Topological string theory derived from string geometry for non-perturbative effects.
problem Deriving non-perturbative effects in string theory.
method Formulating topological string geometry theory and deriving the partition function from fluctuations around a classical solution.
result Perturbative partition function of topological string theory derived.
Introduces a new geometric framework for non-perturbative BV-theory.
problem Non-perturbative generalization of BV-theory in infinite-dimensional spaces.
method Derived differential geometry and homotopical algebraic geometry.
result Concrete model of derived smooth stacks for encoding non-perturbative BV-theory.
String geometry theory uniquely determines classical action with T-symmetry.
problem Non-renormalizability and loop corrections in string theory.
method Distinguishes effects of β and ħ parameters, proving no loop corrections.
result No loop corrections in string geometry theory, avoiding non-renormalizability.
We show that the four derivative terms in the effective action of three-dimensional N=8 Yang-Mills theory are determined by supersymmetry. These terms receive both perturbative and non-perturbative corrections. Using our technique for constraining the effective action, we are able to determine the exact form of the eig…
We propose a conjecture to compute the all-order asymptotic expansion of the colored Jones polynomial of the complement of a hyperbolic knot, J_N(q = exp(2u/N)) when N goes to infinity. Our conjecture claims that the asymptotic expansion of the colored Jones polynomial is a the formal wave function of an integrable sys…
Formally equates two quantization methods and constructs non-commutative algebras.
problem Equivalence of deformation and geometric quantization methods.
method Symplectic reduction and Lie 2-groupoid quantization.
result Recovery of strict deformation quantizations and non-associative products.
New non-perturbative counterexamples to Min-Oo's Conjecture are created.
problem Min-Oo's Conjecture on positive curvature and mass.
method Quantitative Gromov-Lawson Schoen-Yau surgery.
result Construction of new non-perturbative counterexamples with more complex topology.
Study of harmonic maps and instantons in 4D.
problem Constructing non-spin, simply-connected Ricci-flat 4-manifolds.
method Non-perturbative approach ruling out conical singularities from axisymmetric harmonic maps.
result Systematic counterexamples to Riemannian black hole uniqueness conjecture.
We use the twistorial construction of D-instantons in Calabi-Yau compactifications of type II string theory to compute an explicit expression for the metric on the hypermultiplet moduli space affected by these non-perturbative corrections. In this way we obtain an exact quaternion-Kahler metric which is a non-trivial d…
This paper analyzes Δa invariants in non-perturbative complex Chern-Simons theory.
problem Analyzing the structure and properties of Δa invariants. method Reviewing foundations and analyzing structure for a subclass of integer homology spheres.
result The Δa invariants are not homology cobordism invariants. New method proves instability of naked singularity and censors it.
problem Proving instability and censoring naked singularity.
method Einstein-scalar field system, hyperbolic short-pulse method, non-perturbative elliptic arguments.
result Tiny anisotropic perturbation leads to anisotropic apparent horizon censoring the naked singularity.
Study non-perturbative quantum geometry of string theories using finite difference equations and resurgence analysis.
problem Non-perturbative quantum geometry of open and closed topological string on the resolved conifold.
method Finite difference equations, resurgence analysis, exact WKB techniques.
result Identify 5d BPS states and relate spectral problems to quantum integrable systems.
Lectures detail field theory dynamics and exact WKB analysis.
problem Understanding quantum field theories with four supercharges.
method Combining WKB analysis with 2D quantum field theories.
result Partition function characterizes non-perturbative dynamics.
We define string geometry: spaces of superstrings including the interactions, their topologies, charts, and metrics. Trajectories in asymptotic processes on a space of strings reproduce the right moduli space of the super Riemann surfaces in a target manifold. Based on the string geometry, we define Einstein-Hilbert ac…
We consider the non-perturbative superpotential for a class of four-dimensional N=1 vacua obtained from M-theory on seven-manifolds with holonomy G2. The class of G2-holonomy manifolds we consider are so-called twisted connected sum (TCS) constructions, which have the topology of a K3-fibration over $S…
Singular fiber resolution does not describe the spontaneous breaking of gauge symmetry in F-theory, as the corresponding branch of the moduli space does not exist in the theory. Accordingly, even non-abelian gauge theories have not been fully understood in global F-theory compactifications. We present a systematic disc…
Mathematical structures link Gromov-Witten to Donaldson-Thomas invariants.
problem Understanding non-perturbative topological string theory.
method Borel summation of Gromov-Witten potential and analysis of Stokes phenomena.
result Stokes phenomena encode Donaldson-Thomas invariants of the resolved conifold.
