Related papers: IMPANGA lecture notes on log canonical thresholds
Let $\varphi$ be a plurisubharmonic function defined in a neighborhood of the origin in $\mathbb C^n$. For each real number $t>-n$, we associate to $\varphi$ the weighted log canonical threshold \[ c_t(\varphi):=\sup\Bigl\{c\geq…
Procedural computer languages have long been used in many aspects of mathematics pedagogy. In this work, we examine the use of Prolog, a declarative language for the same purpose. We find the facts+rules aspect of Prolog to be a novel…
The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at Oxford over the past few years. They contain…
We give tight bounds for logarithmic mean. We also give new Frobenius norm inequalities for two positive semidefinite matrices. In addition, we give some matrix inequalities on matrix power mean.
In these three lectures a review is provided of the properties of galaxy systems as determined from optical and infrared measurements. Covered topics are: clusters identification, global cluster properties and their scaling relations,…
We study algebraic tangles as fundamental components in knot theory, developing a systematic approach to classify and tabulate prime tangles using a novel canonical representation. The canonical representation enables us to distinguish…
Quantum Computing is an exciting field that draws from information theory, computer science, mathematics, and quantum physics to process information in fundamentally new ways. There is an ongoing race to develop practical quantum computers…
Survey article on loop groups and their representations, following a course of three lectures held at the summer school "algebraic groups" at the Georg-August-Universitaet zu Goettingen, June 27--July 13, 2005. We discuss loop groups, their…
These are notes from a lecture course on symmetric spaces by the second author given at the University of Pittsburgh in the fall of 2010.
These lecture notes were prepared for a mixed audience of students, postdocs and faculty from the Indian Institute of Technology Madras, India and neighboring institutions, particularly the Institute of Mathematical Sciences. I am not an…
These lecture notes discuss classical models of liquid crystals, and the different ways in which defects are described according to the different models.
The paper is devoted to the properties of the Lagrange spectrum left endpoints and so-called attainable numbers.
Large Language Models (LLMs) have become a focal point of research across various domains, including software engineering, where their capabilities are increasingly leveraged. Recent studies have explored the integration of LLMs into…
In these 4 lectures, I give a brief introduction to the principles of effective field theory and discuss their application via 3 examples: (i) the Standard Model as an effective theory; (ii) non-linear sigma models and the composite Higgs;…
We show that minimal models of log canonical pairs exist, assuming the existence of minimal models of smooth varieties.
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
We provide a brief tutorial on the use of concentration inequalities as they apply to system identification of state-space parameters of linear time invariant systems, with a focus on the fully observed setting. We draw upon tools from the…
These are lecture notes for a series of lectures given at the Les Houches Summer School on Integrability in Atomic and Condensed Matter Physics, 30 July to 24 August 2018. The same series of lectures has also been given at the Tokyo…
Microcanonical inflection-point analysis (MIPA) identifies third-order transitions from derivatives of the microcanonical entropy, but whether such transitions admit a direct canonical formulation has remained unclear. Here we establish a…
We introduce several properties of forcing notions which imply that their lambda-support iterations are lambda-proper. Our methods and techniques refine those studied in math.LO/9906024, math.LO/0210205, math.LO/0508272 and math.LO/0605067,…