Youtube Video Abstract: We show that Polchinski’s equation for exact renormalization group flow is equivalent to the optimal transport gradient flow of a field-theoretic relative entropy. This gives a surprising information-theoretic formulation of the exact renormalization group, expressed in the language of optimal transport. We will provide reviews of both the exact renormalization group, as well as the theory of optimal transportation. Our […]
https://youtu.be/5AoOpFFjW28 Speaker: Yuhuai Wu, Stanford and Google Title: Memorizing Transformers Abstract: Language models typically need to be trained or fine-tuned in order to acquire new knowledge, which involves updating their weights. We instead envision language models that can simply read and memorize new data at inference time, thus acquiring new knowledge immediately. In this talk, I […]
Abstract: Matroids are combinatorial abstractions of vector spaces embedded in a coordinate space. Many fundamental questions have been open for these classical objects. We highlight some recent progress that arise from the interaction between matroid theory and algebraic geometry. Key objects involve compactifications of embedded vector spaces, and an exceptional Hirzebruch-Riemann-Roch isomorphism between the K-ring of vector […]
Member Seminar Speaker: Farzan Vafa Title: Diffusive growth sourced by topological defects Abstract: In this talk, we develop a minimal model of morphogenesis of a surface where the dynamics of the intrinsic geometry is diffusive growth sourced by topological defects. We show that a positive (negative) defect can dynamically generate a cone (hyperbolic cone). We […]
https://www.youtube.com/playlist?list=PL0NRmB0fnLJTTVV5eLYJbJUHxi-3BipfS Schedule | April 4–8, 2022 Monday, April 4, 2022 Time (ET) Speaker Title/Abstract 9:30 am–10:30 am Pieter Blue, University of Edinburgh, UK (virtual) Title: Linear stability of the Kerr spacetime in the outgoing radiation gauge Abstract: This talk will discuss a new gauge condition (i.e. coordinate condition) for the Einstein equation, the linearisation of […]
Swampland Seminar Speakers: Simon Caron-Huot (McGill University) and Julio Parra (Caltech) Title: Causality constraints on corrections to Einstein gravity Abstract: We study constraints from causality and unitarity on 2→2 graviton scattering in four-dimensional weakly-coupled effective field theories. Together, causality and unitarity imply dispersion relations that connect low-energy observables to high-energy data. Using such dispersion relations, we derive two-sided bounds on gravitational Wilson coefficients […]
Harvard CMSA hosted the second annual Yip Lecture on April 4, 2022. The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip. This year’s speaker was Avi Loeb (Harvard). https://youtu.be/YV4Ki7x_yRc Extraterrestrial Life Abstract: Are we alone? It would be arrogant to think that we are, given that a quarter of all […]
Abstract: I will report a recent approach of regularizing divergent integrals on configuration spaces of Riemann surfaces, introduced by Si Li and myself in arXiv:2008.07503, with an emphasis on genus one cases where modular forms arise naturally. I will then talk about some applications in studying correlation functions in 2d chiral CFTs, holomorphic anomaly equations, […]
Speaker: Johannes Kleiner, LMU München Title: What is Mathematical Consciousness Science? Abstract: In the last three decades, the problem of consciousness – how and why physical systems such as the brain have conscious experiences – has received increasing attention among neuroscientists, psychologists, and philosophers. Recently, a decidedly mathematical perspective has emerged as well, which is now […]
Youtube Video Abstract: Characterizing many-body entanglement is one of the most important problems in quantum physics. We present our studies on the steady state von Neumann entropy and its transition in Brownian SYK models. For unitary evolution, we show that the correlations between different replicas account for the Page curve at late time, and a […]
Random Matrix & Probability Theory Seminar Speaker: Minh-Binh TRAN (SMU & MIT) Location: CMSA, Room G02 Title: On the wave turbulence theory for a stochastic KdV type equation Abstract: We report recent progress, in collaboration with Gigliola Staffilani (MIT), on the problem of deriving kinetic equations from dispersive equations. To be more precise, starting from the stochastic […]
Abstract: Gromov-Witten invariants of holomorphic symplectic 4-folds vanish and one can consider the corresponding reduced theory. In this talk, we will explain a definition of Gopakumar-Vafa type invariants for such a reduced theory. These invariants are conjectured to be integers and have alternative interpretations using sheaf theoretic moduli spaces. Our conjecture is proved for the product of […]