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ICMS - International Centre for Mathematical Sciences

Topology is likely to be featured prominently in any truly useful quantum computation scheme. The hurdle of scalable fault-tolerance is insurmountable with the current incremental progress -- while it is possible to engineer systems supporting hundreds of physical qubits, applications beyond academic interest require millions of qubits to implement robust error correction. Topological quantum computation (TQC) relies upon the preparation of topological phases of matter supporting non-abelian anyons to perform inherently fault-tolerant operations. As errors are corrected at the hardware level through the topological nature of anyons, the problem of scalability is simultaneously overcome. On the other hand, despite years of effort we still don't have unassailable confirmation that non-abelian anyons exist. This workshop will bring together researchers in a diversity of fields in and around TQC for the purpose of broadening and deepening the subject, with an eye towards accelerating the realization of scalable technology.

Matériaux quantiques, basses températures,    Mécanique quantique et technologie quantique

Isaac Newton Institute for Mathematical Sciences (INI)

The programme will start with an introductory school on equivariant methods in algebraic and differential geometry for graduate students, postdocs and those who are interested in learning background material for the programme.

Algèbre,    Cours et évènements pour étudiants en mathématiques

Isaac Newton Institute for Mathematical Sciences (INI)

This workshop focuses on the following themes and their interactions: 1. Geometric and equivariant aspects of algebraic statistics 2. Computation of invariants in algebraic (especially toric) geometry 3. Algebraic group actions on combinatorial spaces

Algèbre,    Théorie des graphes et combinatoire

Isaac Newton Institute for Mathematical Sciences (INI)

The workshop focuses on recent equivariant techniques in enumerative geometry of holomorphic maps between complex manifolds. It will bring together researchers working on global singularity theory (multisingularity classes of holomorphic maps, Thom polynomials, multiple-point formulas), and on complex manifolds with positivity properties (hyperbolicity, ample cotangent bundle, jet differentials). The mini-courses aim to explain the central role of the Hilbert scheme of points on complex manifolds in these problems.

Isaac Newton Institute for Mathematical Sciences (INI)

The goal of this conference is to bring together researchers in complex algebraic and differential geometry, working on notions of stability for algebraic varieties such as K-stability (and in particular the construction of moduli spaces of algebraic varieties), the existence of canonical metrics in Kähler geometry and the many nearby topics that interact with these areas. The relationship between K-stability and the existence of canonical Kähler metrics goes by the name of the Yau-Tian-Donaldson conjecture, and is motivated by a more classical correspondence between stability in the sense of geometric invariant theory and properties of moment maps as used in symplectic geometry—two of the overarching themes of the wider programme. This conference will emphasise the deep links between Kähler geometry, stability conditions and various related problems in equivariant algebraic and differential geometry.

Isaac Newton Institute for Mathematical Sciences (INI)

The workshop focuses on the role of equivariant techniques in enumerative geometry and moduli stacks. It will bring together researchers working on the relationship between concepts of stability and wall-crossing in different settings such as moduli stacks, geometric invariant theory, Bridgeland stability and K-stability, as well as enumerative geometers studying the geometry and topology of Hilbert schemes of points on surfaces and higher dimensional manifolds and related invariants.

Isaac Newton Institute for Mathematical Sciences

The workshop focuses on the role of equivariant techniques in enumerative geometry and moduli stacks. It will bring together researchers working on the relationship between concepts of stability and wall-crossing in different settings such as moduli stacks, geometric invariant theory, Bridgeland stability and K-stability, as well as enumerative geometers studying the geometry and topology of Hilbert schemes of points on surfaces and higher dimensional manifolds and related invariants.

Isaac Newton Institute for Mathematical Sciences

This workshop will focus on various aspects of the geometry of interacting random paths. The aim is to bring together researchers specialising in random processes such as branching random walks, activated random walks, random interlacements, and other models of interacting random walks, as well as their continuous time counterparts. The workshop will explore questions and results concerning the geometry of the ranges of these processes, and further properties of their occupation time fields, for instance, their associated “thick points”. It will include two-mini courses in addition to the programme of research talks.

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".

Algèbre,    Cours et évènements pour étudiants en mathématiques

Isaac Newton Institute for Mathematical Sciences

Algèbre,    Cours et évènements pour étudiants en mathématiques

Isaac Newton Institute for Mathematical Sciences

Algèbre,    Cours et évènements pour étudiants en mathématiques

Isaac Newton Institute for Mathematical Sciences

Equivariant homotopy theory in context

Algèbre,    Cours et évènements pour étudiants en mathématiques