25 citations · 79 across the 20 of their papers we have counts for
20 papers
The U(1)-topological elliptic genus is surjective
Tilman Bauer, Mayuko Yamashita
We show that the topological elliptic genus from the cobordism ring of SU-manifolds to topological Jacobi forms lifts to connective topological Jacobi forms, and that this lift is…
Genuine -equivariant
Ying-Hsuan Lin, Akira Tominaga, Mayuko Yamashita
We determine the -module structures of the genuine -equivariant with -gradings and of the -equivariant . More…
Topological Elliptic Genera I -- The mathematical foundation
Ying-Hsuan Lin, Mayuko Yamashita
We construct {\it Topological Elliptic Genera}, homotopy-theoretic refinements of the elliptic genera for -manifolds and variants including the Witten-Landweber-Ochanine genus.…
On the 576-fold periodicity of the spectrum SQFT: The proof of the lower bound via the Anderson duality pairing
Theo Johnson-Freyd, Mayuko Yamashita
We are aimed at giving a differential geometric, and accordingly physical, explanation of the 576-periodicity of TMF. In this paper, we settle the problem of giving the lower bound…
Anderson duality of topological modular forms and its differential-geometric manifestations
Yuji Tachikawa, Mayuko Yamashita
We construct and study a morphism of spectra implementing the Anderson duality of topological modular forms (). Its differential version will then be introduced, allo…
Invertible QFTs and differential Anderson duals
Mayuko Yamashita
This is the proceeding of a talk given at Stringmath 2022. We introduce a Cheeger-Simons type model for the differential extension of Anderson dual to generalized homology theory w…
Remarks on mod-2 elliptic genus
Yuji Tachikawa, Mayuko Yamashita, Kazuya Yonekura
For physicists: For supersymmetric quantum mechanics, there are cases when a mod-2 Witten index can be defined, even when a more ordinary -valued Witten index vanishes.…
A physicist-friendly reformulation of the mod-two Atiyah-Patodi-Singer index
Hidenori Fukaya, Mikio Furuta, Yoshiyuki Matsuki +4
Gauge anomaly in 4-dimensions can be viewed as a current inflow into an extra-dimension, where the total phase of the fermion partition function is given in a gauge invariant way b…
Differential -theory via gradations and mass terms
Kiyonori Gomi, Mayuko Yamashita
We construct models of the differential -theory and the twisted differential -theory, by refining Karoubi's -theory [Kar78] in terms of gradations on Clifford modules.…
Differential models for the Anderson dual to bordism theories and invertible QFT's, II
Mayuko Yamashita
This is the second part of the work on differential models of the Anderson duals to the stable tangential -bordism theories , motivated by classifications of invertible QF…
Topological modular forms and the absence of all heterotic global anomalies
Yuji Tachikawa, Mayuko Yamashita
We reformulate the question of the absence of global anomalies of heterotic string theory mathematically in terms of a certain natural transformation $\mathrm{TMF}^\bullet\to (I_{\…
Differential models for the Anderson dual to bordism theories and invertible QFT's, I
Mayuko Yamashita, Kazuya Yonekura
In this paper, we construct new models for the Anderson duals to the stable tangential -bordism theories and their differential extensions. The cohomology theory $(IΩ…
Mod-two APS index and domain-wall fermion
Hidenori Fukaya, Mikio Furuta, Yoshiyuki Matsuki +4
We reformulate the mod-two Atiyah-Patodi-Singer (APS) index in a physicist-friendly way using the domain-wall fermion. Our new formulation is given on a closed manifold, which is e…
A lattice version of the Atiyah-Singer index theorem
Mayuko Yamashita
We formulate and prove a lattice version of the Atiyah-Singer index theorem. The main theorem gives a -theoretic formula for an index-type invariant of operators on lattice appr…
A new construction of strict deformation quantization for Lagrangian fiber bundles
Mayuko Yamashita
We give a new construction of strict deformation quantization of symplectic manifolds equipped with a proper Lagrangian fiber bundle structure, whose representation spaces are the…
Spectral convergence in geometric quantization --- the case of toric symplectic manifolds
Kota Hattori, Mayuko Yamashita
In this paper, we show the spectral convergence result of -Laplacians when is a compact toric symplectic manifold equipped with the natural prequantum…
A physicist-friendly reformulation of the Atiyah-Patodi-Singer index and its mathematical justification
Hidenori Fukaya, Mikio Furuta, Shinichiroh Matsuo +3
The Atiyah-Patodi-Singer index theorem describes the bulk-edge correspondence of symmetry protected topological insulators. The mathematical setup for this theorem is, however, not…
Spectral convergence in geometric quantization -- the case of non-singular Langrangian fibrations
Kota Hattori, Mayuko Yamashita
We develop a new approach to geometric quantization using the theory of convergence of metric measure spaces. Given a family of Kähler polarizations converging to a non-singular re…
The Atiyah-Patodi-Singer index and domain-wall fermion Dirac operators
Hidenori Fukaya, Mikio Furuta, Shinichiroh Matsuo +3
We introduce a mathematician-friendly formulation of the physicist-friendly derivation of the Atiyah-Patodi-Singer index of our previous paper. Our viewpoint sheds some new light o…
A topological approach to indices of geometric operators on manifolds with fibered boundaries
Mayuko Yamashita
In this paper, we investigate topological aspects of indices of twisted geometric operators on manifolds equipped with fibered boundaries. We define -groups relative to the push…