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Farey’s Legacy in Frieze Patterns and Discrete Geometry

Frieze patterns are celebrated for their ubiquity in mathematics, featuring in cluster algebras, continued fraction theory, difference equations, hyperbolic geometry, and moduli space theory. This workshop brings together researchers from frieze patterns and the cognate fields of continued fractions and discrete geometry to promote cross-disciplinary interactions in these fertile subjects. The event is framed around the legacy of the English geologist John Farey (1766–1826), who inspired the development of Farey sequences and the Farey tessellation, which are common themes of the workshop. There will be a mathematical art gallery accompanying the workshop to share the outputs of our research.

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Venue: ICMS Edinburgh

Geometry, Higher Structures, and Physics

The interplay between geometry and physics has been a driving force for new developments in both mathematics and physics for a very long time. In the last two decades, higher category theory has become a fine contributor in this dialogue, providing many invaluable ideas and very useful heuristics. This workshop aims to present the latest results in the application of (higher) geometry to theoretical physics and to foster new collaborations between mathematicians and theoretical physicists. Focal points of the workshop will be algebraic and symplectic geometry, mirror symmetry, generalised geometry and T-/U-duality, higher gauge theory and its applications, higher and generalised symmetries, and the application of homotopy algebras in the context quantum field theory.

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Venue: ICMS Edinburgh

Operator Algebras and Mathematical Physics

Quantum Field Theory (QFT) stands as one of the pivotal theories in physics, holding a significant position over a multitude of subjects. Within various mathematical approaches to QFT, we emphasize the operator algebraic methods. Ever since von Neumann’s initiation, the theory of operator algebras has been closely related to quantum physics. Jones’ work on subfactors, including its application to low-dimensional topology such as the Jones polynomial, has produced a substantial influence across a broad spectrum of mathematical and physical topics.

Two-dimensional conformal field theory serves as a particularly fertile example of a QFT. It represents one of the rare instances where everything can be treated with mathematical rigor and the operator algebraic approach has been quite successful.

Von Neumann algebras have also gained interest recently in the context of entanglement entropy calculations. Bringing quantum reference frames and gravity into the description of quantum fields affects what physical observables one considers. This is tightly connected to von Neumann algebra types and it is timely to provide a link between the existing physical examples and rigorous results in mathematics.

Both classical and quantum statistical mechanics have also had interactions with operator algebras over decades. Profound connections to subfactor theory are exemplified by the Temperley-Lieb algebra since early days and recent advances in topological phases of matter, a hot topic in contemporary physics, have led to even deeper relations with operator algebras.

With the rapid advancements in operator algebras and related areas in mathematical physics, understanding the complete landscape is a challenge for both senior  and junior researchers. This presents a perfect moment for this workshop, where experts from various fields can converge and acquaint younger researchers with these dynamic domains.

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Venue: ICMS Edinburgh

Symplectic Topology, a Conference in Honor of Kai Cieliebak

This international conference on symplectic topology and dynamics will bring together a group of established, world-leading experts in the field with young researchers, who have made groundbreaking contributions to the development of symplectic geometry in recent years, to discuss the latest developments and identify major remaining challenges with the goal of exploring their interrelationships, becoming a reference point for the state of the art, and fostering new collaborations. The workshop will be a unique opportunity for both young and established researchers to get first-hand information about the current state and the future of symplectic geometry.

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Venue: University of Augsburg

Second African Women in Algebra Workshop

This African Women in Algebra Workshop is the second workshop in a series of initiatives designed by African Women in Algebra to address the gender gap in STEM fields, particularly within the realm of algebra.  The motivation behind these workshops stems from a pressing issue facing African women in academia-the challenge of ascending the academic ladder due to the requirement of a prescribed number of research publications. For many career women in Africa, the delicate balance between family and work responsibilities often leaves them with limited time and mobility, hindering their ability to meet academic publication requirements. This not only affects their individual career trajectories but also contributes to the widening gender gap in STEM fields.

The African Women in Algebra Workshops aim to provide a supportive and collaborative research environment tailored to the unique challenges faced by African women. These workshops are strategically designed to empower women in algebraic careers, fostering their interest and advancement in algebra

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Venue: University of Abuja, Nigeria

37th Automorphic Forms Workshop

Over the past 37 years, the Annual Workshop on Automorphic Forms and Related Topics has remained a welcoming and friendly conference. Those attending range from students to new PhD’s to established researchers. For young researchers, the conference has provided support and encouragement. For accomplished researchers, it has provided the opportunity to mentor as well as a forum for exchanging ideas.

The workshop has become internationally recognized for both its high-quality research talks and its supportive atmosphere for junior researchers. Participants present cutting-edge research in all areas related to automorphic forms. These include mock modular forms, Maass wave forms, elliptic curves, Siegel and Jacobi modular forms, special values of L-functions, random matrices, quadratic forms, applications of modular forms, and many other topics.

