Talks

The coordinate functions on a Poisson variety are log-canonical if the Poisson bracket of two coordinate functions equals a constant times the product of these functions. We consider the symplectic groupoid of unipotent upper-triangular matrices equipped with canonical Poisson bracket. We described a system of log-canonical coordinates and the corresponding cluster structure. As a bonus, we discovered a system of log-canonical coordinates on Teichmueller space of closed genus 2 surfaces. This is joint work with L. Chekhov.

Zoom link:  https://pitp.zoom.us/j/94716952708?pwd=R2RiQWRpcHFMYlJLMlB0UjlPVGZkQT09

In recent years, machine learning has been successfully used to identify phase transitions and classify phases of matter in a data-driven manner. Neural network (NN)-based approaches are particularly appealing due to the ability of NNs to learn arbitrary functions. However, the larger an NN, the more computational resources are needed to train it, and the more difficult it is to understand its decision making. Thus, we still understand little about the working principle of such machine learning approaches, when they fail or succeed, and how they differ from traditional approaches. In this talk, I will present analytical expressions for the optimal predictions of three popular NN-based methods for detecting phase transitions that rely on solving classification and regression tasks using supervised learning at their core. These predictions are optimal in the sense that they minimize the target loss function. Therefore, in practice, optimal predictive models are well approximated by high-capacity predictive models, such as large NNs after ideal training. I will show that the analytical expressions we have derived provide a deeper understanding of a variety of previous NN-based studies and enable a more efficient numerical routine for detecting phase transitions from data.

Zoom Link: https://pitp.zoom.us/j/91642481966?pwd=alkrWEFFcFBvRlJEbDRBZWV3MFFDUT09

Zoom link: https://pitp.zoom.us/j/96212372067?pwd=dWVaUFFFc3c5NTlVTDFHOGhCV2pXdz09

In this talk, I will discuss our work on using models inspired by natural language processing in the realm of many-body physics. Specifically, I will demonstrate their utility in reconstructing quantum states and simulating the real-time dynamics of closed and open quantum systems. Finally, I will show the efficacy of using these models for combinatorial optimization, yielding solutions of exceptional accuracy compared to traditional simulated and simulated quantum annealing methods.

Zoom link:  https://pitp.zoom.us/j/99042603813?pwd=eWl2eC90bXFXVHdJeG9zb3lIQVZKUT09

Experimental searches for new fundamental physics are increasingly adopting an Effective Field Theory (EFT) approach, in which the phenomenological effects of the underlying high-energy (UV) physics are parametrised by a series of EFT coefficients that can be readily compared with data.
While pragmatically useful, this begs the question: what UV information can be extracted from our measurements of these EFT coefficients?
In this talk, I will describe how scattering amplitudes techniques ("sum rules") can establish precise connections between EFT coefficients and the underlying UV physics.
In particular, I will focus on recent progress in applying these techniques in cosmology, where they have been used to connect our large-scale measurements of dark energy, gravitational waves and the CMB with properties of the underlying UV completion.

Zoom Link: https://pitp.zoom.us/j/99740767444?pwd=OTMxWlVDYitSTXdKdmlFRWxhdGl1dz09

In an isolated quantum many-body system undergoing unitary evolution, the entropy of a subsystem (smaller than half the system size) thermalizes if at long times, it is to leading order equal to the thermodynamic entropy of the subsystem at the same energy. We prove entropy thermalization for a nearly integrable Sachdev-Ye-Kitaev model initialized in a pure product state. The model is obtained by adding random all-to-all 4-body interactions as a perturbation to a random free-fermion model. In this model, there is a regime of “thermalization without eigenstate thermalization.” Thus, the eigenstate thermalization hypothesis is not a necessary condition for thermalization. Joint work with Aram W. Harrow

Zoom Link: https://pitp.zoom.us/j/91710478120?pwd=OVRDOStOSkdIVG9mcGJqMWJlU1FRdz09

I will revisit the physics of Heterotic Strings on four-dimensional ADE singularities in light of recent progress in the context of higher global symmetries combined with our improved understanding of 6d SCFTs over the past decade. In particular, on ADE singularities the fractional heterotic little string instantons enjoy a continuous 2 group symmetry that one can exploit to constrain possible networks of T-dualities. These predictions are confirmed exploiting duality with F-theory, and also shed light on the question of the geometric engineering limit of heterotic strings on ALE spaces. Based on joint works with Kantaro Ohmori, Paul-Konstantin Öhlmann and Muyang Liu.

Zoom Link: https://pitp.zoom.us/j/92559165562?pwd=R3NLRktuWFYyKzFNQmhFeS9sQ2tQZz09

This talk will consider a stochastic multiple-timescale dynamical system modeling a biological neuron. With this model, we will separately uncover the mechanisms underlying two different ways biological neurons encode information with stochastic perturbations: self-induced stochastic resonance (SISR) and inverse stochastic resonance (ISR). We will then show that in the same weak noise limit, SISR and ISR are related through the relative geometric positioning (and stability) of the fixed point and the generic folded singularity of the model’s critical manifold.  This mathematical result could explain the experimental observation where neurons with identical morphological features sometimes encode different information with identical synaptic input. Finally, if time permits, we shall discuss the plausible applications of this result in neuro-biologically inspired machine learning algorithms, particularly reservoir computing based on liquid-state machines.

Zoom link:  https://pitp.zoom.us/j/94345141890?pwd=aTRFM3M0a0xCOEM3aXZjY2hFYzVrQT09