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.

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

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).

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.

Tech Topology brings together researchers in low-dimensional, geometric, contact, and symplectic topology for a weekend of invited talks, lightning talks, and mathematical conversation at Georgia Tech. This year's Tech Topology Conference will be from December 11 to 13. We have a great lineup this year:

• Eduardo Fernández Fuertes (Georgia Tech) • David Gay (University of Georgia) • Sherry Gong (Texas A&M) • Mark Hughes (BYU) • Isabella Kahn (Georgia Tech) • Adam Levine (Duke University) • Luya Wang (IAS)

You can find out more at

  ttc.gatech.edu

(If you have recently visited the website above, you might have the forwarding link cached to go to last year's website. Try clearing the cache on your browser or use the direct link https://johnetnyre.github.io/TechTopology/ )

Even if you do not need funding, please register if you plan to attend any of the talks so we can add you to the participants page and add you to the conference email list (and make sure we have enough food). If you would like to give a lightning talk, you can also apply for that on the web page too.

Dear colleagues,

This is the second announcement of our workshop

Synthetic Spectra

at the Bergische Universität Wuppertal, 15–19 March 2027.

The category of synthetic spectra is an exciting new tool in homotopy theory that categorifies the Adams spectral sequence. The workshop is aimed at both the theory and computational sides of this new tool and the interplay between them.

There will be two lecture series, of three talks each, by Irakli Patchkoria (Aberdeen) on the theoretical side and Dan Isaksen (Wayne State) on the computational side. The remaining talks are given by participants: Monday is devoted to background talks, and the rest of the week is built around two participant-given series, one on Lin–Wang–Xu's solution of the last Kervaire invariant problem and one on Burklund's multiplicative structures on Moore spectra.

The full program, abstracts, and registration form can be found on the workshop webpage:

https://sites.google.com/view/workshop-ss2027/

Participants are warmly encouraged to give a talk, and you can apply to do so on the registration form. You may submit written material in support of your application — a paper, a section of a thesis, lecture notes, or anything else that helps us judge how you write and explain mathematics.

Funding is available to support participants, with priority for graduate students and postdocs without access to their own travel money. You can apply for this on the same form.

Two deadlines: 1 November 2026 — to apply to give a talk (and for funding). 1 March 2027 — to register to attend.

Giving a talk is not required for participation. We expect the audience to be mainly PhD students and postdocs, and we assume familiarity with spectra, ∞-categories and spectral sequences, but nothing beyond that.

The workshop is supported by the topology group at Wuppertal and by GRK 2240.

We hope to see many of you in Wuppertal in March.

With best wishes, Christian Carrick, Sven van Nigtevecht, and Fei Ren

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.