This international conference focuses on the interplay between modular forms, geometry, complex analysis, dynamical systems, and combinatorics. Modular forms encode deep arithmetic information through L-functions and Galois representations. Complex analytic methods (Bergman spaces, growth estimates, analytic continuation) investigate hyperbolicity in complex geometry. Dynamics such as Perron numbers and β‑expansions illustrate how symbolic dynamics encodes arithmetic information. Special functions (theta functions, hypergeometric series, orthogonal polynomials) and combinatorics serve as a bridge linking these areas.

The nineteenth annual Binghamton University Graduate Combinatorics Algebra and Topology Conference (BUGCAT Conference) will meet November 21-22, 2026 at Binghamton University. Graduate students at all levels, as well as faculty, are invited to give a 20-minute talk; talks may be expository or on current research. This year, we have three distinguished keynote speakers: Casey Donoven (Montana State University Northern), Ben Knudsen (Colorado State University) and Pablo Soberón (City University of New York).

NeuralFEM Workshop 2026

Strasbourg, France — 14–18 December 2026 IRMA, University of Strasbourg

The NeuralFEM workshop is the first meeting of the NeuralFEM MATH-AmSud project (Uruguay, Colombia, Chile, France), devoted to the certified approximation of partial differential equations by neural networks.

Topics

• Neural network methods for nonlinear and non-smooth problems (contact, plasticity, fractional operators) and hybrid neural network / finite element schemes
• A priori error analysis of network approximations
• A posteriori error estimation and adaptive strategies
• Reduced basis methods
• Applications in biomechanics and biomedicine

Participation

The workshop is open to everyone working on these questions. Participation is free, but registration is mandatory before 30 October 2026. Contributed talks are welcome.

Scientific committee

• Rodolfo Araya (Universidad de Concepción, Chile)
• Manuela Bastidas (Universidad Nacional de Colombia, Medellín)
• Franz Chouly (Universidad de la República, Montevideo, Uruguay)
• Michel Duprez (Inria, Strasbourg, France)
• Virginie Ehrlacher (CERMICS, École nationale des ponts et chaussées, France)

More information

• Website: https://michelduprez.fr/neuralFEM/
• Registration: https://michelduprez.fr/neuralFEM/registration.html
• Contact: neuralfem-workshop@inria.fr

We are delighted to announce the Second International Conference on Advances in Operator Theory and Applications (ICAOTA'2027), which will be held from March 22 to 24, 2027, in the beautiful coastal city of Hammamet, Tunisia.

This conference will gather renowned experts, emerging researchers, and professionals to explore cutting-edge advancements in operator theory and its wide-ranging applications. Set against the stunning Mediterranean backdrop of Hammamet, ICAOTA'2027 offers a unique blend of academic excellence and cultural immersion.

The deep connection between geometry and physics dates back to ancient times. Applications of calculus, differential equations, and other ideas from analysis to geometry and physics began at the birth of modern science with the foundational works of Newton 350 years ago, and has since continued unabated.

The specific subfield of Differential Geometry that is commonly called Geometric Analysis (previously also referred to as global analysis) exploded onto the scene in the 1970s, due in large part to the solution by Shing-Tung Yau of the celebrated Calabi conjecture using methods of elliptic partial differential equations, demonstrating the existence of a particular class of geometric structures (now called Calabi-Yau structures) on compact manifolds satisfying certain conditions. Completely unexpectedly, these Calabi-Yau structures turned out to be exactly the objects required by theoretical physicists in the 1980s to establish the link between abstract string theory and 4-dimensional particle physics.

It was also the 1970s that witnessed the explicit reconciliation between geometry and physics, two subjects which had been inextricably intertwined since antiquity but had undergone an estrangement in the 20th century due to the increasing abstraction in pure mathematics. This remarriage between the disciplines was due to interactions between mathematicians such as Atiyah, Bott, Hitchin, Simons, and Singer with physicists such as Yang and Mills, which resulted in the discovery that the mathematical ideas of connections and curvature on vector bundles was essentially identical to the physical ideas of gauge potentials and gauge fields. This realization ignited the area of mathematical gauge theory, leading to spectacular work of Donaldson, Taubes, Uhlenbeck, Yau, and others in the 1980s and beyond.

