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The Langlands Programme: Recent Trends, New Developments, and Applications

The Langlands programme has become a cornerstone of modern number theory, and predicts the existence of a bridge relating harmonic analysis and arithmetic.

This symposium will focus on four themes, and the interconnections and synergies between them.  The themes are:

(A) Recent trends in the Langlands programme
(B) Explicit constructions in the Langlands programme
(C) The relative Langlands programme
(D) The Langlands programme and analytic number theory

CMI Enhancement and Partnership Program

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Venue: University of Sheffield

Algorithmic Number Theory Symposium (ANTS XVII)

The Algorithmic Number Theory Symposium (ANTS) is the premier international forum for the presentation of new research in computational number theory and its applications, devoted to algorithmic aspects of number theory and related fields, including elementary number theory, algebraic number theory, analytic number theory, the geometry of numbers, arithmetic geometry, finite fields, cryptography, and coding theory. Each symposium consists of several invited talks, presenting results of current interest to a broad audience, together with contributed talks chosen through a competitive submission and review process.

CMI Enhancement and Partnership Program

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Venue: University of Groningen

Number Theory in the Americas 2

In 2019, the organisers created a workshop called Number Theory in the Americas, which brought together junior and senior mathematicians from North, Central, and South America to work together on research projects. The workshop resulted in at least seven publications, and served as a first collaboration experience for many of the junior researchers. The organizers propose to create a follow-up workshop in order to provide collaboration opportunities for the PhD students and postdocs who were too young to participate the last time. The workshop will be held in Spanish, the organisers welcome native and non-native speakers alike. 

This workshop is modeled after several other workshops that have been successful at fostering mathematical collaboration. Participants will be divided into small project groups (3-5 participants) containing a mix of junior and senior researchers. Each group will be led by one or two senior mathematicians. Project groups will be assigned based on research area, with care taken to ensure that each group contains researchers from both continents who have not previously worked together. Background reading will be sent to project group members several months in advance so that they are prepared to work on their respective problems together when they arrive in Oaxaca. The bulk of the workshop will be devoted to working in the project groups, but there will be introductory talks on the first day and final reports on the last day. There will also be panel discussions on topics of particular interest to junior researchers. The expectation is not that each project group will write a paper by the end of the week. Rather, it is meant to be an opportunity to exchange ideas and a starting point for potential future collaboration.

CMI Enhancement and Partnership Program

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Venue: Casa Matemática Oaxaca

Advances in Spectral Theory: LMS-Bath Symposium

Spectral theory (ST) is a relatively old and well-established subject within mathematics. In addition to a great number of important results of intrinsic interest and value, spectral theory has a number of applications and interconnections to various parts of mathematics, ranging from mathematical physics to number theory; representation theory to geometric analysis. Three such areas that have seen a surge of exciting results in the last ten years are: periodic and almost-periodic operators, random matrices and operators, and spectral geometry.

The INI-Bath symposium will consist of a one week summer school followed by a one week conference. The first week will consist of 6 short courses in topics of recent interest in periodic and almost-periodic operators, random matrices and operators, and spectral geometry. The goal of these courses will be to introduce non-experts; both junior researchers and researchers from the two other fields to some methods that have been instrumental in recent advances. The courses will also prepare junior researchers to understand the conference in the following week and help them to attack future problems in the area. The conference will then consist of approximately 25-30 talks by leaders in these fields.

CMI Enhancement and Partnership Program

Photo: Ben Walker

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Venue: University of Bath