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16th ALGA: Commutative Algebra and Algebraic Geometry

Since 1997, the ALGA meetings (Álgebra Comutativa e Geometria Algébrica) have served as a vital forum for the Brazilian community working in Commutative Algebra and Algebraic Geometry, as well as their international collaborators. Over the years, ALGA has played a central role in fostering research, collaboration, and the growth of this vibrant mathematical community.

The 16th edition of ALGA will be a special occasion as the 60th birthday of Eduardo Esteves, a central and beloved figure in the field and an influential presence in the Brazilian algebraic community, is celebrated.

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Venue: IMPA, Rio de Janeiro

Partial Differential Equations, Analysis and Geometry: a Conference in Honor of Sergiu Klainerman’s 75th Birthday

Sergiu Klainerman, Eugene Higgins Professor of Mathematics at Princeton University, has made seminal contributions to nonlinear partial differential equations, analysis, differential geometry, and mathematical general relativity. He pioneered the vector field method for nonlinear wave equations, developed multilinear techniques for low-regularity analysis, and established landmark results on the stability of Minkowski space and Kerr black holes. His work has reshaped PDE, analysis, geometry, and relativity, training and inspiring generations of mathematicians.

This conference will celebrate Sergiu Klainerman’s 75th birthday by bringing together experts to present recent advances in analysis, PDE, geometry, and general relativity, with the aim of fostering interaction across fields and engaging early-career researchers in these exciting developments.

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Venue: IHES

Geometry and Topology in Low Dimensions: Lasting Trends and Emerging Directions

This conference will bring together experts from various fields of low-dimensional topology. Each day will focus on one of the following topics:

  • Exotic phenomena
  • Contact and symplectic geometry
  • Heegaard Floer homology
  • Gauge theory
  • Knots and knotted surfaces

A panoramic talk by a distinguished speaker will introduce the day’s special topic and will be followed by research talks on that topic.

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Image: Wikimedia Commons

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Venue: Hungarian Academy of Sciences

The Gross-Zagier Formula, 40 Years Later

To mark 40 years since the publication of the paper “Heegner points and derivatives of L-series”, a conference will be held with lectures covering a broad range of topics connected with the Gross–Zagier formula, its generalizations, related future directions, and other work that it has inspired.

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Venue: Massachusetts Institute of Technology

Foundations of Computational Mathematics (FoCM 2026)

The FoCM conference series has become a leading international forum for advances on the broad interface between mathematics and contemporary computation. The growing impact of computational tools in areas such as simulation, machine learning, encryption, data management and signal processing has only deepened the need for mathematical understanding of these technologies. FoCM conferences bring together researchers across mathematics, computer science, and related disciplines to explore the fundamental aspects of these connections. The interdisciplinary nature of the event and its emphasis on the foundational aspects distinguish it from other meetings in related fields.

FoCM 2026 will maintain this tradition, offering a unique meeting point for specialists from across the globe. The emphasis will be on multidisciplinary interactions across subjects in an open-minded and congenial atmosphere. Mornings feature plenary lectures from world-renowned experts; afternoons are devoted to parallel workshops of the highest scientific caliber.

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Venue: University of Vienna

Geometric Structures and Stability

In recent years, several significant breakthroughs have occurred in the theory of moduli spaces, Bridgeland stability conditions, K-stability, geometric invariant theory, and the theory of canonical metrics. At the same time, profound new connections have emerged between these diverse areas. This convergence has inspired far-reaching conjectures and ambitious research programs aimed at uncovering the hidden unifying structures underlying these developments. This program seeks to bring together leading experts and early-career researchers from across these fields to explore their synergies and advance these research directions.

A key feature of the program will be the special “Ramanujan Lectures” by Professor Nigel Hitchin. These lectures will weave together the various thematic threads of the conference, offering a comprehensive overview of the deep interconnections between the subjects represented and articulating a vision for their future development.

A central component of the program will be a pedagogical series of four minicourses, each consisting of approximately three lectures, designed to provide foundational background and cutting-edge perspectives on the core themes of the program. They will serve as an accessible entry point for graduate students and early-career researchers, helping to bridge the gap between current research and foundational knowledge. Through these minicourses, participants will gain the tools and conceptual frameworks necessary to engage deeply with the program’s advanced topics and open problems.

