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Explore the sophisticated mathematical relationship between refined Donaldson-Thomas invariants and Milnor fibres in this 51-minute conference lecture by Felipe Espreafico from Sorbonne Université. Delve into the construction of a quadratic, A¹-version of Donaldson-Thomas invariants derived from motivic refinements originally introduced by Kontsevich-Soibelman. Learn how to apply ideas from Behrend, Bryan and Szendroi to generate predictions for these invariants through concrete examples, particularly focusing on the computation of DT invariants of A³. Discover how these mathematical constructions recover invariants previously considered in physics by Krefl and Walcher when working over real numbers. Examine refinements of the Euler characteristic of Milnor fibres for critical loci and investigate the properties of Behrend functions throughout the construction process. Connect this work to broader mathematical literature including contributions from Levine, Denef and Loser, Azouri, Pepin-Lehaulleur, Srinivas, Comte and Fichou. Consider open questions and future research directions in this active area of singularity theory, including insights from joint work with Johannes Walcher and ongoing collaboration with Ran Azouri. This presentation was delivered at the "New Developments in Singularity Theory" conference, a joint IMSA & ICMS event supported by the Simons Foundation, National Science Foundation and the University of Miami.
