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Item Mathematical Musings on the External Anatomy of the Novel Corona Virus Part 1: The Overall Shape of the n-CoV(Springer, 2022) Sarkar, Jyotirmoy; Rashid, Mamunur; Mathematical Sciences, School of ScienceWhat is the shape of the novel coronavirus which has turned our world upside down? Even though under a microscope it looks dull, unattractive, and even disgusting, creative artists have attributed to it bright colors, made it look pretty, and depicted it as a thing of beauty. What can a mathematician contribute to this effort? We take a purist’s point of view by imposing on it a quasi-symmetry and then deriving some consequences. In an idealistic world, far removed from reality but still obeying the rules of mathematics, anyone can enjoy this ethereal beauty of the mind’s creation, beckoning others to join in the pleasure. Our musings are split into four parts. We fondly hope that while readers await the future parts to appear, they will indulge in their own musings, tell others about them, and propagate the good virus of mathematical thinking.Item Mathematical Musings on the External Anatomy of the Novel Corona Virus Part 4: Models of n-Cov(Springer, 2022) Sarkar, Jyotirmoy; Rashid, Mamunur; Mathematical Sciences, School of ScienceWhat is the shape of the novel coronavirus (n-CoV) which has turned our world upside down? Even though under a microscope, it looks dull, unattractive, and even disgusting, creative artists have attributed to it bright colors, made it look pretty, and depicted it as a thing of beauty. What can a mathematician contribute to this effort? We take a purist’s point of view by imposing on it a quasi-symmetry and then deriving some consequences. In an idealistic world, far removed from reality but still constrained by the rules of mathematics, anyone can enjoy this ethereal beauty of the mind’s creation, beckoning others to join in the pleasure. Our musings end with this Part 4. We fondly hope readers have benefited from our suggestion that they indulge in their own musings, tell others about them, and propagate the good virus of mathematical thinking.Item Mathematical Musings on the External Anatomy of the Novel Corona Virus, Part 3: Spherical Triangles(Springer Nature, 2022) Sarkar, Jyotirmoy; Rashid, Mamunur; Mathematical Sciences, School of ScienceWhat is the shape of the novel coronavirus (n-CoV) which has turned our world upside down? Even though under a microscope, it looks dull, unattractive, and even disgusting, creative artists have attributed to it bright colors, made it look pretty, and depicted it as a thing of beauty. What can a mathematician contribute to this effort? We take a purist’s point of view by imposing on it a quasi-symmetry and then deriving some consequences. In an idealistic world, far removed from reality but still constrained by the rules of mathematics, anyone can enjoy this ethereal beauty of the mind’s creation, beckoning others to join in the pleasure. Our musings are split into four parts. We fondly hope while readers wait for the future parts to appear, they will indulge in their own musings, tell others about them, and propagate the good virus of mathematical thinking.Item Mathematical Musings on the External Anatomy of the Novel Coronavirus Part 2: Chasing After Quasi-Symmetry(Springer, 2022) Sarkar, Jyotirmoy; Rashid, Mamunur; Mathematical Sciences, School of ScienceWhat is the shape of the novel Coronavirus which has turned our world upside down? Even though it looks dull, unattractive, and even disgusting under a microscope, creative artists have attributed to it bright colors, made it look pretty, and depicted it as a thing of beauty. What can a mathematician contribute to this effort? We take a purist’s point of view by imposing on it a quasi-symmetry and then deriving some consequences. In an idealistic world, far removed from reality but still constrained by the rules of mathematics, anyone can enjoy this ethereal beauty of the mind’s creation, beckoning others to join in the pleasure. Our musings are split into four parts. We fondly hope while readers wait for the future parts to appear, they will indulge in their own musings, tell others about them, and propagate the good virus of mathematical thinking.Item On the Gaudin and XXX models associated to Lie superalgebras(2020-08) Huang, Chenliang; Mukhin, Evgeny; Bleher, Pavel; Roeder, Roland; Tarasov, VitalyWe describe a reproduction procedure which, given a solution of the gl(m|n) Gaudin Bethe ansatz equation associated to a tensor product of polynomial modules, produces a family P of other solutions called the population. To a population we associate a rational pseudodifferential operator R and a superspace W of rational functions. We show that if at least one module is typical then the population P is canonically identified with the set of minimal factorizations of R and with the space of full superflags in W. We conjecture that the singular eigenvectors (up to rescaling) of all gl(m|n) Gaudin Hamiltonians are in a bijective correspondence with certain superspaces of rational functions. We establish a duality of the non-periodic Gaudin model associated with superalgebra gl(m|n) and the non-periodic Gaudin model associated with algebra gl(k). The Hamiltonians of the Gaudin models are given by expansions of a Berezinian of an (m+n) by (m+n) matrix in the case of gl(m|n) and of a column determinant of a k by k matrix in the case of gl(k). We obtain our results by proving Capelli type identities for both cases and comparing the results. We study solutions of the Bethe ansatz equations of the non-homogeneous periodic XXX model associated to super Yangian Y(gl(m|n)). To a solution we associate a rational difference operator D and a superspace of rational functions W. We show that the set of complete factorizations of D is in canonical bijection with the variety of superflags in W and that each generic superflag defines a solution of the Bethe ansatz equation. We also give the analogous statements for the quasi-periodic supersymmetric spin chains.