ACTION NOW — October 25–26, 2026

Manchester Building, Room 2 · Hebrew University of Jerusalem

Schedule

Sunday Evening, October 25 — Special Events

Talk Titles & Abstracts

Talks are listed in program order: Sunday first, followed by Monday. Click a speaker's name in the schedule to jump to the corresponding abstract.

1. Guy Blachar (Université Paris Dauphine-PSL)

   Random semigroups à la Gromov

   We introduce a model of random semigroups analogous to Gromov’s density model for random groups. Fixing $n\ge 2$ generators, we impose $\lfloor n^{2\delta l}\rfloor$ uniformly chosen relations between distinct words of length at most $l$, and study the resulting semigroup as $l$ tends to infinity. We show a phase transition at density $1/2$: with probability tending to one, above this density the semigroup is trivial, while below it the semigroup contains a free subsemigroup of rank two and is neither left nor right amenable. We will also discuss small cancellation and residual finiteness at low densities. Finally, for $n\ge 3$, at the critical density $1/2$ the semigroup is finite with high probability, while both the probability of being trivial and, for every fixed $m$, the probability of having more than $m$ elements remain bounded away from zero. This stands in contrast to the random group model at critical density, where the group is trivial or cyclic of order two with high probability.

   Based on a joint work with Be'eri Greenfeld and Margaret Shideler.

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2. Yuval Yifrach (University of Zurich)

   Effective growth of injectivity radius and a quantitative theory of stationary measures

   For higher rank center free simple Lie groups $G$ and discrete subgroups $\Gamma$ of them, we quantify the growth of injectivity radius in $G/\Gamma$ as a function of the covolume of $\Gamma$ in $G$ (which may be infinite).

   This result is used to prove quantitative versions of three results in the field of discrete subgroups of Lie groups and invariant measures: Stuck-Zimmer theorem, the (quite) recent Fraczyk-Gelander theorem, and the Benjamini-Schramm convergence of symmetric spaces to the universal cover. This also gives a new proof of Stuck Zimmer theorem.

   In particular, we prove that whenever $\Gamma$ is not a lattice, one can find a point (in fact high measure of points) in the ball of radius $R$ in $G$ where the injectivity radius of $G/\Gamma$ is at least $\log\log\log\log(R)$, thereby quantifying the result of Fraczyk-Gelander which states unboundedness without any rate.

   This growth of injectivity radius with the volume is proved using a new structure theory for almost stationary measures (itself a new notion), and a corresponding quantitative version of the Nevo-Zimmer structure theorem.

   In the talk we will to discuss the main theorem, how to derive its applications, and some of the methods used to prove it.

   This talk is based on two joint works with Ilya Gekhtman, Simon Machado and Omri Solan.

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3. Shaked Bader (Oxford)

   Isoperimetric inequalities

   In this talk I will discuss homological and homotopical isoperimetric inequalities, including those of higher rank. I will emphasise what is known (and not known) in the non-positive curvature case.

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4. Ido Grayevsky (Bristol)

   Better recall Sol

   The QI classification of solvable Lie groups is a major open problem. The first substantial step in this context was the ground-breaking work of Eskin-Fisher-Whyte, proving the QI-rigidity of SOL, a horosphere in a product of two hyperbolic planes.

   In an ongoing work, we tackle the QI classification of horospheres in $SL_3(\mathbb{R})$. I will discuss the SOL case and the new challenges one is faced with for more general horospheres.

   Joint with Cornelia Drutu and Gabriel Pallier.

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5. Michael Bersudsky (Max Planck Institute, Leipzig)

   Distributions in the space of $k$-lattices in $\mathbb{R}^n$

   The talk will concern the space of homothety classes of rank-$k$ discrete subgroups of $\mathbb{R}^n$ and some natural asymptotic distribution problems that arise in this setting.

   I will focus on ongoing joint work with Seonhee Lim and Seongmin Kim, which describes limiting distributions for the irreducible action of lattices in $SL(2,\mathbb{R})$ on this space, with averages taken over growing norm balls. I will also present new applications to the distribution of Frobenius numbers.

