Integrated Calendar

A foremost longstanding open problem in the Ribe program is to find a purely metric reformulation of the Banach space property of having an equivalent norm whose modulus of uniform smoothness has a given power type. In this talk we will present a solution of this problem. All of the relevant background and concepts will be explained, and no prerequisites will be assumed beyond rudimentary undergraduate functional analysis and probability. Based on joint work with Alexandros Eskenazis.

While AI has been disrupting conventional weatherforecasting, we are only beginning to witness theimpact of AI on long-term climate simulations. Thefidelity and reliability of climate models have beenlimited by computing capabilities. These limitationslead to inaccurate representations of key processessuch as convection, cloud, or mixing or restrict theensemble size of climate predictions. Therefore, theseissues are a significant hurdle in enhancing climatesimulations and their predictions.Here, I will discuss a new generation of climatemodels with AI representations of unresolved oceanphysics, learned from high-fidelity simulations, andtheir impact on reducing biases in climatesimulations. The simulations are performed withoperational ocean model components. I will furtherdemonstrate the potential of AI to accelerate climatepredictions and increase their reliability through thegeneration of fully AI-driven emulators, which canreproduce decades of climate model output in secondswith high accuracy

Olfactory perception raises two fundamental questions:  ‘What is an odor?’ — its identity—and  ‘How strong is an odor?’ — its intensity. While significant progress has been made in characterizing these perceptual variables in humans in relation to odor composition and concentration, limitations in human neuroscience methods restrict our ability to probe their neural correlates with high temporal and spatial resolution. To address this gap, we developed a novel behavioral paradigm in mice to study the neural computations underlying odor perception. First, we trained mice to report perceptual distances between odors, enabling us to construct a mouse odor perceptual space that links perceptual odor identity to neural representations. Second, we trained mice to match the perceived intensities of different odors, creating a framework to probe the neural coding of odor intensity. This approach offers a path to connecting perceptual judgments to neural activity and may be extensible to other sensory systems. 

Cosmological observations suggest that about 85% of the universe’s mass is made up of matter that neither emits nor absorbs light. The existence of this mysterious component—dark matter—is inferred from its gravitational effects and is theorized to interact only very weakly with ordinary matter. The XENON detector, located deep underground in Italy’s Gran Sasso Laboratory, employs a large reservoir of ultrapure liquid xenon to search for the faint signals produced when a dark matter particle collides with a xenon atom. By suppressing background radiation and using highly sensitive sensors, the experiment strives to observe these extremely rare events. Although dark matter remains undetected, XENON continues to search while also shaping future searches.

The central limit theorem (CLT) and related results for stationary weakly dependent sequences of random variables have been extensively studied in the past century, starting from a pioneering work of Berenstien (1927).  However, in many physical  phenomena there are external forces, measurement errors and unknown variables (e.g. storms, the observer effect, the uncertainty principle etc.). This means that the local laws of physics depend on time, and it leads us to studying non-stationary sequences. 

The asymptotic behaviour of non-stationary sequences have been studied extensively in the past decades, but it is still developing compared with the theory of stationary processes. In this talk we will focus on inhomogeneous Markov chains. For sufficiently well contracting Markov chains the CLT was first proven by Dobrushin (1956). Since then many results were proven for stationary chains. In 2021 Dolgopyat and Sarig proved local central limit theorems (LCLT) for inhomogeneous Markov chains. In 2022 Dolgopyat and H proved optimal CLT rates in Dobrusin's CLT. These results closed a big gap in literature concerning the non-stationary case. 

An open problem raised by Dolgopyat and Sarig in their 2021 book concerns limit theorems for Markov shifts, that is when the underlying sequence of functions that forms the partial sums depend on the entire path of the chain. Two circumstances where such dependence arises are products of random matrices and random iterated functions, and there are many other instances when the functionals depend on the entire path. 

In this talk we will present our solution to the above problem. More precisely, we prove CLT, optimal CLT rates and LCLT for a wide class of sufficiently well mixing Markov chains and functionals with infinite memory. Even though the inhomogeneous case is more complicated, our results seem to be new already for stationary chains.

Abstract: How voluntary, self-paced intentions emerge in the brain and translate into action remains one of the most fundamental open questions in neuroscience. Leveraging rare access to intracranial neuronal recordings from human motor cortex, we built a real-time, online closed-loop system that allowed us to study the formation of voluntary actions under competitive conditions.We show that participants have only limited capacity to voluntarily steer their motor-cortex activity when doing so is strategically advantageous-revealing tight constraints on intentional control at the neural population level. Yet the commitment to act can be decoded reliably from motor-cortex activity roughly 250 ms before movement onset, at a time point when participants report already being consciously aware of their decision. We also find that brain–computer interfaces trained in one cognitive context transfer seamlessly to another, despite substantial differences in neural trajectories and force profiles-suggesting a shared underlying representational structure for volitional actions in motor cortex.Offline analyses further uncovered the specific neural patterns that signal commitment to action, shedding new light on how early voluntary actions can be reliably predicted from motor-cortex activity. We will conclude by discussing how these and related results inform emerging efforts to track and interpret intentions in advanced AI systems (ai-intentions.org).

Glucose can enter the blood following a meal, and/or can be produced by the liver and kidneys at times of need such as fasting. An elevation in blood glucose beyond steady state levels leads to secretion of the hormone insulin, leading to increase in glucose uptake into muscle and adipose tissues. Diabetes Mellitus arises when insufficient levels of insulin are secreted into the blood, manifesting as a chronic elevation in blood glucose levels. A reduction in glucose levels can lead to secretion of a large number of hormones, such as glucagon, cortisol and adrenaline, which cause endogenous glucose production and secretion into the blood,  maintaining homeostasis of glucose levels. In this talk we will use mathematical modeling and biochemical measurements to study the dynamics of hormone secretion in healthy individuals and Diabetes patients, and (hopefully) provide an answer to a key question: does the "body" measure glucose levels and regulates glucose levels accordingly by secreting insulin/glucose, as expected by a standard negative feedback system, or does it estimate future glucose levels and secretes hormones/glucose in a feedforward mechanism?Students interested in meeting the speaker after the seminar may sign up here:LINKFOR THE LATEST UPDATES AND CONTENT ON SOFT MATTER AND BIOLOGICAL PHYSICS AT THE WEIZMANN, VISIT OUR WEBSITE: https://www.bio

Ensuring that AI systems behave as intended is a central challenge in contemporary AI. This talk offers an exposition of provable mathematical guarantees for learning and security in AI systems.

Starting with a classic learning-theoretic perspective on generalization guarantees, we present two results quantifying the amount of training data that is provably necessary and sufficient for learning: (1) In online learning, we show that access to unlabeled data can reduce the number of prediction mistakes quadratically, but no more than quadratically [NeurIPS23, NeurIPS25 Best Paper Runner-Up]. (2) In statistical learning, we discuss how much labeled data is actually necessary for learning—resolving a long-standing gap left open by the celebrated VC theorem [COLT23].

Provable guarantees are especially valuable in settings that require security in the face of malicious adversaries. The main part of the talk adopts a cryptographic perspective,  showing how to: (1) Utilize interactive proof systems to delegate data collection and AI training tasks to an untrusted party [ITCS21, COLT23, NeurIPS25]. (2) Leverage random self-reducibility to provably remove backdoors from AI models, even when those backdoors are themselves provably undetectable [STOC25].

The talk concludes with an exploration of future directions concerning generalization in generative models, and AI alignment against malicious and deceptive AI.