Weekly Bulletin

An oriented Lagrangian in a Calabi–Yau manifold is called positive if the real part of the holomorphic volume form restricts to a positive volume form on it. A conjecture of Joyce, within the Thomas–Yau program, predicts that positive Lagrangian branes form an abelian subcategory of the derived Fukaya category. In this lecture, I will introduce a geometric construction whose terminal configuration determines the kernel and cokernel of a morphism between positive Lagrangian branes. Thus, if the construction always terminates, it establishes Joyce’s conjecture. The resulting abelian category admits Harder–Narasimhan filtrations for the geometric central charge. Under suitable split-generation assumptions, we also obtain a Bridgeland stability condition whose stable objects admit special Lagrangian representatives, as predicted by the Thomas–Yau conjecture. The construction is based on a one-parameter family of special Lagrangian submanifolds with boundary. Surgeries occur as the family encounters singularities or obstruction walls. I will illustrate this process through concrete examples, including the elliptic-curve case, where we prove that the construction always terminates. This is joint work with Jake Solomon.

<div dir="auto" data-olk-copy-source="MessageBody">Given a split reductive group G, Katsuyuki Bando has</div> <div dir="auto" data-olk-copy-source="MessageBody">constructed a family of affine grassmannians that interpolate</div> <div dir="auto" data-olk-copy-source="MessageBody">between the equal characteristic and Witt vector versions.</div> <div dir="auto" data-olk-copy-source="MessageBody">Using this family and properties of universally locally acyclic</div> <div dir="auto" data-olk-copy-source="MessageBody">sheaves, he has proven that constructible étale sheaves on</div> <div dir="auto" data-olk-copy-source="MessageBody">Hecke stacks agree between equal and mixed characteristic</div> <div dir="auto" data-olk-copy-source="MessageBody">versions.</div> <div dir="auto"> </div> <div dir="auto">I will report on joint work with Sebastian Bartling, in which we</div> <div dir="auto">generalize this result in 2 directions: from étale sheaves to étale</div> <div dir="auto">motives, and from split reductive groups to parahoric models of</div> <div dir="auto">tamely ramified reductive groups constructed by Pappas-Zhu.</div>

We study maps from the circle to itself that minimize the W^{s,1/s} energy, s\in(0,1), among maps of prescribed degree. The basic question is: for which degrees do minimizers exist? Sacks–Uhlenbeck theory guarantees their existence for a set of degrees generating the group \mathbb Z. We show that, for s>1/4, minimizers exist in every homotopy class and classify them: for positive degrees, they are precisely the finite Blaschke products. Moreover, we show that, for s<1/8, the identity map does not minimize the energy among maps of degree one. This talk is based on joint works with Dorian Martino and Armin Schikorra.

Background independence raises a fundamental question in quantum gravity: where does physical information reside when spacetime itself is dynamical? A relational approach addresses this question by defining observables through relations between dynamical degrees of freedom rather than fixed spacetime coordinates. From this perspective, correlations are not quantities computed on spacetime,but are part of how we understand the structure of spacetime itself. In this talk, I will present my research on relational quantum gravity, based on the path integral formulation and methods from quantum field theory, particularly the renormalization group. This framework offers a way to investigate how quantum correlations are encoded across scales, opening new connections between quantum gravity and quantum information, with potential applications to cosmology and black holes as natural laboratories of quantum gravity.

More information: https://eth-its.ethz.ch/activities/seminars-and-talks-2026-to-2027/renata-ferrero.htmlcall_made

<div class="x_elementToProof" data-ogsc="rgb(0, 0, 0)" data-olk-copy-source="MessageBody">This work is joint with Thomas Lehéricy, Pierre-Loic Méliot and Ashkan Nikeghbali.   </div> <div class="x_elementToProof" data-ogsc="rgb(0, 0, 0)"> </div> <div class="x_elementToProof" data-ogsc="rgb(0, 0, 0)">We obtain precise large deviations for the random number \(K_n\) of partition sets of \([n] = \{1, \dotsc, n\}\) in the Ewens-Pitman model with \(\alpha \in (0,1)\) and \(\theta > -\alpha\).</div> <div class="x_elementToProof" data-ogsc="rgb(0, 0, 0)">In this seminar, we consider what approaches exist for obtaining precise large deviation principle, consider new method for this goal, apply it to the Ewens-Pitman model and discuss why we cannot apply some already known results of Large Deviation theory.</div>

The precise simulation of quantum lattice models is of high technological relevance, yet computations suffer from the curse of dimensionality, as the Hilbert space of the eigenvalue problem grows exponentially with system size. Linked-cluster expansions provide access to the infinite system limit, yet require the evaluation of high-dimensional oscillatory sums with a graph structure, so far approached using Monte Carlo runs suffering from cluster-scale runtimes and statistical noise. In this talk, I present a general method for computing the appearing graph sums deterministically and efficiently [1,2]. This is achieved by factorizing each graph sum into blocks and subsequently treating each block according to its treewidth. Low-treewidth blocks, such as trees and cycles, are evaluated analytically using an algebra based on generalized zeta functions accompanied by a rapidly decaying Fourier series, while high-treewidth graphs are computed using tensor network bucket elimination. This results in a scaling exponent for numerical work and memory that only depends on the treewidth and not on the number of nodes in the graph. The method is applicable to general gapped quantum lattice models and reproduces cluster-size Monte Carlo runs within minutes for 1D, 2D, and 3D lattices. In addition, it provides the full momentum grid at the cost of a single momentum evaluation, allowing for the study of finely resolved dispersion relations. We then use the method at scale and analyze new dipolar interaction models for three-dimensional quantum magnets, showing that they describe the measured dispersion curves best [3]. The method is implemented in the open-source Graph Zeta Library (GZL), allowing to reproduce all results on standard desktop hardware [4]. [1] A. A. Buchheit and A. Rupp, “Graph lattice sums and graph zeta functions for long-range interacting quantum lattice models”, arXiv:2609.18918 (2026) [2] A. A. Buchheit and J. K. Busse, “Epstein zeta method for many-body lattice sums”, Numer. Math. (2026) [3] A. Duft, P. Adelhardt, J. A. Koziol, A. A. Buchheit, K. P. Schmidt, “Exact and fast series expansions for quantum models with long-range interactions”, arXiv:2609.18761 (2026) [4] A. A. Buchheit, “Graph Zeta Library (GZL)“, github.com/graph-zeta/gzl (2026)

Let $G(n,m)$ be the Erdős-Rényi random graph with $n$ vertices and $m$ edges. Using the L\'ovasz local lemma, Alon and Krivelevich [Combinatorica 1997] proved that for $m=o(n^{3/2})$ there \emph{exists} $q=q(n,m)$ such that the chromatic number of $G(n,m)$ equals either $q$ or $q+1$ with probability tending to one as $n\to\infty$. In this talk we determine $q$ explicitly. We also show that for `most' $m$ in a certain precise sense the chromatic number of the random graph equals $q$, i.e., concentrates on just a single explicit value. The talk is based on joint work with Michael Isaev, Mihyun Kang and Pavel Zakharov.

Beyond their foundational roots in statistical and stochastic process theory, Gaussian processes (GPs) are now central to a versatile and widely used framework spanning applied mathematics and probabilistic machine learning. Despite well-known limitations, GP-based methods continue to show remarkable adaptability, often outlasting shifting methodological trends. In this talk, I will highlight developments in modeling, prediction, and active learning with GPs, offering perspectives on their enduring role as a powerful building block for function approximation and uncertainty quantification.

The universe builds a great deal of structure out of very little. I will discuss three places where this is less obvious than it sounds. The first is the origin of cosmic structure. The standard story needs an inflaton, a scalar field whose nature nobody knows. We find that de Sitter space alone is enough: its quantum gravitational waves generate, at second order, a nearly scale-invariant spectrum of density fluctuations. De Sitter cannot last forever, because the information it stores weighs on it, and treating that memory as a quantum chaotic system, with the tools of random matrix theory, sets how long inflation lasts and how large the fluctuations are. The second is turbulence. A single-valued velocity field, written down by hand rather than obtained from Navier–Stokes, already shows Richardson’s explosive separation of particle pairs and a scalar that keeps dissipating as its diffusivity goes to zero; I will also say what survives when the flow becomes compressible and full of shocks. The third is nonlinear PDEs. When a neural network learns whole families of their solutions, the families turn out to live on manifolds of only a few dimensions. The same networks can run holography backwards, reconstructing the gravitational dual of a strongly coupled field theory from its thermodynamics, including renormalization group flows that skip intermediate fixed points. Each case asks the same question: what is the least nature needs to produce the complexity we see?

More information: https://eth-its.ethz.ch/activities/its-chalk-cheese-2026-2027.htmlcall_made

We extend Malliavin differentiability results for stochastic differential equations (SDEs) and backward stochastic differential equations (BSDEs) with path-dependent coefficients from the Brownian framework to the Lévy setting. The coefficients are assumed to be Lipschitz continuous with respect to the supremum norm. The resulting differentiation formula for the coefficients enables us to establish existence and uniqueness of solutions for a class of forward-backward SDEs with locally Lipschitz coefficients.

Regulators are fundamental in number theory, appearing in formulas such as Dirichlet's unit theorem. In this talk I will focus on the p-adic analogue of this story. Then, following Beilinson and Gros' ideas of generalising p-adic regulators using Chern classes in some p-adic cohomology theories, I will present a new integral cohomology theory which specialises to the previous p-adic cohomology theories while being computable and integral.