Date: August 19, 2026 (Wednesday) at 4PM (UK time)

Speaker: Prof. Marc Lackenby, University of Oxford, UK

Topic: Knots, Links, and Polynomial Bounds

About the Talk: Prof. Marc Lackenby is a leading mathematician in topology, geometry, and group theory, with major contributions to knot theory and low-dimensional topology. In this talk, he will discuss Reidemeister moves, the elementary transformations that relate different diagrams of the same knot or link, and the question of how efficiently one can pass between such diagrams. The talk will highlight his polynomial bounds for simplifying diagrams of the unknot, and explain recent work extending these ideas to every fixed link type. It will also describe the consequences for the computational complexity of recognizing knots and links. See the blog announcement

https://functor.network/user/3333/entry/1896

of this talk for more details.

Link to join: At the scheduled time, joint the talk here: link. No registration required.

CAIM series provide a forum for the review of the recent trends in applied and industrial mathematics either from a qualitative or from a numerical point of view. Computer science communications are welcome. Since theoretical studies find sooner or later their applicability, the conference has also sections for the theoretical branches of mathematics like algebra, probability theory, mathematical statistics or geometry. A special section of the conference is dedicated to the mathematical teaching.

The conference Moduli and Friends II will take place at the Simion Stoilow Institute of Mathematics of the Romanian Academy (IMAR), Bucharest, during the week 24-28 August 2026.

This conference is focused on topics related to moduli spaces, including configuration spaces, hyperplane arrangements, homological representations and geometric aspects of quantum invariants. The goal is to bring together researchers from different domains under the general umbrella of "moduli spaces" and to encourage the discovery of new connections between these areas. It is a successor to the conference "Moduli and Friends", which took place in September 2023. For more details, see the conference website: https://sites.google.com/view/moduliandfriends2

Registration is open until 10 August 2026 or until the maximal number of participants is reached. We have (limited) funding to cover accommodation costs. If you would like to request funding for accommodation, please register by the earlier deadline of 15 June 2026.

The invited speakers are:

• Takuro Abe (Rikkyo University)
• Enrique Artal Bartolo (Universidad de Zaragoza)
• Karin Baur (Ruhr-Universität Bochum)
• Valentina Beorchia (Università di Trieste)
• José Ignacio Cogolludo Agustín (Universidad de Zaragoza)
• Adrian Diaconu (University of Minnesota)
• Olivia Dumitrescu (University of North Carolina at Chapel Hill)
• Louis Funar (Université Grenoble Alpes)
• Pierre Godfard (University of North Carolina at Chapel Hill)
• Rinat Kashaev (Université de Genève)
• Aaron Landesman (Harvard University)
• Ishan Levy (Institute for Advanced Study)
• Erik Lindell (University of Copenhagen)
• Gwénaël Massuyeau (Université Bourgogne Europe)
• Catherine Meusburger (Universität Erlangen-Nürnberg)
• Rosa Maria Miró-Roig (Universitat de Barcelona)
• Motohico Mulase (University of California, Davis)
• Jun Murakami (Waseda University)
• Sam Nariman (Purdue University)
• Ralf Schiffler (University of Connecticut)
• Andreas Stavrou (University of Chicago)
• Ulrike Tillmann (University of Oxford / Isaac Newton Institute, Cambridge)
• Christine Vespa (Aix-Marseille Université)

Organisers:

• Cristina Anghel (Université Clermont Auvergne, France / IMAR, Romania)
• Anca Măcinic (IMAR, Romania)
• Martin Palmer (IMAR, Romania)
• Arthur Soulié (CNRS - Université Caen Normandie, France)

This summer school aims to train a new generation of young researchers in subjects at the interface of complex differential geometry, geometric analysis, and algebraic and arithmetic geometry.

Mini-course speakers:

• Dan Abramovich, Brown University
• Benoît Claudon (to be confirmed), Université de Rennes
• Hélène Esnault, Freie Universität Berlin
• Philippe Eyssidieux, Université Grenoble-Alpes
• Robert Lazarsfeld, Stony Brook University

The Annual International Conference of the Georgian Mathematical Union was established in 2010 and has been held traditionally at Batumi Shota Rustaveli State University. Batumi is the city of Georgia and the capital of the Autonomous Republic of Adjara. It is located along the coast of the Black Sea in the southwest region of Georgia. In accordance with recent developments, the conference has been conducted in a hybrid format since 2021. The purpose of the conference is to bring together mathematicians from various fields to present their original research results and provide opportunities to establish new connections within the fields of pure and applied mathematics, as well as science, engineering, and technology. The conference also provides valuable networking opportunities for you to meet great personnel in these fields.

