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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

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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

The William Rowan Hamilton Geometry and Topology Workshop: Celebrating Martin Bridson’s 60th Birthday

Geometric Group Theory began in the 1980s and 90s, formed from a rich synthesis of ideas from areas including geometry, topology, algebra, analysis and dynamics. One of its central themes is non-positive curvature – a fundamental concept in the geometry of manifolds for at least 200 years – and how this can manifest in a vast range of geometric spaces and their groups of symmetries. This was the topic of Martin Bridson’s highly influential book with André Haefliger, Metric Spaces of Non-Positive Curvature. Geometric Group Theory has led to spectacular advances in the study of 3-manifolds, algorithmic properties of groups, automorphisms of groups, and many other areas.

The workshop will be a major event in the field, presenting an unrivaled opportunity for researchers around the globe to interact and learn about some of the area’s best cutting-edge research through the workshop’s program of talks.

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Venue: Trinity College Dublin

Women in Numbers Europe 5

This workshop aims to foster and support new collaborations for women in number theory. Prior to the conference, the project leaders will design projects based on open research problems in number theory and provide background reading and references for their groups. Each participant will be assigned to a working group according to their research interests and background. The workshop will begin with presentations of projects and end with presentations of initial findings of each project by the youngest member of each group.

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Venue: University of Split

UK Workshop on Spectral Theory

Spectral Theory in the UK has a longstanding history, encompassing the influential works of scientists such as Titchmarsh, Born and Dirac. It naturally sits at the crossroads of numerous branches of mathematics, from the very pure to the more applied side of the subject, including but not limited to operator theory, analysis of PDEs, harmonic analysis, differential geometry, numerical analysis, number theory and mathematical physics.

Research in Spectral Theory is currently expanding rapidly on multiple fronts and experiencing worldwide growth. By bringing together leading experts in the field from all around the world, this workshop will provide an effective environment for exchanging ideas, developing new collaborations, and inspiring future generations in the field, building upon the rich and diverse research landscape in Spectral Theory in the UK.

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Venue: ICMS Edinburgh

Self-interacting Process

This workshop will focus on the analysis of processes which interact locally with their own past. These self-interacting processes arise in a variety of models used in the physical sciences, e.g., describing experimentally observed behaviours in biology (ants preferentially following previous pheromone trails), or physical processes (polymers cannot intersect themselves). They can also appear as mathematical objects, for instance as a description of the effective interaction of a stochastic process in an annealed random environment, or as representations of correlations in random fields (random walk representations of spin systems).  We will concentrate both on specific memory or learning mechanisms that arise in concrete problems, as well as on general theory and methods for studying the effects of that memory.

The areas of interest of the workshop include, but are not limited to, (i) random walks arising in the study of statistical mechanics, both quantum and classical, (ii) stochastic processes in random environments, and (iii) the effects of long-range correlations.

This workshop will be held during the extended programme, Stochastic Systems for Anomalous Diffusion. Professor Gordon Slade will deliver the Clay Lecture

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Venue: Isaac Newton Institute

Structure and Randomness – a celebration of the mathematics of Timothy Gowers

This workshop is a celebration of the mathematics of Timothy Gowers, on the occasion of his 60th birthday. There will be speakers from across the spectrum of Gowers’s mathematical interests, from Banach Space Theory to Combinatorics and Additive Number Theory, Theoretical Computer Science and Pedagogy. 

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Venue: Isaac Newton Institute