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Geometrie und Topologie,    Mathematische Logik, Grundlagen der Mathematik

ICMS, Bayes Centre, Edinburgh

The idea of p-adic families of automorphic forms grew out of work of Serre and Swinnerton-Dyer in the 70s exploring congruences between the q-expansion coefficients of modular forms. Work of Hida, Coleman and Mazur made the investigation of p-adic families one of the central topics in the arithmetic of modular forms. In the following decades there were striking applications to the construction of p-adic L-functions, Iwasawa theory and modularity of Galois representations. One powerful organising principle has been to parametrize p-adic modular forms (or, more generally, p-adic automorphic forms) by p-adic analytic spaces known as eigenvarieties (or eigencurves, in the one-dimensional case originally considered by Coleman and Mazur). Our understanding of the geometry of eigenvarieties and their relationship to moduli spaces of Galois representations has rapidly developed, but there are still many important open questions. An overarching objective of this meeting will be to bring together people working on the different theories of p-adic automorphic forms and various applications (or potential applications). We hope that this will inspire new collaborations and insights.

University of Warwick, Mathematics Institute

Roger William Carter was a towering figure in Mathematics for over 40 years. He would be 90 in August of 2024. This memorial conference will celebrate Roger's life and scientific endeavours by bringing together a diverse group of mathematicians who knew him personally or were affected by his scientific craft.

Email: MRC@warwick.ac.uk

The UK Spectral Theory Network aims to strengthen the research interaction among people working in spectral theory and adjoining fields in the UK. It offers Early Career Researchers, PhD students and members of the network an effective platform for exploring connections between the multifaceted strands of the subject, exchanging ideas and developing new collaborations. It promotes equality, diversity and inclusion in mathematics, and inspires future generations of researchers in the field.

Isaac Newton Institute for Mathematical Sciences

Over the past few years, several remarkable links between quantum information, quantum groups, and operator algebras have been discovered. This includes in particular the study of non-local games, quantum automorphism groups, and the resolution of Connes’ Embedding problem announced by Ji, Natarajan, Vidick, Wright and Yuen in 2020. The focus of this workshop is the state of the art in this highly active area, covering the latest developments and potential future directions.

Isaac Newton Institute for Mathematical Sciences

Equivariant techniques have played a critical role in the proofs of several major results and developments in algebraic topology over the past decade. Examples include the solution of the famous Kervaire invariant one problem, computations of previously inaccessible homotopy groups of spheres based on the motivic Adams spectral sequence, and the new equivariant approach to THH, TC, and algebraic K- theory. The programme will unite experts and young researchers who apply homotopic methods in algebra (operads), algebraic topology, and algebraic geometry (motivic homotopy theory) around the common theme of equivariant methods. Though these methods have already led to significant breakthroughs, their potential is clearly far from exhausted. We foresee that this programme will incite further developments and greater synergies between equivariant homotopy theory and the themes of the programme centred around three workshops: "Operads and calculus", "Chromatic and motivic homotopy theory" and "THH, TC and algebraic K- theory".

Geometrie und Topologie,    Kurse und Veranstaltungen für Studenten der Mathematik

Isaac Newton Institute for Mathematical Sciences

Geometrie und Topologie,    Kurse und Veranstaltungen für Studenten der Mathematik

Isaac Newton Institute for Mathematical Sciences

Geometrie und Topologie,    Kurse und Veranstaltungen für Studenten der Mathematik

Isaac Newton Institute for Mathematical Sciences

Equivariant homotopy theory in context

Geometrie und Topologie,    Kurse und Veranstaltungen für Studenten der Mathematik