In this paper we prescribe a fourth order conformal invariant on the standard n−sphere, with n≥5, and study the related fourth order elliptic equation. We first find some existence results in the perturbative case. After some blow up analysis we build a homotopy to pass from the perturbative case to the non-pert…
We identify a large class R of three-dimensional N=2 superconformal field theories. This class includes the effective theories T_M of M5-branes wrapped on 3-manifolds M, discussed in previous work by the authors, and more generally comprises theories that admit a UV description as abelian Chern-Simons-matter theories w…
We consider Chern-Simons theory with complex gauge group and present a complete non-perturbative evaluation of the path integral (the partition function and certain expectation values of Wilson loops) on Seifert fibred 3-Manifolds. We use the method of Abelianisation. In certain cases the path integral can be seen to f…
ContrastiveVI+ models CRISPR screens with noisy guide efficiency.
problem Noisy guide efficiency in CRISPR screens.
method Generative modeling framework that disentangles perturbation-induced from shared variations.
result ContrastiveVI+ better recovers perturbation-induced variations and identifies cells without edits.
Identifies all perturbative vacua in bosonic string theory.
problem Identifying all perturbative vacua in bosonic string theory.
method Completely identified perturbative vacua through string fluctuations.
result Derivation of path-integrals up to any order from fluctuations.
Alternative finance models from physics for non-equilibrium systems.
problem Inequities of classical finance models in physics-based perspective.
method Physics-based insights for non-equilibrium finance models.
result Alternative models for non-equilibrium finance systems.
Derives path-integrals for superstrings on curved backgrounds using string geometry theory.
problem Calculating path-integrals for superstrings on curved backgrounds.
method Derives path-integrals from string geometry theory by considering fluctuations around string backgrounds.
result Derives path-integrals for perturbative superstrings on all string backgrounds.
Study 3d N=1 vacua from M-theory compactification on Spin(7) space.
problem Quantum corrections in 3d N=1 vacua from M-theory compactification.
method Use Higgs bundles to analyze 3d N=1 vacua and track corrections.
result Topological anomalies are robust and calculable in 3d effective field theory.
Novel mathematical approach using resurgent analysis reveals new structures in complex Chern-Simons theory.
problem Curious bijection in vertex algebras and SCFTs.
method Resurgent analysis, numerical algorithms, singularity elimination.
result New structures and patterns in complex Chern-Simons theory on hyperbolic 3-manifolds.
Derives path integrals for perturbative strings on various backgrounds.
problem Calculating path integrals for strings on curved backgrounds.
method Derives path integrals from string geometry theory by considering fluctuations around string backgrounds.
result Derives path integrals of all order perturbative strings on various backgrounds.
Study of rotating gravastars with de Sitter interiors and Kerr exteriors.
problem Understanding the spacetime structure of rotating gravastars and black hole mimickers.
method Exact analytical solutions for Cn metrics with de Sitter interiors and Kerr exteriors. result Existence of Cn metrics with arbitrary differentiability, respecting energy conditions. New method extends knot theory to non-bipartite knots, revealing PDs.
problem Extending knot theory to non-bipartite knots.
method Developed a new positive decomposition (PD) for HOMFLY polynomials of non-bipartite knots.
result PD exists for non-bipartite knots, not just bipartite ones.
Identifies most probable flows for Kunita SDEs in fluid dynamics.
problem Modeling stochastic processes with Eulerian noise and deterministic drifts.
method Equipping the domain with a Riemannian metric from the noise, solving the resulting PDEs.
result Most probable flows differ from deterministic flows, especially under noise.
Study on 4D Einstein manifolds with Kähler conformal geometry.
problem Exploring 4D Poincaré-Einstein manifolds with Kähler metrics.
method Formulated a Dirichlet boundary value problem and established existence and uniqueness theory.
result Existence and uniqueness of new Poincaré-Einstein metrics.
Lectures on deep learning properties in infinite and large-width networks.
problem Understanding deep neural networks in extreme width conditions.
method Analysis of random deep neural networks, connections to linear models, kernels, and Gaussian processes, perturbative and non-perturbative treatments.
result Properties and behaviors of deep neural networks in the infinite-width limit and large-width regime.
New approach predicts generalization of deep neural networks in proportional-width regime.
problem Predicting generalization of deep neural networks in proportional-width regime.
method Equivalent Wishart Ansatz for hierarchical empirical kernels, renormalized NNGP kernel.
result Renormalized NNGP kernel captures dominant stochastic fluctuations in deep neural networks.
