Homotopy Theory Conference 2026

The Homotopy Theory Conference 2026 will take place on Sunday and Monday, October 25–26, 2026, in the particle accelerator building at the Weizmann Institute of Science, Rehovot, Israel.

This two-day event will feature talks on homotopy theory and related topics, given by students, postdocs and faculty. There will also be free time for discussions to foster collaborations and informal exchanges. The conference is open to all mathematics students and researchers.

Organizers: Shachar Carmeli, Noam Nissan and Shay Ben-Moshe.
For inquiries, please contact Shay at shaybm9@gmail.com.

Registration

Register here!

Registration is free, but unfortunately we have a limited number of seats. Please sign up to help us with logistics.

Schedule

The schedule is still being finalized and subject to changes.

Sunday, October 25

Monday, October 26

Abstracts

Lior Yanovski – TBA

TBA

Shai Keidar – TBA

TBA

Yuval Lotenberg – Power Operations in Morava E-Theory of Flat Ring Spectra

Power operations provide a rich algebraic structure on the homotopy groups of $E_{\infty}$-ring spectra. For K(n)-local algebras over Morava E theory, these operations have a particularly clean geometric interpretation, developed by Rezk. In this talk, I describe the power operations on Morava E-theory of p-adically flat ring spectra. A key ingredient is the Tate-valued Frobenius, which is closely related to power operations and gives rise to a natural δ-ring structure. If time permits, I will discuss the proof, which in particular goes through algebro-geometric interpertations for Morava E-theory cohomology of commutative groups.

David Corwin – TBA

TBA

Guy Kapon – Six functor formalisms and internal higher algebra

I will talk about a recent joint work with Noam Nissan and Schahar Caremeli, in which we enhance six functor formalisms via internal higher algebra. Six functor formalisms were introduced by Grothendieck to formalise the functoriality of categories of sheaves, and has since been applied in many subjects. The classic method of constructing six functor formalisms is by a suitable decomposition of maps into open inclusions and proper maps. This was upgraded by Cnossen, Lenz and Linskens to a universal property of a certain 2-category. We prove a variant of this universal property, that doesn't assume a suitable decomposition, and instead enhances any six functor formalism to a functor from a 2 category. In the talk I will define the relevant notions and explain the general ideas of the proof.

Tamir Buqaie – TBA

TBA

Ishai Dan-Cohen – Towards coarse moduli of motivic augmentations

A variety $X$ over a suitable base $Z$ gives rise to a highly structured algebra $C^*(X)$ in motives over $Z$. In turn, a $Z$-point gives rise to an augmentation $C^*(X) \to 1$. The resulting assignment $X(Z) \to \operatorname{Aug} ( C^*(X) )$ factors the so-called "unipotent Kummer map" to torsors under the unipotent fundamental group in realizations. This suggests the possibility of performing Chabauty-Kim theory motivically without waiting for a motivic t-structure. For this purpose, the coarse space for motivic augmentations $\operatorname{Aug} ( C^*(X) )$ would benefit from a structure of finite type $\mathbb{Q}$-variety, and similarly, the coarse space $\operatorname{Aug} ( C^*_{F\phi}(X) )$ of augmentations in filtered $\phi$ modules would benefit from a structure of finite type $\mathbb{Q}_p$-variety. We establish two criteria for representability, compute these spaces in several examples, and construct a comparison with Selmer varieties. Finally, we demonstrate how these constructions lead to K-theoretic finiteness criteria in an example.