In addition to research talks, the workshop has, in the past years, featured panel discussion sessions on the topics of grant writing, mentoring and research partnerships, REUs and outreach, and opportunities for international collaborations. Based on the success of these sessions, we have similar panel sessions this year as well.

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Venue: University of North Texas

10th Nairobi Workshop in Algebraic Geometry

Pre-workshop School: 11-13 September Workshop: 15-19 September

Topics to be discussed include foundations, projective and tropical algebraic geometry, vector bundles on projective varieties, and commutative and non-commutative algebra around the McKay correspondence

Invited speakers:  Olivia Caramello (Insubria) tbc, Aurelio Carlucci (Oxford), Laura Costa (Barcelona) tbc, Ben Davison (Edinburgh), Andrés Jaramillo Puentes (Duisburg-Essen), Annet Kyomuhangi (Busitema), Brian Makonzi (Muni), Damas Mgani (Dar es Salaam), Francesco Malaspina (Politechnico di Torino) tbc, Sophie Marques (Stellenbosch), Caroline Namanya (Makerere)

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Venue: University of Nairobi

Beyond the Horizon: Navigating Turbulence, Irregularity, and Stochasticity in Fluid Dynamics

Fluid is one of the most omnipresent substances on the planet. Mathematical analysis of the fundamental partial differential equations of fluid dynamics such as the Navier-Stokes equations was pioneered by Leray in 1934. Gaining insights into the behavior of the solutions to such equations is crucial for our understanding of the physical phenomena that we experience in our daily lives. Very recently, multiple breakthrough works such as the blow-up of three-dimensional Euler equations, the development of the convex integration technique, and the solution theory of singular stochastic partial differential equations, have intensified the research on the partial differential equations of fluid dynamics. Many long-standing conjectures from physicists and mathematicians have come to a resolution. This interdisciplinary conference will serve as a forum for leading experts, emerging early-career researchers, and under-represented groups with complementary strength to explore recent developments, exchange insights, and address key challenges in the pursuit of better understanding of various issues. Through collaborative engagement and discussions, we aspire to deepen our understanding of the intricate interplay within the phenomena of irregularity, turbulence, and stochasticity in fluid dynamics. 

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Venue: ICMS Edinburgh

Geometry and Integrability

The area of integrable systems is a large and active area of research with lots of fruitful connections with algebra, geometry, analysis and theoretical physics. The workshop is devoted to interactions between integrability and geometry, highlighting recent developments where there has been substantial progress both in terms of establishing new connections and new structures.

The workshop will be centred around the following overlapping topics: (1) Cherednik algebras and many-body problems, (2) Poisson geometry, deformations and quantisation, (3) Frobenius manifolds, (4) discrete geometry and discrete dynamics.

The workshop will also be an occasion to celebrate the 70th birthday of Alexander Veselov who made foundational contributions to Integrable Systems and related areas. 

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Venue: ICMS Edinburgh

Geometric Problems in Linear and Nonlinear PDEs

Geometric analysis has intrigued mathematicians for centuries and remains a vibrant area of modern mathematics. Central to this field are the formulation of both linear and nonlinear partial differential equations (PDEs) on manifolds and the minimization of energy functionals in infinite-dimensional spaces. Our workshop will focus on four closely interconnected areas within geometric analysis: characterizing solutions to PDEs, Euler equations, minimal surface theory, and spectral geometry. The event aims to bring together leading experts and early-career researchers from around the world to discuss the latest advancements, exchange ideas, and explore major challenges and open problems in the field. 

Photo: Wikimedia Commons

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Venue: Sabhal Mor Ostaig, the Isle of Skye

Geometric Moduli Spaces – Rigidity, Genericity, Stability

The workshop’s goal is to explore connections across mathematical communities that study different geometric moduli spaces. Our workshop will bring together researchers from positive scalar curvature geometry, minimal surface theory, harmonic mapping theory, and special geometries. The study of moduli spaces naturally draws on a confluence of ideas from neighbouring fields, and in each of these areas there is a tradition of exploiting rigidity, genericity, and stability phenomena.
 
Despite many parallel developments, there has been surprisingly limited interaction and cross-collaboration across these communities. This workshop aims to foster new connections and to elucidate future research directions.

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Venue: ICMS Edinburgh

Arithmetic, Geometry, Space and Time: a Workshop on the Occasion of Minhyong Kim’s 61st Birthday

The aim of this workshop is to survey recent developments in reciprocity laws in arithmetic algebraic geometry, and in the nascent field of arithmetic quantum field theory. The event is also in celebration of the work of Minhyong Kim, who has made pioneering contributions to both subjects. This presents a chance to bring together world class researchers working on reciprocity laws in Diophantine geometry, p-adic Hodge theory, anabelian geometry, Iwasawa theory and the arithmetic and geometric Langlands programmes.

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Venue: ICMS Edinburgh