Higher Homotopy Algebras in Topology III will take place in Seville on June 3–5 at IMUS (Mathematical Institute of the University of Seville). The meeting brings together researchers working on higher and homotopical algebra, operads, and their interactions with topology.
This is the third edition of the event 'Higher Homotopy Algebras in Topology' whose first edition took place in Bonn in 2019 and the second one in Dublin in 2020.
Speakers, titles and abstracts:
Oisín Flynn-Connolly (Leiden University)
Combinatorial obstructions to quasi-isomorphism
This talk surveys recent advances in the study of Massey products, a classical algebraic invariant of homotopy types introduced in the 1960s by Massey, and subsequently built upon by May, Retkah and Allday. Recently, thanks to the work of Buijs, Moreno-Fernández and Murillo, these objects have once again emerged as a significant focus of interest in homotopical algebra. Over the past five years, several generalisations have been introduced: 1) operadic Massey products for Koszul operads, 2) cotriple products in positive characteristic, and 3) determinant Massey products capturing more complex relations in CDGAs. In this talk, we survey these recent developments and explain how these obstructions offer a toolkit for treating the associative and commutative quasi-isomorphism problem in various contexts. We conclude with some open problems. Part of this talk is based on joint work with Moreno-Fernández and Muro.
Marie-Camille Delarue (Université Paris Cité)
Stable homology of braided Higman--Thompson groups
Thompson's groups are groups of piecewise linear self-homeomorphisms of an interval where the cut points are dyadic rationals. Braided versions were introduced independently by Brin and Dehornoy. We build a topological model for these groups in the form of categories of 1-"cobordisms" in R^3 where objects are configurations of points and morphisms are paths of configurations which are allowed to collide in certain ways. We then construct a scanning map on these topological models to compute the stable homology of the braided variants of the Thompson groups.
Clovis Chabertier (Université Paris Cité)
Postnikov invariants in rational homotopy theory
Algebraic models for rational homotopy types were proposed by Quillen in 1969 and later by Sullivan in 1977. Quillen’s model, based on Lie algebras, makes it possible to describe simply connected rational homotopy types, whereas Sullivan’s model, based on commutative algebras, describes finite and nilpotent homotopy types. More recently, Buijs, Félix, Murillo and Tanré on the one hand, and Robert-Nicoud and Vallette on the other, extended Quillen’s model to the non-simply connected case.
In this talk, we will present a theory of Postnikov invariants for complete (homotopy) Lie algebras that is compatible with the integration functor of Robert-Nicoud and Vallette. We will then deduce an integration of Chevalley–Eilenberg cohomology into the cohomology of spaces with local coefficients.
Gereon Quick (Norwegian University of Science and Technology)
Julian Holstein (Universität Hamburg)
TBA
C*-categorical prefactorization algebras of superselection sectors
A major result by Doplicher, Haag, and Roberts in algebraic quantum field theory shows that one can derive particle statistics from local quantum observables using first principles. While this may sound like a string of technical jargon, the core mathematical idea is neat: there exists a braided (or symmetric) monoidal category of superselection sectors—interpreted as charges or direct summands of the Hilbert space of states—that can be constructed entirely from the net of algebras of local observables. The statistics (i.e. what distinguishes bosons from fermions) of an irreducible sector can then be extracted from the action of the braid (or symmetric) group on tensor powers of that sector within the aforementioned category.
In this talk, we aim to introduce these ideas to the audience, assuming no prior background. We will also present a new construction of the braided monoidal category of superselection sectors, employing tools from higher algebra, which makes transparent the geometry/topology underlying this theory. This is based on joint work with Benini, Naaijkens, and Schenkel [arXiv:2505.07960] and with Benini, and Schenkel [arXiv:2604.24865].
Martin Markl (Institute of Mathematics – Czech Academy of Sciences)
Homotopy category of homotopy algebras (after B. Vallette)
I will explain that the category of strongly homotopy algebras over quadratic Koszul operads (which includes the Three Graces: A-infinity, L-infinity, and C-infinity) possesses an "almost" model structure, such that the localization obtained by inverting weak equivalences is equivalent to the category of suitable homotopy classes. The central reference for the material of my talk is B. Vallette: Homotopy theory of homotopy algebras, Ann. Inst. Fourier 70(2), 2020, 683-738.