Roy Magen – How to construct 6-functor formalisms for homotopy theories

6-functor formalisms are highly structured categorical invariants that enhance cohomology theories with various structures, such as Künneth formulas and Poincaré duality, and allow us to make sense of variants such as Borel-Moore homology. On the other hand, homotopy theories can often be seen as categorical invariants that are constructed out of suitable notions of smooth maps or submersions, which are the maps for which we expect to have Poincaré duality. Indeed, G-equivariant homotopy categories can be constructed using G-equivariant manifolds (submersions over BG), and the standard constructions of motivic homotopy categories are given in terms of schemes smooth over a base. These constructions of homotopy theories naturally have that the "smooth" maps behave as if they satisfy Poincaré duality, even though we need a 6-functor formalism in order to fully express this.
In this talk, we will show how to induce the structure of a 6-functor formalism in this situation so that the "smooth" maps truly satisfy Poincaré duality. This provides a modern and abstract version of a strategy first outlined by Voevodsky in 2001 in the setting of schemes, and later generalized by others to various algebro-geometric contexts, eventually leading to the 6-functor formalism of stable motivic homotopy theory on stacks, as well as the universality of stable motivic homotopy theory as a 6-functor formalism on schemes. Some applications of the new techniques include the universality of stable motivic homotopy theory as a 6-functor formalism on stacks, extending work of Khan-Ravi, a 6-functor formalism of "complex analytic stable motivic homotopy theory", and Betti realization functors over stacks that are compatible with the six operations, extending work of Ayoub.

Avital Binyamin – The Chromatic Fourier Transform and Cartier Duality

For an abelian group, the discrete Fourier transform relates its group algebra to functions on its Pontryagin dual, turning convolution into pointwise multiplication. For finite groups, both algebras admit a canonical Hopf algebra structure and the Fourier transform can be promoted to a map of Hopf algebras. At higher chromatic heights, Barthel-Carmeli-Schlank-Yanovski constructed an analogue that retains many properties of the classical transform. In this talk, we will construct the chromatic Fourier transform as a map of Hopf algebras using pairings, and show that its transpose under Cartier duality is naturally equivalent to the Fourier transform of the n-shifted Brown-Comenetz dual.

Tomer Schlank – TBA

TBA

Boris Chorny – On the enriched approximate completeness

Let A be a category, the universal cocompletion of a category is called the category of small presheaves PA and the canonical functor Y: A -> PA is called the Yoneda embedding. In this talk we will give a definition of the approximate completeness, a condition equivalent to the completeness of PA by P. Freyd's theorem. Next we will discuss a generalization of this concept to enriched settings and give examples and applications to homotopy theory. Joint work with Giuseppe Leoncini.

Semyon Abramyan – Embedding calculus for parallelized manifolds

We study a variant of the embedding functor $Emb(M, N)$ that incorporates homotopical data from the frame bundle of the target manifold $N$. Given a parallelized $m$-manifold $M$ and an $n$-manifold $N$ equipped with a section of its $m$-frame bundle, we define a modified embedding functor $\widetilde{Emb}(M, N)$ that interpolates between the standard embedding and a reference framing. Using the manifold calculus of functors, we identify the Taylor tower of $\widetilde{Emb}(M, N)$ with a mapping space of right modules over the Fulton–MacPherson operad. We prove a convergence theorem under a codimension condition, establishing a weak equivalence between $\widetilde{Emb}(M, N)$ and its Taylor approximation. Finally, under rationalization, we describe the derived mapping space in terms of a combinatorial hairy graph complex, enabling computational access to the rational homotopy type of the space of embeddings.

Amos Kaminski – Local structure of smooth p-adic analytic Artin stacks

A natural goal in the study of smooth p-adic analytic Artin stacks is a six-functor formalism for étale sheaves of spectra on their associated light condensed anima. Clausen conjectured that these anima are étale-locally light profinite, and observed that this local structure would ensure the applicability of his formalism. In this talk, I will explain a proof of this conjecture. The argument uses a groupoid analogue of van Dantzig's theorem to produce compact open subgroupoids, followed by a passage to closed skeletons and a reconstruction as inverse limits of finite groupoids. As a consequence, Clausen's six-functor formalism is available for all morphisms between smooth p-adic analytic Artin stacks.

Yonatan Harpaz – TBA

TBA