Events

The (naive) Ramanujan conjecture says that the spectrum of Hecke operators acting on the space of cuspidal automorphic functions is unitary. While this is true for the group GL_n, this is false for other reductive groups. The corrected conjecture, due to J. Arthur, describes the spectrum in terms of nilpotent orbits in the Langlands-dual Lie algebra.  In this talk, I'll outline the recently obtained proof of this conjecture (for function fields). This is joint work with V. Lafforgue and S. Raskin. 

Foundation models are a key platform which implicitly encodes world knowledge. In this talk we first focus on vision-language models, such as CLIP, and investigate their geometric behavior and logic behind the high-dimensional feature encoding. For instance, we find that as image or text become more rare and distinct they are encoded further from the center of the embedding. We explain why InfoNCE loss leads to that behavior. We also find out empirically that each modality can be well modeled statistically as admitting a multivariate Gaussian distribution. This finding is then proved formally, where we show InfoNCE asymptotically induces Gaussian statistics. Finally, we connect two major image foundation models – encoders and generators, through a universal normal embedding hypothesis. A surprising consequence of this hypothesis is demonstrated, where generative diffusion “noise” contains semantic data which can be accessed by linear probing for either classification or editing. This talk is based on 6 recent papers in the group published at ICML 2025, ICLR 2026 and CVPR 2026.

Bio:

Prof. Guy Gilboa is a faculty member at the Electrical and Computer Engineering Department, Technion – Israel Institute of Technology since 2013. Previously he has been a postdoctoral fellow at UCLA and a senior researcher at Microsoft and Philips Healthcare. His main research areas are mathematical image processing and machine learning, focusing on representation learning of foundation models.