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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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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.

CMI Enhancement and Partnership Program

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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.

CMIU Enhancement and Partnership Program

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Venue: CIMAT, Guanajuato, Mexico

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.

CMI Enhancement and Partnership Program

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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.

CMI Enhancement and Partneship Program

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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.

CMI Enhancement and Partnership Program

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Venue: Saint Helens, UK

A Tour through Algebraic Geometry

Algebraic geometry, a foundational discipline that studies geometric objects defined by polynomial equations (algebraic varieties), continues to be one of the most vibrant and dynamic areas of contemporary mathematics. It is at the forefront of numerous exciting developments, many of which intersect with and draw on other branches of mathematics, including topology, differential geometry, and commutative algebra. These interactions foster new insights and advance our understanding of complex geometric and topological structures.

This conference, celebrating Alessio Corti’s contribution to the field of algebraic geometry, will include topics that reflect the breadth of these developments, showcasing cutting-edge research at the confluence of algebraic geometry and related fields. In particular, recent advances in the theory of moduli spaces, singularity theory, and mirror symmetry are reshaping our understanding of algebraic varieties, with profound implications not only within mathematics but also in related areas of physics and string theory. The growing synergy between algebraic geometry and adjacent disciplines, such as category theory and representation theory, has opened up fresh avenues for exploration, and has led to new tools and techniques that promise to yield deeper results in both pure and applied mathematics.

The conference will highlight these trends, which attest to the continued relevance and vitality of algebraic geometry today, and have grown out of foundational work carried out by Corti among others. The talks and discussions will present some of the most exciting open problems in the field and explore future directions of research in algebraic geometry in its dialogue with other areas of mathematics.

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Venue: Cortona, Italy

Arithmetic, K-theory, and Algebraic Cycles

The conference will feature several key-note talks which will survey the historical background, current state of development and prospects for future progress in all of the focused areas. These talks will provide an opportunity to take a longer view than is customary at many research conferences and should be particularly valuable for young researchers. In addition, there will be a number of talks concerning recent developments in all the focused areas. We plan to fund a number of young people, at both the post-doctoral and advanced graduate student level so that the conference will serve to stimulate future interest in these areas.

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Venue: Ohio State University