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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.
CMI Enhancement and Partnership Program
Venue: Universidad de la República, Uruguay
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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
Venue: CIRM
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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.
CMI Enhancement and Partnership Program
Venue: Fields Institute
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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
Venue: Northeastern University
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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
Venue: Saint Helens, UK
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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.
CMI Enhancement and Partnership Program
Venue: Cortona, Italy
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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.
CMI Enhancement and Partnership program
Venue: Ohio State University
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The Young Topologists Meeting (YTM) is an annual conference for graduate students, recent PhDs, and other junior researchers in topology, both pure and applied. This meeting is an opportunity for young researchers in topology to share their work and make new connections. In addition to short talks given by the participants and a poster session, the program features three guest lecture series, by Frédéric Chazal (Inria Saclay), Manuel Krannich (Karlsruhe Institute of Technology), and Maria Yakerson (Oxford University/IMJ-PRG).
CMI Enhancement and Partnership program
Venue: KTH/Stockholm University
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The main activity of the conference will be four mini-courses, each consisting of four 60-minute lectures. These lectures are intended to present a panoramic overview of some important developments in their field with the goal of enabling the participants to actively participate in the new directions of research emerging from these developments.
Mini-courses will be supplemented by a number of shorter presentations by plenary speakers. The goal of these presentations is to make the participants aware of recent developments in geometric group theory, which are not covered by the main lectures.
CMI Enhancement and Partnership Program
Venue: University of Copenhagen
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The Joint British Mathematical Colloquium & British Applied Mathematic Colloquium is a major general meeting for both pure and applied mathematicians in the UK. This joint meeting occurs once every five years, and offers a unique opportunity to bring together a large cross-section of the UK mathematical community.
CMI Enhancement and Partnership program
Venue: University of Exeter
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Algebraic Geometry and Commutative Algebra are among the oldest yet most vibrant branches of mathematics, and have important applications throughout the sciences in light of the rich structure and computational elegance of polynomial equations. Over the past decade, these fields have experienced spectacular advances due to the cross-fertilization of techniques and perspectives. These developments have also made significant impacts in other areas, including cluster algebras and number theory. The conference “Singularities in Algebra and Geometry” aims to bring together leading experts in these and related areas to continue the exchange of ideas and methodologies, further enriching this dynamic field. In addition to fostering a broader research community, the conference will offer professional development opportunities for early career researchers, supporting the next generation of mathematicians in their professional growth.
CMI Enhancement and Partnership program
Venue: CIMAT
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The goal of this conference and school is to introduce graduate students, advanced undergraduate students, young researchers, and interested mathematicians in Vietnam, Southeast Asia, and other countries in Asia, to basics of quantum topology and its connection to many branches of mathematics, including low-dimensional topology, representations of quantum groups, combinatorics, and in particular hyperbolic geometry. It will also introduce the audience to applications of quantum topology to various areas of mathematics.
CMI Enhancement and Partnership program
Venue: VIASM