Proposes a lattice formulation of APS index using η invariant.
problem Calculating APS index in lattice gauge theory.
method Uses η invariant of domain-wall Dirac operator.
result Index is always an integer with finite lattice spacing.
Study on fluctuations in neural network kernels and predictions, focusing on finite width effects.
problem Characterizing fluctuations in finite width neural networks.
method Dynamical mean field theory analysis of wide but finite feature learning neural networks.
result Fluctuations in kernels and predictions are dynamically coupled, leading to reduced variance in feature learning regimes.
The standard Black-Scholes theory of option pricing is extended to cope with underlying return fluctuations described by general probability distributions. A Langevin process and its related Fokker-Planck equation are devised to model the market stochastic dynamics, allowing us to write and formally solve the generaliz…
The paper explores how fields in higher dimensions are quantized.
problem Understanding non-perturbative completions of higher gauge fields.
method Generalizes the Chern-Dold character map to higher-dimensional supergravity theories.
result Flux and charge quantization laws for higher gauge fields are understood via non-linear Bianchi identities.
Formalizes quantum path integrals using groupoids and differential forms.
problem Formalizing Feynman's path integral in quantum mechanics.
method Shifted focus to pair groupoid, using van Est map and piecewise linear structures.
result Developed a coordinate-free approach to integration of differential forms.
Quantum Kerr learning shows enhancements in convergence and generalization for kernel-based methods.
problem Improving convergence and generalization in kernel-based methods for quantum computing.
method Combining quantum mechanics with neural tangent kernel theory and first-order perturbation theory.
result Quantum enhancements in terms of convergence time and generalization error.
We consider aspects of Chern-Simons theory on L(p,q) lens spaces and its relation with matrix models and topological string theory on Calabi-Yau threefolds, searching for possible new large N dualities via geometric transition for non-SU(2) cyclic quotients of the conifold. To this aim we find, on one hand, some novel …
NAPP-ERM improves ERM with differential privacy guarantees by iteratively achieving target regularization and delivering strong convexity.
problem Over-regularization in privacy-preserving ERM approaches.
method Noise-Augmented Privacy-Preserving Empirical Risk Minimization (NAPP-ERM) with a dual-purpose l2 regularizer and privacy budget retrieval strategy.
result Mitigates over-regularization and achieves strong convexity through a single regularizer.
In this thesis, we study moduli in compactifications of ten-dimensional heterotic supergravity. We consider supersymmetric compactifications to four-dimensional maximally symmetric space, commonly referred to as the Strominger system. The compact part of space-time X is a six-dimensional manifold of what we refer to …
Study wave functions in complex Chern-Simons theory, finding integrality and rational points.
problem Understanding wave functions in complex Chern-Simons theory.
method Conjecture and prove integrality structure, develop techniques to determine wave functions at rational points.
result Wave functions have integrality structure and can be determined at rational points.
New insights connect strong coupling SYM amplitudes to hyperkähler geometry.
problem Understanding strong coupling SYM amplitudes.
method Integrable systems, pseudo-hyperkähler geometry, twistor theory.
result Remainder function is a pseudo-Kähler scalar in hyperkähler geometry.
We use the 3d-3d correspondence together with the DGG construction of theories Tn[M] labelled by 3-manifolds M to define a non-perturbative state-integral model for SL(n,C) Chern-Simons theory at any level k, based on ideal triangulations. The resulting partition functions generalize a widely studied k=1 state-integ…
Extract anomalies from 5D SCFTs using extra-dimensional η-invariants.
problem Anomalies in quantum field theories.
method Use extra-dimensional η-invariants to bypass traditional blowup techniques.
result Anomalies can be determined directly from η-invariants of asymptotic boundaries.
Study of IR phases in 3D class R theories linked to non-hyperbolic 3-manifolds.
problem Understanding IR phases of 3D class R theories associated with non-hyperbolic 3-manifolds.
method Analysis of IR phenomena through `exceptional' Dehn fillings and gauging of flavor symmetries.
result 3D class R theories associated with certain atoroidal non-hyperbolic 3-manifolds exhibit supersymmetry enhancement at low energy.
Using probabilistic methods, we first define Liouville quantum field theory on Riemann surfaces of genus g≥2 and show that it is a conformal field theory. We use the partition function of Liouville quantum field theory to give a mathematical sense to Polyakov's partition function of noncritical bosonic s…