Related papers: LonTI Lectures on Sine-Gordon and Thirring
Open-sourced large language models (LLMs) have demonstrated remarkable efficacy in various tasks with instruction tuning. However, these models can sometimes struggle with tasks that require more specialized knowledge such as translation.…
We reconsider the mass spectrum of double sine-Gordon theory where recent semiclassical results called into question the previously accepted picture. We use the Truncated Conformal Space Approach (TCSA) to investigate the claims. We…
Learning to disentangle the hidden factors of variations within a set of observations is a key task for artificial intelligence. We present a unified formulation for class and content disentanglement and use it to illustrate the limitations…
In these lectures I will discuss the following topics: (1) Twistors in 4 flat dimensions: Massless particles; constrained phase space (x,p) versus twistors; Physical states in twistor space. (2) Introduction to 2T-physics and derivation of…
This set of lecture notes presents a pedantic derivation of the connection between the $ {\hat A} $-genus of spacetime's loop space and the genus one partition function of the $ N=1/2 $ sigma model. It concludes with some remarks on…
The Loop-Tree Duality (LTD) is a novel perturbative method in QFT that establishes a relation between loop-level and tree-level amplitudes, which gives rise to the idea of treating them simultaneously in a common Monte Carlo. Initially…
This talk is divided into two parts. The first part reviews some of the duality relationships between superstring theories. These relationships are interpreted as providing evidence for the existence of a unique underlying fundamental…
Generating user interpretable multi-class predictions in data rich environments with many classes and explanatory covariates is a daunting task. We introduce Diagonal Orthant Latent Dirichlet Allocation (DOLDA), a supervised topic model for…
These are notes of a series of lectures on mirror symmetry and topological string theory given at the Mathematical Sciences Center at Tsinghua University. The N=2 superconformal algebra, its deformations and its chiral ring are reviewed. A…
We generalize the notion of length to an ordinal-valued invariant defined on the class of finitely generated modules over a Noetherian ring. A key property of this invariant is its semi-additivity on short exact sequences. As an…
Gordon and Litherland's paper $\textit{On the Signature of a link}$ introduced a bilinear form that simultaneously unifies both the quadratic forms of Trotter and Goeritz. This remarkable pairing of combinatorics and topology has had…
This is the draft of lecture notes for Phd students in Sichuan University. In this notes we expand Li-Ruan's paper with much more detailed explanations and calculations.
Graduate courses can provide specialized knowledge for Ph.D. and Master's students and contribute to develop their hard and soft skills. At the same time, Systematic Literature Review (SLR) has been increasingly adopted in the computing…
A class of two-dimensional globally scale-invariant, but not conformally invariant, theories is obtained. These systems are identified in the process of discussing global and local scaling properties of models related by duality…
We describe a non-extensional variant of Martin-L\"of type theory which we call two-dimensional type theory, and equip it with a sound and complete semantics valued in 2-categories.
We revisit the double copy description for linearized gravity and point out various technical issues and subtleties, associated with setting up the double copy description, including the problem of matching degrees of freedom on both sides…
This chapter provides an overview of research works that present approaches with some degree of cross-fertilisation between Computational Argumentation and Machine Learning. Our review of the literature identified two broad themes…
In this paper, we examine the complex sine-Gordon model in the presence of a boundary, and derive boundary conditions that preserve integrability. We present soliton and breather solutions, investigate the scattering of particles and…
These are yet another lecture notes on Seiberg-Witten invariants, where no claim of originality is made, they contain a discussion of some related results from the recent literature.
A number of models of linear logic are based on or closely related to linear algebra, in the sense that morphisms are "matrices" over appropriate coefficient sets. Examples include models based on coherence spaces, finiteness spaces and…