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Venue: ICTS-TIFR, Bengaluru

Vector Bundles on Algebraic Curves: Curves, Surfaces and Moduli

The main purposes of the VBAC research group are to stimulate research in the area, map out directions for future investigations, and promote the integration of junior researchers in the community. The VBAC conferences are one of the important instruments for achieving these purposes. The 2026 conference will focus on the following themes: bundles and their generalisations including on higher dimensional varieties, Brill-Noether theory, tropical geometry, as well as the geometry of moduli spaces. These are very active topics of research which interact with many areas of geometry and promise to generate a lot of new activity and progress in the future.

The organisers will bring together many of the established leaders in the field as well as younger researchers who have recently done important work, with a view to both fostering interactions and allowing the participants, especially junior researchers, to get up-to-date on the latest developments and map out directions for future work.

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Venue: Universidad Autónoma de Yucatán

VIII Encuentro Regional de Teoría de Números

The purpose of these meetings is to promote the development of research in number theory, encouraging exchange between researchers and students. The meetings are aimed at researchers, graduate students and advanced undergraduate students with interests in number theory topics.

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Venue: Universidad de la República, Uruguay

Trisections and their Generalizations

The notion of trisection for a smooth 4-manifold, introduced by David Gay and Robion Kirby, is an analogue of a Heegaard splitting in dimension 3, a key notion in the study of 3-manifolds. The theory of trisections provides a new tool to study smooth 4-manifolds, where we are very much in need of new approaches that could eventually lead to progress on some of the most important open problems in topology, such as the smooth 4-dimensional Poincaré conjecture and the smooth 4-dimensional Schoenflies problem. Since the 2016 publication of Gay and Kirby’s original paper on trisections, fundamental questions have been answered and extensive generalizations have been developed, broadening the reach of the field to include contact and symplectic topology, higher dimensional manifolds, piecewise linear topology, and other geometric structures on manifolds.

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Venue: CIRM

Trace Formula, Endoscopic Classification and Beyond: the Mathematical Legacy of James Arthur

James Arthur’s work on the Langlands program has fundamentally shaped the modern theory of automorphic forms and representations. His development of the Arthur-Selberg trace formula provided a rigorous framework connecting the geometric and spectral aspects of automorphic representations. His mathematical legacy includes not only the trace formula but also significant advances in the theory of endoscopy, which connects representations of certain different reductive groups. His current thought provides key insights into Langlands functoriality more generally. The applications of Arthur’s work extend across several mathematical domains. The Arthur-Selberg trace formula has found applications in base change, period relations, and various aspects of the Langlands program. His ideas have influenced developments in p-adic groups, motivic Galois theory, and geometric Langlands theory. His research continues to generate new directions in representation theory and automorphic forms. The stabilization of the trace formula and the theory of Arthur packets remain active areas of investigation, with ongoing applications in number theory and representation theory. The mathematical legacy of James Arthur reaches around the globe, as reflected in this highly international conference to celebrate his work and to discuss recent developments that are central to the Langlands program.

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Venue: Fields Institute

Advances in Representation Theory

The focus of the first week of this conference/ school, June 3-7, will be on Categorification and Symplectic duality and will showcase the participants’ work through a series of lectures on the state of the art of the field, provide an introduction to the area for graduate students and postdocs, as well as create new connections and initiate collaborations through identifying open problems. The second week, June 9-13, will concentrate on the Langlands program and will feature 3 or 4 minicourses, each with three 1-hour talks, 8 invited 1-hour talks, and about 4 contributed 45-min talks. Both weeks will emphasize lectures by junior mathematicians.

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Venue: Northeastern University

Women in Number Theory and Geometry Spring Retreat 2025

This is the fifth edition of the Women in Number Theory and Geometry Spring Retreat (WINGs), aimed at early-career female and gender-minority mathematicians working in number theory and geometry. Following last year’s model, talks will serve the dual role of sharing new research topics in number theory and geometry, at the same time as sharing the journeys of the speakers in their mathematical careers, focusing on overcoming the obstacles arising from being an under-represented gender in the field.

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Venue: Saint Helens, UK