Bruno Stonek (University of Warsaw)
TBA
Daria Pavlova (Institute of Mathematics – Czech Academy of Sciences)
TBA
Joost Nuiten (Université de Toulouse)
PD operads and partition Lie algebras
Partition Lie algebras have been introduced by Brantner and Mathew as certain homotopy theoretic refinements of dg-Lie algebras that control deformation problems in positive characteristic. In this talk, I will try to explain how partition Lie algebras (and other types of Lie algebras) can be understood as certain types of algebras over a PD operad, a refinement of the usual notion of an operad. A version of Koszul duality for such PD operads gives rise to Lie-algebraic descriptions of various types of formal problems appearing in derived algebraic geometry. Based on joint work with Lukas Brantner and Ricardo Campos.
Registration:
There will be a registration fee of €95 to cover the costs of coffee breaks, lunches on Wednesday 3, Thursday 4, and Friday 5 at the university canteen, the social dinner on Thursday evening, and other administrative expenses. This is the reduced fee, and all participants can directly choose this option.
The registration deadline is May 12.
Schedule:
The talks will take place on Wednesday afternoon, Thursday morning, and Friday morning.
On Wednesday and Friday, the talks will take place in Seminar Room II at IMUS. Lunch will be at the canteen of the Instituto de Idiomas (in another part of the same building). Lunch is included upon presentation of a ticket. To obtain the ticket, you may come to IMUS to register before lunchtime, or contact the organizers if you do not have time to register before lunch.
On Thursday, since it is a local holiday, IMUS will be closed, and the activities will take place in Room 2.1 of the Faculty of Mathematics. Since the canteen will also be closed, lunch will take place at the nearby Bar Metropolis 1985.
Thursday afternoon will be free, and the social dinner will take place at 19:30 at the restaurant Salsamento.
Venue:
IMUS (Instituto de Matemáticas de la Universidad de Sevilla)
https://maps.app.goo.gl/r6SUhmWHGpDrDPvTA
Accommodation:
Here is a list of possible accommodations close to IMUS (approximately 5–15 minutes on foot).
Affordable student residences:
• Colegio Mayor Hernando Colón
• R.U. Rector Estanislao del Campo
• Hubr Xior Student Residence Seville
• Residencia Yugo Los Bermejales
Nearby hotels:
About Sevilla:
Sevilla is a wonderfully lively and very popular tourist destination in Spain, known for its monumental heritage, beautiful squares, and distinctive atmosphere.
A few highlights
The Cathedral area is the heart of the historic centre, and nearby you will find the Catedral and its tower, the Giralda, the Real Alcázar, and the Archivo de Indias. Other well-known places worth mentioning include Barrio de Santa Cruz, Plaza de España / Parque de María Luisa, and Triana.
Getting around
Sevilla is very walkable in the centre, and public transport makes it easy to move between areas. The university campus is slightly outside the city centre, so here are a few convenient ways to reach the Cathedral area:
Bus 34 (TUSSAM) from Reina Mercedes to Prado de San Sebastián.
Walking through Parque de María Luisa: about a 45-minute walk from IMUS to the Cathedral. This also gives you the opportunity to visit Parque de María Luisa and its famous Plaza de España, built for the 1929 Exposition.
By bike: Cycling is also a very practical way to get around. Sevilla has an extensive network of cycle lanes. The public bike system SEVICI has many stations across the city, and you can pick up and return bikes at different locations. It costs €2.59 per day or €13.33 for 7 days.
Acknowledgements:
The conference is hosted by IMUS (Mathematical Institute of the University of Sevilla), and we warmly thank IMUS for its essential support in the organization of the event. We also gratefully acknowledge the support and funding provided by the University of Sevilla and the University of Malaga, as well as by the research project Teoría de homotopía superior (TEHOS, PID2023-149804NB-I00 ). With special thanks to Felix Wierstra, a dear friend and former co-organizer, for his foundational contributions to this event.
Organizers:
Mario Fuentes Rumí (mario.fuentes.rumi@gmail.com)
José Manuel Moreno Fernández (josemoreno@uma.es)