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Malchiodi received his Ph.D. in mathematics from the International School for Advanced Studies in 2000 under the supervision of Antonio Ambrosetti.[citation needed] He is a professor of mathematics at the Scuola Normale Superiore at Pisa. He was previously professor of mathematics at the International School for Advanced Studies and at the University of Warwick.[citation needed] Malchiodi has developed topological and analytical methods allowing to deal with a number of questions in geometric analysis, such as the Yamabe problem, the scalar curvature problem, problems coming from fourth order conformal geometry and concentration for singular perturbation problems. In particular, he proved some new intricate forms of improved Moser-Trudinger inequalities allowing to prove existence results for singular Liouville equations. Similar types of inequalities allow to prove existence results for Toda systems on surfaces. Malchiodi has been visiting professor in many universities and institutions, amongst which are Stanford University, The Institute for Advanced Study at Princeton, and ETH at Zurich.[citation needed] He belongs to the editorial board of several mathematical journals and is one of the managing editors of the journal Calculus of Variations & PDE
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Advances in Mathematics (2024): 109548
Annals of PDEno. 1 (2024): 1-86
arXiv (Cornell University) (2023)
REVISTA MATEMATICA IBEROAMERICANAno. 6 (2023): 2017-2066
arXiv (Cornell University) (2023)
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