Cross-pollination between geometry and physics continues and is increasing. One notable aspect of this is the phenomenon known as mirror symmetry, which mysteriously relates topologically distinct 6-dimensional Calabi-Yau manifolds in complicated ways, involving algebraic geometry, symplectic geometry, differential geometry, and homological algebra. Significant advances have been made in the understanding of mirror symmetry, but much remains to be done. One approach, known as the Strominger–Yau–Zaslow conjecture, crucially involves the notion of special Lagrangian submanifolds, which are particular first order volume minimizing examples of submanifolds with vanishing mean curvature. Similar ideas are expected to be manifest in 7 and 8-dimensional geometries related to the octonions. Another important development in the geometry/physics interactions is the AdS/CFT correspondence, which relates quantum field theories with gravity theories in one higher dimension.

This Thematic Program on Geometric Analysis and Mathematical Physics will focus on three broad areas of active current research at the interface of geometric analysis and mathematical physics:

• Calabi-Yau manifolds and Special Lagrangian submanifolds

• Special geometries in dimensions 6,7,8

• Mathematical aspects of holography

These three focus areas will be the subject of three week-long workshops, respectively.

FDIS is an international conference series held approximately every two years, each time in a different location. Previous editions took place in Jena (Germany, 2011), Luminy (France, 2013), Będlewo (Poland, 2015), Barcelona (Spain, 2017), Shanghai (China, 2019), Tel Aviv (Israel, 2022), Antwerp (Belgium, 2023), and Guanajuato (Mexico, 20259). The Tel Aviv and Guanajuato editions were organised in partnership with the Clay Mathematics Institute (CMI); the Tel Aviv meeting was postponed from 2021 due to the pandemic.

The guiding idea of FDIS is that major advances in integrable systems often come from researchers whose main expertise lies in neighbouring disciplines, including differential and algebraic geometry, symplectic geometry, partial differential equations, and mathematical physics. FDIS brings these communities together to exchange methods, discuss open problems, and initiate collaborations. Leading specialists in integrable systems are also invited to present broader perspectives and highlight promising research directions.

The conference welcomes contributed talks and posters. Generous breaks encourage the informal discussions that have become a hallmark of the series.

FDIS 2027 will take place at the Research and Conference Centre of the Institute of Mathematics of the Polish Academy of Sciences in Będlewo, near Poznań, in partnership with CMI.

Organizing Committee: Andrzej J. Maciejewski (University of Zielona Góra, Poland), Vladimir Matveev (Friedrich Schiller University Jena, Germany), Maria Przybylska (University of Zielona Góra, Poland), Sergei Tabachnikov (Pennsylvania State University, USA)

Research in Geometric Analysis requires a lot of background knowledge to get started in, including partial differential equations and functional analysis, differential geometry, algebraic topology, and often also employs tools and techniques from algebraic geometry, especially in the context of Kahler and Calabi-Yau geometries. The aim of this summer school is to prepare the participants for the rest of the program and to give them a first-rate head-start for their future research careers.

Confirmed Lecturers:

Bobby Acharya (ICTP)

Lara Anderson (Virginia Tech)

Lorenzon Foscolo (Sapienza Roma)

Sebastien Picard (UBC)

Thomas Walpuski (Humboldt Berlin)

GAFA 2027 is an international conference on Geometric and Functional Analysis, taking place on 24–27 August 2027 in Astana, Kazakhstan, at the Kazakhstan Branch of Lomonosov Moscow State University. The conference is organised in partnership with the Clay Mathematics Institute.

The conference brings together researchers working in functional analysis, geometric analysis, and differential geometry. These areas have many deep connections, and important problems in one field can often be approached using methods and ideas developed in another. The main goal of GAFA 2027 is to encourage interaction between these research communities, facilitate the exchange of ideas and techniques, and stimulate new collaborations.

The scientific program will feature plenary and invited lectures by leading international researchers, including survey talks highlighting connections between different areas of analysis and geometry. Speakers will be encouraged to discuss recent developments, important open problems, and promising directions for future research.

A special feature of GAFA 2027 will be thematic sessions celebrating the anniversaries of two distinguished mathematicians: Erlan Nursultanov, known for his contributions to functional analysis, and Alexey Bolsinov, known for his work in differential geometry, integrable systems, and geometric analysis.