The conference sections: Algebra and Number Theory; Differential and Integral Equations, and Their Applications; Geometry and Topology; Logic, Language, Artificial Intelligence; Mathematical Education and History of Mathematics; Mathematical Logic and Discrete Mathematics; Mathematical Modeling and Numerical Analysis; Theoretical Physics; Probability Theory and Statistics, Financial Mathematics; Real and Complex Analysis.

Around 60 years ago, pseudodifferential operators were introduced as a tool for singular integral and elliptic problems in PDE. They quickly became relevant due to their usefulness, exemplified by their role in the Atiyah–Singer index theorem. In the subsequent years, the theory has found new depths and domains of application, and is today very much alive, in particular in the context of singular analytical and geometrical structures.

The goal of this conference is to bring together experts and young researchers from various backgrounds who are interested in the use of pseudodifferential operators in singular settings to discuss their recent projects and results, and foster the communication between the diverse perspectives on the topic.

The ATSF 2026 Conference is the 9th event of the Approximation Theory and Special Functions (ATSF) series. The conference aims to bring together researchers working in approximation theory, special functions, numerical analysis, and related areas, fostering interaction between theoretical developments and applications.

The aim of the summer school is to bring together early career researchers working in motives (in a broad sense) and neighbouring areas (including but not limited to algebraic geometry and number theory), who want to learn more about the subject and its applications.

The event will consist of four mini-courses. There will be an introductory course:

• Introduction to motives (Alexander Vishik);

and three topic-focused courses on the following themes:

• Motives in algebraic geometry and moduli theory (Victoria Hoskins);
• Applications of motives to number theory and periods (Francis Brown);
• Introduction to (motivic) tensor-triangular geometry (Martin Gallauer).

We will also feature a handful of contributed research talks from participants.

We kindly thank our sponsors for supporting this event:

• Heilbronn Institute for Mathematical Research;
• UKRI/EPSRC Additional Funding Programme for Mathematical Sciences;
• Foundation Compositio Mathematica;
• K-Theory Foundation.

Please share this opportunity with potentially interested students and postdocs.

The application deadline for the Heidelberg Laureate Forum (HLF) 2026 is Feb 11, 2026. See https://www.heidelberg-laureate-forum.org/ for details.

The HLF offers a rare opportunity for students, PhD candidates, and postdocs in mathematics and computer science to spend a week interacting with Abel Prize, Fields Medal, Turing Prize, ACM Prize in Computing, IMU Abacus Medal and Nevanlinna Prize laureates, as well as with other outstanding international early-career mathematicians and computer scientists from around the world, and a variety of distinguished guests. The program includes lectures, workshops, panel discussions, networking events, and more. All local expenses (hotel and meals) are covered and an option to apply for travel funding exists if needed.

Participating in an HLF is a wonderful opportunity in many ways.

Spatial structures appear throughout mathematics, connecting topology, combinatorics, and geometry in surprising and beautiful ways, capturing how objects sit and interact within the spaces around them.

This workshop aims to bring together researchers from a range of backgrounds to strengthen the community and to discuss developments in the theory of spatial structures, with a particular focus on topological graph theory, spatial graphs, braids, and periodic tillings.

The international scientific conference organised by the Kaunas University of Technology (KTU) and the Georg-August-Universität Göttingen (Germany) is dedicated to the memory of Professor Dr. Hermann Minkowski. The conference will be held on September 23-25, 2026 in the historic Aula, A. Mickevičius st. 37, Kaunas. The University of Lithuania was solemnly opened in this Aula in February 16 1922. Summaries of the accepted presentations will be published in an e-publication, which will have an ISBN. The selected papers of the Conference will be published in the Lithuanian Mathematical Journal, Editor-in-Chief Olga Štikonienė, https://link.springer.com/journal/10986. All papers will be peer-reviewed. The Special Issue will be coordinated by Guest Editors J. Brüdern, D. Bahns, M. Kopa and M. Ragulskis.

