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Even after one hundred years, the circle method remains one of the most important tools in the analytic theory of numbers. Over the years the method has gone through several modifications, resulting in novel applications. Originally introduced to study the partition function and the Waring problem, the circle method quickly became the most powerful analytic tool to count rational points on varieties. It was also adopted to study problems in the prime number theory. Recently the circle method has been extended to function fields and general number fields, and has been put on a broader adelic and geometric setting. We have also seen some striking recent applications in areas such as analytic theory of L-functions, ergodic theory, and the Langlands program. This workshop will present accessible short lecture series on the circle method and related topics, from experts in the field, aimed at senior graduate students and post-docs. The main aim will be to introduce the audience to various f...

The aim of this course is to explore the main ideas of the statistical physics approach to critical phenomena. We will discuss phase transitions, using the ferromagnetic phase transition and the Ising model as our primary example, with particular emphasis on the renormalisation group approach. Instructor: Emilie Huffman / Maite Dupuis Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

The first half of the course explains why fields are desirable when quantum mechanics meets special relativity. The second half introduces different kinds of spinor fields and their interactions. Instructor: Gang Xu Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

Recent advancements in photodetection technologies and spectroscopy hold the promise of transforming intensity interferometry, thereby revolutionizing observational Astronomy by enabling observations to resolve significantly fainter objects than currently possible. This workshop serves as a platform to unite experts in photodetection, theoretical and observational astronomy, as well as observers and theorists from diverse disciplines, to explore the multifaceted capabilities of intensity interferometry.

The workshop's focus spans three key objectives:

• Develop and disseminate novel ideas concerning science cases unique to intensity interferometry.
• Synthesize insights from observers and photodetector experts concerning the requisite technologies and experimental techniques which will allow for new science with intensity interferometry.
• Initiate a concentrated effort to propel the development of large telescope arrays dedicated to intensity interferometry.

This workshop will be exclusively organized in plenary sessions, providing ample time for engaging discussions among participants.

Scientific Organizers

Masha Baryakhtar - University of Washington
Neal Dalal - Perimeter Institute
Marios Galanis - Perimeter Institute
Junwu Huang - Perimeter Institute

 

 

Integrable systems share the properties of being exactly solvable in some sense and of having many conserved quantities. Investigating their behavior is key to understanding the wealth of non-integrable models falling in the same universality class. While the first examples of integrable systems were continuous, a large array of discrete integrable systems have been discovered over the last 60 years. These discrete systems hail from various branches of theoretical physics (statistical physics, string theory) and mathematics (combinatorics, representation theory, geometry, probability). They all possess remarkable algebraic structures.This program proposes to explore several interrelated aspects of discrete integrable systems. We will focus on three aspects that are currently active topics of research:1. Integrable difference equations, their soliton solutions and the rich structure of their singularities. Ultradiscretization of these equations, yielding cellular automata (e.g. box-ball...

Gravitation and cosmology allow us to probe the nature of the universe at its largest scales and gain insights into the underlying structure and dynamics of the universe. New observational techniques in the field of cosmology have allowed us to estimate various cosmological parameters with remarkable precision. Recent advancements in observational techniques have revolutionized our understanding of the universe. Some of these techniques include Cosmic Microwave Background (CMB) Observations, Large-Scale Structure Surveys, Supernova Cosmology, Baryon Acoustic Oscillations (BAO), Gravitational Lensing, Redshift Surveys etc. These techniques have collectively allowed cosmologists to estimate parameters such as the Hubble constant, the density of dark matter and dark energy, the curvature of space and the composition of the universe with remarkable accuracy.The third Indian Association for General Relativity and Gravitation (IAGRG) school on Gravitation and Cosmology aims to train young re...

This is a theoretical physics course that aims to review the basics of theoretical mechanics, special relativity, and classical field theory, with the emphasis on geometrical notions and relativistic formalism, thus setting the stage for the forthcoming courses in Quantum Mechanics, and Quantum Field Theory in particular, as well as in General Relativity and Quantum Gravity. Instructor: Aldo Riello Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses