• Address - Givat Ram. Jerusalem, 9190401, Israel.

• Email -  lior.yanovski@gmail.com.

• CV (not up to date) -  Lior Yanovski - CV.

1. Chromatic Cardinalities via Redshift (with S. Ben-Moshe, S. Carmeli and T. Schlank) - IMRN, 2024.14 (2024): 10918-10924. 

We reprove Lurie's result (from Elliptic Chomology III) that the semiadditive cardinality of a p-typical pi-finite space A in pi_0(E_n) is an integer given by the Baez-Dolan homotopy cardinality of the n-fold free loop space L^n A. Our method differs drastically from Lurie's, which relies on tempered cohomology, and employs the higher descent results on chromatically localized algebraic K-theory from our previous paper. 

2. Descent and Cyclotomic Redshift for Chromatically Localized Algebraic K-theory (with S. Ben-Moshe, S. Carmeli and T. Schlank) - JAMS, 38.2 (2025): 521-583. 

We show that T(n+1)-localized algebraic K-theory of stable oo-categories of chromatic height up to n satisfies descent with respect to p-local pi-finite group actions (aka higher descent). We deduce from this that it also takes height n cyclotomic extensions to height n+1 cyclotomic extensions (aka cyclotomic redshift).   We deduce that K(n+1)-locally algebraic K-theory satisfies hyperdescent along the cyclotomic tower. The interest in this example stems from the fact that T(n+1)-locally this fails by the work of Burklund, Hahn, Levy, and Schlank, which therefore disproves the telescope conjecture at all primes and all heights n > 1. 

3. Homotopy Cardinality via Extrapolation of Morava-Euler Characteristics - Selecta Mathematica, 29.5 (2023): 81. 

This paper partially answers the question of Baez on formalizing the relationship between classical Euler characteristic and the Baez-Dolan homotopy cardinality, suggested by many heuristics. The answer is given by a common p-typical generalization for every odd prime p. This generalization is obtained by an l-adic extrapolation of  Euler characteristics with respect to the Morava K(n)-s to n = -1.

4. Characters and transfer maps via categorified traces (with S. Carmeli, B. Cnossen and M. Ramzi) - Forum of Mathematics, Sigma (to appear).

We develop a general character theory for pointwise dualizable local systems on suitably finite spaces, using the higher categorical perspective on topological Hochschild homology. A key ingredient is a very general form of the induced character formula.  As an application, we reprove and sharpen results on Becker-Gottlieb transfers, the Hochschild homology of Thom spectra, and the additivity of traces in stable oo-categories.

5.  The Chromatic Fourier Transform (with T. Barthel, S. Carmeli and T. Schlank) - Forum of Mathematics, Pi, Vol. 12. Cambridge University Press, 2024.

We extend the classical Discrete Fourier Transform (DFT) to higher chromatic heights generalizing the work of Hopkins and Lurie. Some of the applications include affineness and Eilenberg-Moore type results in T(n)-local spectra and the computation of the discrepancy spectrum of  Morava E-theory. 

6. A Remark on the Number of Maximal Abelian Subgroups  - arxiv preprint.

The number of maximal (with respect to inclusion) abelian subgroups of a given finite p-group is shown to be congruent to 1 modulo p. This elementary observation has some relevance to the computation of Euler characteristics of classifying spaces of finite groups with respect to the Morava K-theories,   

7. Chromatic Cyclotomic Extensions (with S. Carmeli and T. Schlank) -  Geometry & Topology, 28.8 (2024): 3511-3564. 

We lift all the abelian Galois extensions of the K(n)-local sphere to Galois extensions of the T(n)-local sphere,  by realizing them as higher semiadditive analogues of cyclotomic extensions. This relies on the oo-semiadditivity of the T(n)-local categories and the theory of semiadditive height from our previous work. We also use this to construct some non-trivial elements of the T(n)-local Picard group, by a general form of Kummer theory and discrete Fourier transform, which we also develop in this paper.  

8. The Monadic Tower for ∞-Categories - Journal of Pure and Applied Algebra 226.6 (2022): 106975 

For every right adjoint functor of oo-categories, we have a factorization through a transfinite tower of monadic functors.  Under presentability assumptions, this tower stabilizes on a coreflection onto a full subcategory of the source.  A dual construction (which inspired this work) recovers the "long homology localization tower" of Dwyer and Farjoun. 

9. Ambidexterity in Chromatic Homotopy Theory (with S. Carmeli and T. Schlank) - Inventiones Mathematicae 228.3 (2022): 1145-1254. 