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6. Omri Solan (Princeton, IAS)

   TBA

   TBA

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7. Amichai Lampert (University of Michigan)

   Strength, singularities and representation theory

   Strength is an algebraic invariant measuring nondegeneracy of homogeneous polynomials. Introduced by Schmidt in 1985, it has found a variety of applications in number theory, additive combinatorics and commutative algebra. In 2021, Bik-Danelon-Draisma-Eggermont introduced a vast generalization of strength from the polynomial ring to arbitrary polynomial representations of the general linear group. They showed that this generalization retains many of the good properties of the original. I will discuss work in progress with Andrew Snowden proposing a simpler geometric interpretation of this generalization, yielding effective quantitative bounds as a bonus.

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8. Segev Gonen Cohen (ETH Zürich)

   Actions of Lattices on Manifolds

   In this talk we describe recent progress on the Zimmer Program, the study of actions of lattices in Lie groups on manifolds by diffeomorphisms. We begin by recalling motivations and some important examples, explain the general strategy introduced by Brown-Fisher-Hurtado when the manifold is of low enough dimension, and discuss modifications that allow us to prove results in more general semisimple and S-arithmetic groups.

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9. Daniel Meriaz (Bristol)

   Local Weyl law and length-minimising loops on large hyperbolic surfaces

   Understanding the behaviour of eigenfunctions in (classically) chaotic systems is a central vector in the study of quantum chaos. An important quantity thereof is the (pointwise) local Weyl law, where the $L^2$-distribution of eigenfunctions with frequencies in some range is studied. In this talk, I will present some results and techniques used to study the local Weyl law over a fixed smooth energy window, on random (Weil--Petersson) hyperbolic surfaces. Specifically, I compute large-genus asymptotics of its variance, and show that they are consistent with the eigenfunctions behaving as predicted by Berry's random wave model. The approach taken here allows to explicitly integrate certain test functions which depend on lengths of based geodesic loops. A key ingredient of the proof are “length-minimising loops” which I shall introduce and explain how their properties may be used to bound certain error terms.

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10. Elyasheev Leibtag (Ghent University)

    New directions in irrationality

    When Apéry announced his proof of the irrationality of $\zeta(3)$ in 1978, he was reportedly asked where his formulas came from and replied that they “grow in my garden.” Over the following decades, mathematicians developed a range of constructions in search of further irrationality proofs. In this talk, we revisit this garden and present a construction proving that $(1,\zeta(3),\zeta(4))$ are linearly independent over the rationals.

    Our approach places classical constructions in a common framework of conservative matrix fields (discrete flat connections), where different directions in a parameter lattice produce different rational approximation sequences. This geometric viewpoint relates known constructions, reveals hidden connections between the constants they approximate, and provides a systematic way to generalize them. Varying the direction lets us grow whole families of Diophantine approximations in Apéry’s garden and search for new irrationality proofs.

    The irrationality result is quantitative: for every pair of rational numbers $(A,B)$, not both zero,

    $$\mu\bigl(A\zeta(3)+B\zeta(4)\bigr)<64.983.$$

    This is joint work with the Ramanujan Machine group at the Technion.

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11. Tsviqa Lakrec (University of Geneva)

    The Totally Nonnegative Grassmannian in Combinatorics and Physics

    The totally nonnegative Grassmannian is a central object in the theory of total positivity. I will give a short introduction to its geometry and combinatorics, and explain how they connect with theoretical particle physics via the amplituhedron and with the mathematics of juggling and origami.

    The talk refers to joint works with Even-Zohar, Parisi, Sherman-Bennett, Tessler and Williams.

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12. Raz Slutsky (Oxford)

    Random sparsification, torsion in homology, and fixed price

    Given a complicated geometric object, we often want to simplify it without losing information about the structure we are interested in. In this talk, I will describe a method for doing this by combining a random sparse set with a deterministic one, gaining some of the advantages of both. We will then see how this idea can be used to show that torsion in the first homology of higher-rank lattices grows subexponentially, answering a question of Abért, Gelander, and Nikolov and confirming the degree-one case of several conjectures. We will also use the same principle to give a new general criterion for a property known as fixed price one, which applies to a broad class of groups.

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