Higher Categories and Applications July 5–16, 2027 Buenos Aires & La Plata
Higher Categories and Applications
The inaugural IAS/South America two-week school, Higher Categories and Applications, will take place at two sites: July 5–9, 2027, at the Universidad de Buenos Aires, and July 12–16, 2027, at the Universidad Nacional de La Plata.
Higher category theory gives a flexible language for working with objects "up to equivalence," generalizing the notion of homotopy in topology. Over the past two decades, it has featured in significant applications in many areas of mathematics, including homotopy theory, representation theory, algebraic and symplectic geometry, and number theory. This school brings together leading researchers, senior and junior, who have both laid the foundations of the subject and applied it creatively elsewhere in mathematics, to introduce participants to its core concepts and modern research directions.
Format at a Glance
Online Prequel Lecture Series
In June 2027, prior to the two-week in-person series of minicourses in Argentina, accepted participants will complete three elementary courses online to acquire the necessary background.
- Lecturers and Minicourses
- Guido Arnone (IMaS, Universidad de Buenos Aires): Homological Algebra and Infinity Categories
- Carlos Di Fiore (Universidad de Buenos Aires): Background on Sheaf Theory
- Devarshi Mukherjee (University of Aberdeen): Homotopical Algebra in Functional Analytic Settings
- Format: Four 60-minute lectures per minicourse (via live Zoom or recordings viewed asynchronously)
In-Person Lecture Series
- Two weeks, Monday to Friday, with Friday afternoon, July 9, Argentina's Día de la Independencia, and Wednesday afternoon, July 14, along with weekends, left unscheduled.
- Each minicourse includes four lectures concentrated within a single week.
- Lecture notes will be published.
- Monday-Friday Teaching Blocks: 9:00–10:30, 11:00–12:30, 14:00-15:30, and 16:00–17:30
- Coffee breaks: 10:30-11:00 and 15:30-16:00
- Lunch: 12:30–14:00
Week 1: July 5–9, 2027, Universidad de Buenos Aires
- Benjamin Antieau (Northwestern U): Filtrations and D-modules
- Julie Bergner (University of Virginia): Higher Categories and Higher Segal Spaces
- Kobi Kremnitzer* (Oxford): A Bornological Approach to Derived Analytic and Differential Geometry
- Ishan Levy (Institute for Advanced Study, Princeton): Periodic Phenomena in Stable Homotopy Theory
Week 2: July 12–16, 2027, Universidad Nacional de La Plata
- Alexander Efimov (Steklov Mathematical Institute): Localizing Invariants and Dualizable Categories
- Angélica Osorno (Reed College): Applications of 2-Categorical Techniques to (Equivariant) Homotopy Theory
- Maxime Ramzi (Münster): Localizing Motives and Geometric Topology
Germán Stefanich (MPIM-Johns Hopkins): Higher Algebraic Geometry
(*) To be confirmed.
2027 Programs and Applications
Explore Higher Categories and Applications and The Geometry of Singular Sets: School on Geometric Measure Theory, Harmonic Analysis and PDE, and apply.
The deadline to apply to Higher Categories and Applications (July 5–16, 2027) and to The Geometry of Singular Sets: School on Geometric Measure Theory, Harmonic Analysis and PDE (August 2–13, 2027) via MathPrograms.org is February 15, 2027, at 11:59 pm (Eastern Standard Time).
Applications to each school are linked in the right sidebar.
Also in the right sidebar is the Travel & Participant Information [link to online PDF form], covering questions related to travel, accommodations, meals, and other administrative matters. If you need help or have questions, email [email protected].