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DOE OSTI · 2580027

Learning Homogenization for Elliptic Operators

Bhattacharya, Kaushik·Kovachki, Nikola (ORCID:0000000236502972)·Rajan, Aakila·Stuart, Andrew·Trautner, Margaret (ORCID:0000000199378393)
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Bhattacharya, Kaushik, Kovachki, Nikola (ORCID:0000000236502972), Rajan, Aakila, Stuart, Andrew, Trautner, Margaret (ORCID:0000000199378393). 2024-08-02. Learning Homogenization for Elliptic Operators. https://doi.org/10.1137/23m1585015

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Global Magni4icence, or: 4G Networks

The global magnificent four theory is the homological version of a maximally supersymmetric $(8+1)$-dimensional gauge theory on a Calabi-Yau fourfold fibered over a circle. In the case of a toric fourfold we conjecture the formula for its twisted Witten index. String-theoretically we count the BPS states of a system of $D0$-$D2$-$D4$-$D6$-$D8$-branes on the Calabi-Yau fourfold in the presence of a large Neveu-Schwarz $B$-field. Mathematically, we develop the equivariant $K$-theoretic DT4 theory, by constructing the four-valent vertex with generic plane partition asymptotics. Physically, the vertex is a supersymmetric localization of a non-commutative gauge theory in $8+1$ dimensions.

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