Spring 2026

• • May 192026

  Kirill Magidson (Northwestern University)

  A crystalline perspective on Witt vectors

  The theory of prismatization constructs a universal cohomology theory of $p$-adic schemes, called absolute prismatic cohomology, via a natural algebro-geometric construction involving Witt vectors. Amongst other things, the crystalline cohomology, classically defined using divided power thickenings, is recovered as one of the specializations of this theory.

  The slogan of this talk is that this relation goes deeper, and that a closer study of the algebraic structure of Witt vectors reveals them to be objects of a crystalline nature. I will introduce the infinity-category of derived $\delta$-Cartier rings, which can be viewed as combining divided power and $\delta$-structures, and in which Witt vectors satisfy a universal property refining their classical universal property as cofree $\delta$-rings.

  I will also explain how this connects to the Nygaard filtration on derived crystalline cohomology, and how the sheared Witt vectors recently defined by Drinfeld and studied by Mathew--Vologodsky--Kanaev--Zhang, fit into this story.

• • May 122026

  Piotr Pstrągowski (University of Washington)

  The even filtration and algebraic K-theory

  The even filtration, introduced by Hahn--Raksit--Wilson, is a canonical filtration attached to a commutative ring spectrum which measures its failure to have homotopy groups concentrated in even degrees. Despite its extremely simple definition, the even filtration recovers many geometrically and arithmetically important constructions, such as the Adams--Novikov filtration of the sphere or the various motivic filtrations on topological Hochschild homology and its variants.

  A conjecture of Robert Burklund and Achim Krause predicts that the when applied to $l$-adic algebraic K-theory of a field, the even filtration should recover the motivic filtration of Voevodsky, relating the concept of evenness to algebraic cycles. In this talk, I will talk about a proof of this conjecture for global and local fields.

• • May 052026

  Kenny Schefers (UC Berkeley)

  Decategorifying the singular support of coherent sheaves

  The microlocal homology is a family of chain theories that interpolates between the Borel--Moore homology and singular cohomology of a complex variety in the case when that variety is singular and Poincaré duality fails. Such a device allows one to speak of the singular support of classes in Borel--Moore homology, which we show decategorifies the Arinkin--Gaitsgory singular support of coherent sheaves in a precise sense.

  The connection between these two singular support theories leverages a description of the microlocal homology in terms of the canonical perverse sheaf of vanishing cycles (the DT sheaf) on shifted cotangent bundles, as well as the known relation between vanishing cycles and categories of matrix factorizations.

  We also discuss work-in-progress with Jacob Erlikhman on extending these results to stacks using a K-motivic variant of microlocal homology.

• • Apr 282026

  Christian Kremer (MPIM)

  The Nielsen Realisation Problem for high--dimensional aspherical manifolds

  The classical Nielsen Realisation Problem asks whether a finite subgroup of the mapping class group of a surface can be realised by an actual group action on the surface. It was answered affirmatively by Kerckhoff. In my talk, I will present a generalisation of this problem to high-dimensional aspherical manifolds, and discuss results for group actions of cyclic groups of prime order, based on the newly developed technique of equivariant and isovariant Poincaré duality.

• • Apr 212026

  Florian Reidel (University of Copenhagen)

  Points of $\mathbb{E}_\infty$ rings in positive characteristic

  Given a non-zero $\mathbb{E}_\infty$ ring $A$ and any number $n>0$ we ask: Can a free $A$-module on $n$-many cells admit a cell structure with consisting of $k$-many cells for $k\leq n-1$? For non-connective rings, this is difficult to attack directly. However, if $A$ has a non-zero $K(h)$-localization for some finite $h$, the answer is no by the chromatic Nullstellensatz. We discuss how to deal with the ''infinite height'' case, and give a further negative answer to the question for rings with nonzero $\mathbb{F}_2$-homology. To do this, we investigate nilpotence phenomena for $\mathbb{E}_\infty$-$\mathbb{F}_p$-algebras for any prime $p$ and show that, unlike in the finite height case, the situation differs drastically depending on whether the prime is odd or even.

• • Apr 142026

  Gijs Heuts (Utrecht University)

  Periodic homotopy theory of spaces and Hopf algebras

  I will discuss two ways of thinking about the homotopy theory of spaces ''at height $n$'', namely $v_n$-periodic and $T(n)$-local homotopy theory, as well as the relation between the two. There are different ways to understand these localizations using notions from higher algebra, namely spectral Lie algebras and commutative ring spectra. I’ll try to explain how spectral Hopf algebras can serve as a unifying perspective.

• • Apr 072026

  Lucas Piessevaux (University of Bonn)

  Synthetic equivariant spectra and motivic homotopy theory

  The category of (even, $MU$-based) synthetic spectra may be modeled using cellular motivic homotopy theory by work of Pstrągowski and Gheorghe--Isaksen--Krause--Ricka. In a sense, this comparison follows from the close relation between the oriented motivic spectrum of algebraic cobordism and the usual oriented spectrum $MU$. In this talk I will discuss how ''decompleting'' the notion of orientation to that of a global group law allows us to naturally extend this story to the equivariant setting. This is based on joint work with Keita Allen.

• • Mar 312026

  Nikolai Konovalov (University of Chicago)

  Protosynthetic Kriz theorem

  The Kriz theorem provides an algebraic model for $p$-adic homotopy theory in terms of cosimplicial $p$-Boolean algebras, i.e. $\mathbb{F}_p$-algebras such that $x^p=x$ for any element $x$. Unfortunately, the Koszul duality for $p$-Boolean algebras is unknown, so a Lie model for $p$-homotopy theory remains unknown as well. However, Itamar Mor recently constructed the category $Syn^1$, which degenerates unstable homotopy theory to simplicial restricted Lie algebras. The category $Syn^1$ categorifies the lower central series spectral sequence.

  In my talk, I will present an algebraic model for the category $Syn^1$ which degenerates the Kriz theorem into the Koszul duality between restricted Lie algebras and $\mathbb{F}_p$-algebras with trivial Frobenius. If time permits, I will also explain how the protosynthetic Kriz theorem reveals some interactions between different versions of the unstable Adams spectral sequence.