In this talk, we introduce a new method to obtain lower bounds for moments of L-functions for all real k>0. In particular, our method applies to families of higher degree automorphic L-functions which were previously inaccessible.

TBA

Communication complexity studies how much information must be exchanged to solve a problem whose input is split among two or more parties. The classical setting deals with Boolean inputs split between two parties. In the algebraic variant, inputs, messages, and computation are over some (potentially infinite) field. This variant, introduced by Abelson in 1978 and developed by Grigoriev in 2008, is relatively unexplored. In this talk, I will describe this setting, the hurdles to directly applying Boolean techniques, and the techniques that do work to give lower bounds. I will describe some specific lower bounds we establish. More details can be found in the preprints https://arxiv.org/abs/2609.17082 and https://eccc.weizmann.ac.il/report/2026/182/ This is joint work with Manon Blanc, Prateek Dwivedi, Magnus Hansen, and Nutan Limaye, at ITU Copenhagen. This talk will be in hybrid mode. Please find zoom link below: https://zoom.us/j/99598370034 Meeting ID: 995 9837 0034 Passcode: 941422

Long-range correlations are used to probe collective behavior in many-body systems. In finite systems, however, global conservation of energy, momentum, particle number, and other conserved charges can itself generate correlations between otherwise independent degrees of freedom. It is therefore crucial to remove the contribution of these conservation-induced correlations from observed long-range correlations for understanding the nature of the emergent collectivity. In this talk, I will present a unified conditional-probability framework in which equilibrium statistics and conservation-induced correlations emerge from conditioning on additive conserved quantities. The one-mode conditional law yields the Maxwell–Boltzmann, Bose–Einstein, and Fermi–Dirac distributions at leading saddle order, while the two-mode law gives the leading finite-rank covariance induced by exact conservation. This structure allows us to construct observables orthogonal to selected conserved quantities, for which the leading conservation-induced covariance vanishes. As an application, I will discuss long-range correlations in high-energy p-Pb collisions, which exhibit patterns resembling collective behaviour in collisions of large nuclei where they are commonly associated with hydrodynamic collective response. Conservation effects are particularly relevant in these smaller systems because fewer particles are produced. Using PYTHIA generated events, I will illustrate how conservation-aligned and conservation-orthogonal contributions can be separated, and discuss the implications for interpreting the emergent collective behaviour. [Based on arXiv:2606.29050]