We prove that the oo-categories of T(n)-local spectra are oo-semiadditive for all n, answering a question of Hopkins. This extends the results of Hopkins-Lurie on the higher semiadditivity of the oo-categories of K(n)-local spectra and the results of Kuhn on the 1-semiadditivity of T(n)-local spectra. We further classify all higher semiadditive localizations of spectra with respect to a homotopy ring and show that the T(n)-localizations are in a precise sense the maximal ones.

10. Ambidexterity and Height (with S. Carmeli and T. Schlank) -  Advances in Mathematics 385 (2021), 1-90.

We define and study the notion of semiadditive height for higher semiadditive oo-categories, which generalizes the chromatic height in stable homotopy theory.  We show that a stable higher semiadditive oo-category decomposes into a product according to height and that local systems on an n-connected pi-finite space, valued in a height n higher semiadditive oo-category, exhibit a form of "semicmplicity". We also show that this notion of height exhibits a form of a red-shift principle, similar to the Ausoni-Rognes chromatic red-shift phenomenon in algebraic K-theory.  

11. On d-Categories and d-Operads (with T. Schlank) - Homology, Homotopy and Applications 22.1 (2020), 283 – 295.

A rather technical note on models of oo-categories and oo-operads with (d-1)-truncated (multi-)mapping spaces. The main (model-independent) application is that these form reflective subcategories of the oo-categories of oo-categories and oo-operads respectively, and that the reflection is given by truncating the (multi-)mapping spaces.  

12. The oo-Categorical Eckmann-Hilton Argument (with T. Schlank) - Algebraic & Geometric Topology 19.6 (2019), 3119-3170.

For two reduced oo-operads P and Q, we show that if all the multi-mapping spaces of P are d1-connected and those of Q are d2-connected, then the multi-mapping spaces of the Boardman-Vogt tensor product of P and Q are (d1+d2+2)-connected. We deduce this from a relative version, which might be of interest on its own.  Along the way, we extend some of the truncated/connected calculus of oo-topoi to arbitrary presentable oo-categories. 

13. On Conjugates and Adjoint Descent (with A. Horev) - Topology and its Applications 232 (2017), 140-154.

We give an abstract oo-categorical treatment of "descent along adjoints",  which allows us to neatly unify seemingly different formulas for counting "conjugate objects".  Among the examples: Galois cohomogloy for classifying Galois forms, lim^1 of a tower of groups for classifying Postnikov conjugates of a space, and the double cost formula for the Mislin genus of a nilpotent group. 

14.  Affine Springer Fibers (supervised by Y. Varshavsky) - master thesis, HUJI (2013).

Provides a streamlined and detailed exposition of the work of Kazhdan and Lusztig on the algebro-geometric properties of affine Springer fibers for a connected semisimple algebraic group. 

1. "Chromatic Fourier transform" - MIT, 2021 (slides).

A seminar talk about my joint work with Shachar and Tomer on constructing a chromatic analogue of the discrete Fourier transform and its applications for affiness and Eilenberg-Moore type results in the T(n)-local category. 

2. "Chromatic cyclotomic extensions" - Warwick, 2021  (video, slides).

A seminar talk about my joint work with Shachar and Tomer on constructing Galois extensions of the T(n)-local sphere using higher semiadditivity.  

3. "Ambidexterity in T(n)-local stable homotopy theory" -  Newton institute, Cambridge 2018 (video).

A talk at the HHH program about my joint work with Shachar and Tomer on the higher semiadditivity of the T(n)-local categories. 

4. "oo-categorical Eckmann-Hilton argument" - YTM, Copenhagen  2018 (slides)

A talk at YTM on my joint work with Tomer regarding the connectivity of the Boardman-Vogt tensor product of reduced oo-operads.

5. "Generalized homotopy cardinality" - HUJI, Jerusalem  2018 (slides)

A colloquium talk about an old project with Tomer (waiting to be written). We use l-adic extrapolation of Euler characteristics for Morava K-theories of different height to construct a generalized homotopy cardinality function answering a question of Baez. 

1.  Trace maps.

Review of various trace maps in algebraic K-theory. 

2.  Goerss-Hopkins-Miller obstruction theory. 

A rough overview of the Goerss-Hopkins-Miller obstruction theory for realizing E_oo ring structures, using the theory of synthetic spectra of Pstragowski.  

3. Factorization Homology.

An introduction to factorization homology and tensor-excision, for a workshop on the cobordism hypothesis given by David Ayala and John Francis. at Caesaria 2018.

4. E_oo-rings,  Lubin-Tate theory and Elliptic Cohomology

From the report of the Oberwolfach Arbeitsgemeinschaft: Elliptic Cohomology according to Lurie .

5. Strong Approximation 

Notes for my talks at the workshop on super-strong approximation. Sketches Nori's proof of the "quantitative strong approximation theorem" with an introduction to algebraic geometry and the theory of algebraic groups. 

Lecture 2 - Group Completion