The conference strongly encourages active participation. Researchers are invited to apply to give contributed talks or present posters. Particular attention will be given to early-career researchers, including graduate students and postdoctoral fellows, with dedicated sessions providing opportunities to present their work.

The organisers aim to create a stimulating and collegial scientific atmosphere, with ample opportunities for informal discussions, exchange of ideas, and establishing new research collaborations.

Calabi-Yau metrics and special Lagrangians submanifolds are some of the most fundamental objects in complex geometry and geometric analysis, and they have been a very active subject in recent years. Insights from physics have led to deep conjectures regarding the existence and behaviour of Calabi-Yau manifolds and their special Lagrangian submanifolds. The Strominger–Yau–Zaslow (SYZ) conjecture, originating from string theory, predicts the existence of special Lagrangian torus fibrations within Calabi-Yau manifolds under “large complex structure limits” and offers insight into how these can be used to understand Mirror Symmetry of Calabi-Yau manifolds, while the Thomas–Yau conjecture predicts that existence of special Lagrangians submanifolds is governed by stability conditions. There have been many important developments in these directions in the past few years.

The SYZ conjecture has seen some spectacular progress in recent years due to the breakthroughs of Yang Li, which established a generic form of the conjecture for a large class of Calabi-Yau manifolds, while significant progress was also made towards the Thomas-Yau conjecture, including the work of Lotay–Schulze–Szekelyhidi on the singularities of Lagrangian mean curvature flow, and recent novel constructions of special Lagrangians due to Li and Chiu–Lin following a program of Donaldson and Scaduto. Other important recent developments include a refined understanding of Calabi-Yau metrics under “small complex structure degenerations” due to Sun–Zhang, new analytic developments leading to a regularity theory of singular Calabi-Yau metrics by the work of Guo–Phong–Song–Sturm and Szekelyhidi, and progress on constructions of complete Calabi-Yau metrics of Tian–Yau type by Collins–Li, Collins–Tong–Yau, and Collins–Tong. This is an exciting time for this subject. The tools developed in the past ten years have led to astonishing progress on many old questions, and a long list of conjectures still leaves open many avenues for future investigation.

The goal of this workshop is to bring together the experts in complex geometry, PDEs, and physics, alongside junior researchers in the field, to explore these developments, exchange ideas, and foster new research directions.

The goal of this workshop is to initiate a dialogue between mathematicians and physicists working to understand mathematical aspects of the AdS / CFT correspondence. Some concrete goals include the construction of simple examples of AdS3 / CFT2 correspondence, the development of the mathematical theory of topological twists of AdS / CFT and the construction of new N = 1 CFTs arising from quiver gauge theories dual to non-toric Calabi-Yau cones.

Special geometry in dimensions 6,7,8 is a vibrant research area comprising a global community of researchers, and is greatly inspired by developments in mathematical physics. The field brings together diverse techniques and perspectives from differential geometry, algebraic geometry, gauge theory, geometric analysis, topology, homotopy theory, string theory and gravity. In particular, the analytic approaches that have been successfully applied include both elliptic methods (such as glueing constructions) and parabolic methods (geometric evolution equations). By combining this wide variety of methods, the field has seen important progress in recent years on a number of fronts, including on constructing examples and key steps towards various conjectures and open problems stemming from the celebrated Donaldson-Thomas programme. This programme aims to construct enumerative and gauge-theoretic invariants in dimensions 6,7,8 that generalize the analogous theories in dimensions 2,3,4 that were enormously influential in the development of geometry and topology in the 1980s and 1990s (such as Gromov-Witten invariants from symplectic topology, Floer homology of 3-manifold, and Donaldson and Seiberg-Witten invariants of 4-dimensional gauge theories.) The study of the moduli space of holonomy G2 metrics using analytic invariants is another important recent breakthrough, as was the analysis of adiabatic limits of coassociative fibrations.

However, many major challenges remain, particularly in concretely realising geometry problems arising via considerations from physics, as well as in the fundamental existence questions pertaining to special geometries. For example, the Hull-Strominger system for non-Kahler Calabi-Yau manifolds, and the analogous heterotic G2 system in 7 dimensions are extremely active areas of current research closely connecting mathematicians and physicists. Moreover, recent research and workshops in the field have demonstrated that there are many new avenues that have yet to be explored, which will provide new insight and have the potential to lead to significant progress in the area.