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Recent Advances in Low-dimensional Topology

The past two decades have seen truly remarkable progress in the field of low-dimensional topology, including solutions to the Poincaré conjecture, the geometrisation conjecture, the virtually Haken and virtually fibred conjectures of Thurston, the three- dimensional (generalised) Smale conjectures, the triangulation conjecture, and the four-dimensional Smale conjecture. On the other hand, many problems remain unsolved, for example the Berge and cabling conjectures, the L–space conjecture, the effectiveness of geometrisation, the four-dimensional smooth Poincaré and Schoenflies conjectures, and the full topological surgery conjecture. And, of course, the resolution of old problems has led to new questions regarding the overall structure of low-dimensional manifolds. The goal of this workshop is to bring together experts in these topics and encourage Indian researchers, including PhD students, to engage with these fields.

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Venue: ICTS Bangalore

Sofia Workshop in Analytical Number Theory

This workshop aims to bring world class scientists and promising young researchers together in order to promote the latest key results in analytic number theory, with a particular focus on primes, sieves and multiplicative functions.

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Venue: Bulgarian Academy of Sciences

Strong Convergence, Random Matrices and Discrete Subgroups of Lie Groups

The aim of the workshop is to gather doctorate students and researchers working on probability theory and on discrete subgroups of Lie groups to discuss recent advances around the notion of strong convergence for discrete groups. This notion first appeared about 20 years ago for the free group and was studied for more general discrete subgroups of Lie groups recently, notably by Magee and his collaborators. It has found remarkable applications in differential geometry (for the study of minimal surfaces and of the spectrum of the Laplacian). The program will include two mini-courses to introduce basic notions on Lie groups and their discrete subgroups on the one hand and on strong convergence on the other hand.

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Venue: Universidad Nacional Autónoma de México

New Directions in Nonlinear PDEs

This workshop is designed to provide a week of intensive study and discussion on some of the most pressing themes in contemporary nonlinear analysis, engaging with a broad spectrum of mathematical problems characterised by their complexity and deep interconnections. The program is organised around key topics such as pattern formation in PDEs, phase separation, optimal partition problems, shape optimisation, and free boundary problems, together with the exploration of complex solutions to ordinary differential equations, particularly within celestial mechanics and Hamiltonian systems. Special attention will also be devoted to singular perturbations and concentration phenomena.

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Venue: Ettore Majorana Foundation and Centre for Scientific Culture

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