Events

The well-known Zig-Zag product and related graph operators, like derandomized squaring, are fundamentally combinatorial in nature. Classical bounds on their behavior often rely on a mix of combinatorics and linear algebra. However, these traditional bounds are not tight and frequently fail to align with experimental results. In this talk, we will present a more refined analysis that utilizes the full spectrum of the graph, rather than relying solely on its spectral expansion. This approach produces results that both match experimental observations and, in a sense, are proved to be optimal. Our technique is analytic, diverging from classical methods: for the upper bound, we apply finite free probability, while for the lower bound, we draw on results from analytic combinatorics.
Based on joint works with Itay Cohen, Gal Maor and Yuval Peled. No prior knowledge is required.

Let $\mathcal{R}:L^{\mathrm{\infty }}({\mathbb{S}}^{n-1})\to L^{\mathrm{\infty }}({\mathbb{S}}^{n-1})$ denote the spherical Radon transform, defined as $\mathcal{R}(f)(\theta )={\int }_{{\mathbb{S}}^{n-1}\cap {\theta }^{\perp }}f(u)d\sigma (u)$. A long-standing question in non-linear harmonic analysis due to Lutwak, Gardner, and Fish--Nazarov--Ryabogin--Zvavitch, is to characterize those non-negative $\rho \in L^{\mathrm{\infty }}({\mathbb{S}}^{n-1})$ so that $\mathcal{R}({\rho }^{n-1})=c\rho$ when $n\ge 3$. We show that this holds iff $\rho$ is constant, and moreover, $\mathcal{R}(\mathcal{R}({\rho }^{n-1}{)}^{n-1})=c\rho$ iff $\rho$ is either identically zero or is the reciprocal of some Euclidean norm. Our proof recasts the problem in a geometric language using the intersection body operator $I$,  introduced by Lutwak following the work of Busemann, which plays a central role in the dual Brunn-Minkowski theory. We show that for any star-body $K$ in ${\mathbb{R}}^n$ when $n\ge 3$, $I^{2}K=cK$ iff $K$ is a centered ellipsoid, and hence $IK=cK$ iff $K$ is a centered Euclidean ball. To this end, we interpret the iterated intersection body equation as an Euler-Lagrange equation for a certain volume functional under radial perturbations, derive new formulas for the volume of $IK$, and introduce a continuous version of Steiner symmetrization for Lipschitz star-bodies, which (surprisingly) yields a useful radial perturbation exactly when $n\ge 3$.

Joint work with Shahar Shabelman and Amir Yehudayoff.

Recent advancements in visual content generation have made it easier than ever to generate remarkable imagery, often limited only by one’s imagination. However, unlike images, video generation requires both spatial and, critically, temporal understanding, posing unique and exciting challenges for existing models.

In this talk, I will explore key milestones in achieving coherent video generation through the lens of my works in the field. Each work tackles a different aspect of video generation, from temporal aliasing to video customization and motion comprehension. For each, I will first analyze prior approaches and identify key failure modes that lead to spatial or temporal incoherence. I will then present solutions based on the analyses to mitigate these issues—without requiring any additional data or model scaling. Finally, I will discuss open challenges and propose directions for future research.

Bio:
Hila is a PhD candidate at Tel Aviv University, advised by Prof. Lior Wolf. Her research focuses on understanding, interpreting, and correcting the predictions of deep foundational models. During her PhD, she interned at Google Research, Google DeepMind, and Meta AI, where she worked on video generation. Hila has received several awards, including the Fulbright Postdoctoral Fellowship, the Eric and Wendy Schmidt Postdoctoral Award, the Deutsch Prize for Outstanding PhD Students, and the Council for Higher Education (VATAT) Award for Outstanding PhD Students.

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