3 papers
math.AG2026
Lagrangian correspondences of nonabelian Hodge type and shifted twistor structures
Jacob Kryczka, Yuuji Tanaka, Shing-Tung Yau
Classical nonabelian Hodge theory identifies Dolbeault and de Rham moduli spaces by providing a real-analytic isomorphism. In this paper, motivated by the Kapustin--Witten theory,…
math.AG2025
The Blowup Formula for the Instanton Part of Vafa-Witten Invariants on Projective Surfaces
Nikolas Kuhn, Oliver Leigh, Yuuji Tanaka
We prove a blow-up formula for the generating series of virtual -genera for moduli spaces of sheaves on projective surfaces, which is related to a conjectured formula for top…
quant-ph2025
A Polynomial Time Quantum Algorithm for Exponentially Large Scale Nonlinear Differential Equations via Hamiltonian Simulation
Yu Tanaka, Keisuke Fujii
Quantum computers have the potential to efficiently solve a system of nonlinear ordinary differential equations (ODEs), which play a crucial role in various industries and scientif…