Related papers: Mathematical Encounters
In this survey, we provide an in-depth investigation of exponential Runge-Kutta methods for the numerical integration of initial-value problems. These methods offer a valuable synthesis between classical Runge-Kutta methods, introduced more…
In this article, we present several apparent paradoxes of special relativity and their respective solutions. These paradoxes have appeared since the advent of relativity in 1905, and in fact they are never paradoxes. From a didactic point…
Presents a differentiated teaching proposal that allows the student to be the agent in the construction of knowledge, overcoming the difficulties that Mathematics presents. Aiming to understand how the use of statistical tools can…
This is a survey (21 pages, 124 references) written for the MCQMC 2014 conference in Leuven, April 2014. We start with the seminal paper of Bakhvalov (1959) and end with new results on the curse of dimension and on the complexity of…
This chapter delves into the realm of computational complexity, exploring the world of challenging combinatorial problems and their ties with statistical physics. Our exploration starts by delving deep into the foundations of combinatorial…
This article is based on lecture notes for the Marie Curie Training school "Initial Training on Numerical Methods for Active Matter". It provides an introductory overview of modeling approaches for active matter and is primarily targeted at…
We study equations with infinitely many derivatives. Equations of this type form a new class of equations in mathematical physics. These equations originally appeared in p-adic and later in fermionic string theories and their investigation…
This paper provides some reflections on the field of mathematical software on the occasion of John Rice's 65th birthday. I describe some of the common themes of research in this field and recall some significant events in its evolution.…
Two lectures given at the UK-Japan Winter School on 'Geometry and Analysis Towards Quantum Theory', Durham, January 2004.
For more than half a century, dualities have been at the heart of modern physics. From quantum mechanics to statistical mechanics, condensed matter physics, quantum field theory and quantum gravity, dualities have proven useful in solving…
This list of problems arose as a collaborative effort among the participants of the Arbeitsgemeinschaft on Mathematical Quasicrystals, which was held at the Mathematisches Forschungsinstitut Oberwolfach in October 2015. The purpose of our…
We generalize the approach of Liu and Lawrence (1999) for multiple changepoint problems where the number of changepoints is unknown. The approach is based on dynamic programming recursion for efficient calculation of the marginal…
These notes have been written to complete a mini-course "Introduction to (generalized) Gibbs measures" given at the universities UFMG (Universidade Federal de Minas Gerais, Belo Horizonte, Brasil) and UFRGS (Universidade Federal do Rio…
With the birth of quantum information science, many tools have been developed to deal with many-body quantum systems. Although a complete description of such systems is desirable, it will not always be possible to achieve this goal, as the…
An exceptional point is a special point in parameter space at which two (or more) eigenvalues and eigenvectors coincide. The discovery of exceptional points within mechanical and optical systems has uncovered peculiar effects in their…
These are lecture notes for the AGRA II school, which took place in August 2015 at Universidad de San Antonio Abad del Cusco (Per\'u). They are geared towards graduate students and young researchers. I. Modular forms and Shimura curves (R.…
This essay considers ways that recent uses of computers in mathematics challenge contemporary views on the nature of mathematical understanding. It also puts these challenges in a historical perspective and offers speculation as to a…
These informal notes, initially prepared a few years ago, look at various questions related to infinite processes in several parts of mathematics, with emphasis on examples.
The use of large language models (LLMs) for complex mathematical reasoning is an emergent area of research, with fast progress in methods, models, and benchmark datasets. However, most mathematical reasoning evaluations exhibit a…
The problem of Relativistic Oscillator has been studied in the framework of Path Integral Monte-Carlo(PIMC) approach. Ultra-relativistic and non-relativistic limits have been discussed. We show that PIMC method can be effectively used for…