Analysis and Geometry at the Crossroads

@University of Minho (Braga, Portugal) :: September 30 - October 2, 2026

This conference is conceived as a platform for sustained interaction between Analysis and Geometry, with particular emphasis on the structural, analytical, and geometric frameworks that connect these two areas of mathematics.

Rather than focusing on isolated topics, the meeting aims to encourage a broad exchange of ideas and methods, reflecting the diversity and depth of contemporary research at the interface of these fields.

A central goal of the conference is to bring together researchers at different stages of their academic careers. The programme will include contributions from doctoral students and early-career researchers working on topics related to Analysis and Geometry, as well as invited lectures by senior mathematicians of established international reputation.

This balance is intended to promote rigorous scientific discussion while also supporting the integration of younger researchers into the international research community.

The conference is open to the wider mathematical community with no registration fees.

Plenary Speakers:

Ilka Agricola, Philipps University of Marburg, Germany

Catalin Badea, University of Reading, UK

Miguel Brozos-Vásquez, University of Coruña, Spain

Viviana del Barco, State University of Campinas, Brazil

Persi Diaconis, Standford University, USA

Francisco Gancedo, University of Seville, Spain

Karl Grosse-Erdmann, University of Mons, Belgium

Ines Kath, University of Greifswald, Germany

Registration is now open.

July 15, 2026 — Deadline for contributed talks

September 17, 2026 — Deadline for posters and general participation

All information can be found on the conference website:

https://agcrossroads2026.keniercastillo.com

The British Topology Meeting is the UK’s annual topology conference, bringing together researchers in algebraic, geometric, and low-dimensional topology, as well as related areas. The programme will feature six plenary lectures by Naomi Andrew, Clark Barwick, David Gabai, John Greenlees, Sungkyung Kang, and Clara Löh, alongside several contributed talks.

It is a pleasure to invite you to Advances in Modern Topology 2026, a conference dedicated to fostering cooperation and collaboration among researchers in Algebraic Topology, Algebraic Geometry, and their interdisciplinary applications.

This year’s edition will be held for the first time in the beautiful city of Podgorica, hosted at the prestigious Main Building of the Montenegrin Academy of Sciences and Arts.

Conference Details:

Location: Podgorica, Montenegro

Venue: Montenegrin Academy of Sciences and Arts

Website: https://tinyurl.com/MoTop2026

Invited Speakers include: Anthony Bahri, Djordje Baralić, Ulrich Bauer, Victor Buchstaber, Vladimir Dragović, Alexandar Gaifullin, Jelena Grbić, Shintaro Kuroki, Mikiya Masuda, Taras Panov, Petar Pavešić, Stephen Theriault, and Rade Živaljević. ( * to be confirmed )

Key Deadlines:

Registration Deadline: Friday, August 01, 2026

Abstract Submission Deadline: Friday, August 31, 2026

How to Register: Please complete your registration and abstract submission via the following form: https://forms.gle/Fk1rVbHeUYNRgwCN9

We look forward to welcoming you to Podgorica for what promises to be a stimulating scientific gathering. Should you have any questions, please feel free to contact the organizing committee at [email protected].

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.

For further information, please visit the website

This workshop is sponsored by AIM, NSF, and the Simons Foundation. This activity, which is a part of the New Structures in Low-dimensional topology collaboration, will be devoted to developing an approach to q-series invariants of 3-manifolds and knots via 2-representation theory. Verma modules play a key role in the construction of an analogue for a generic parameter q of the Reshetikhin-Turaev invariants. The workshop will consider the categorification of Verma modules constructed by Naisse-Vaz, their duals and tensor products, as well as braidings and traces. The goal is to apply these constructions to 3-dimensional topology and relate them to known invariants.

Main topics for the workshop are:

• determination of tensor products of 2-Verma modules, braidings and traces
• relation with the Dupont-Naisse construction
• extension to the case of tensor products of 2-Verma modules and their duals
• construction of homological invariants of particular knots and 3-manifolds

This is the sixth workshop on Computational Persistence (ComPer 2026). Invited Speakers: Erin Chambers, Chao Chen, Dmitriy Morozov, Don Sheehy, and Bei Wang. We invite submissions for contributed talks and poster presentations on all aspects of computational topology and topological data analysis. Submission Deadline: August 7, 2026. Notifications: September 4, 2026.

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.

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)

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.