Related papers: Height inequalities and canonical class inequaliti…

This is the note for the four lectures given by the author in the ``International Short-School/Conference on Affine Algebraic Geometry and the Jacobian Conjecture" at Chern Institute of Mathematics, Nankai University, Tianjin, China. July…

These are notes for a graduate-level introductory course on singularity categories.

The "variance method" has been used to prove many classical inequalities in design theory and coding theory. The purpose of this expository note is to review and present some of these inequalities in a unified setting. I will also discuss…

This article offers different proofs of ten inequalities from those already published. So that the readers can see for themselves, the tasks specified in the condition of the source and classical inequalities which used in previously…

This is the written version of a lecture given at KITP in Oct 2014 on Black Holes and quantum complexity. I've included (in boldface) various questions that came up during the lecture and discussions the following day, as well as the…

Notes from the lectures by the author at the 7th Jerusalem Winter School 1990 on Quantum Cosmology and Baby Universes. The lectures covered quantum mechanics for closed systems like the universe, generalized quantum mechanics, time in…

We present a method to analyse the scientific contributions between research groups. Given multiple research groups, we construct their journal/proceeding graphs and then compute the similarity/gap between them using network analysis. This…

These notes are based on the lecture courses given at the Ruhr-Universit{\"a}t-Bochum (03--08.02.1997) and at the Universit{\'e} Paul Sabatier (Toulouse, 08-12.01.1996).

Lectures presented at the Les Houches 2016 Summer School "Integrability: from Statistical Systems to Gauge Theory".

These are notes from my lecture at 4ECM in Stockholm (June 2004).

This is an informal paper presenting historical results around the recent paper of the author about Lang's Conjecture and torsion of elliptic curves. This paper also discusses a few aspects of the proof.

These notes are an extended version of a series of lectures given at the CIME Summer School in Cetraro in June 2022. The goal is to explain questions about optimal functional inequalities on the example of the sharp Sobolev inequality and…

We present a number of questions in commutative algebra posed on the problem solving seminar in algebra at Stockholm University during the period Fall 2014 - Spring 2017.

Symmetries and isomorphisms play similar conceptual roles when we consider how models represent physical situations, but they are formally distinct, as two models related by symmetries are not typically isomorphic. I offer a rigorous…

In the article we prove some inequalities that contain relations between altitudes and medians in triangle. At least one of these inequalities has not been considered in the literature before and the main theorem has also not been proved…

Talk presented by the second author at the Inaugural Coference of the Asia Pacific Center for Theoretical Physics, Seoul, June 1996. The purpose of this note is to give a resume of the Seiberg-Witten theory in the simplest possible…

I present a general overview of the results discussed during the Cracow 1997 workshop on ``Relativistic Jets in AGNs.'' My emphasis will be on showing the significant progress made in several areas over the last few years, pointing out what…

This paper collects and extends the lectures I gave at the "XXIV International Fall Workshop on Geometry and Physics" held in Zaragoza (Spain) August 31 - September 4, 2015. Within these lectures I review the formulation of Quantum…

I give a pedagogical introduction to the concepts and the tools that are necessary to study particle physics models in higher dimensions. I then give a more detailed presentation of warped compactifications and discuss their possible…

The lecture, given at the ICM 2014 in Seoul, explores several problems of analytic number theory in the context of function fields over a finite field, where they can be approached by methods different than those of traditional analytic…