a rational homology 3-sphere may bound a definite four-manifold. As an example we show that small positive surgeries on torus …
Proof of Donaldson's theorem using Seiberg-Witten equations for multiple spinors.
We conjecture two generalisations of Elkies' theorem on unimodular quadratic forms to non-unimodular forms. We give some evidence for these conjectures including a result for determinant 3. These conjectures, when combined with results of Froyshov and of Ozsvath and Szabo, would give a simple test of whether a rational…
Lattices embeddability determined by correction terms.
Machine learning predicts Shafarevich-Tate group orders of elliptic curves.
ACE algorithm detects anomalies faster and uses less memory.