Calendar

This is a report about work in progress with: Adeel Khan, Aloysha Latyntsev, Hyeonjun Park and Charanya Ravi. We will describe a virtual Atiyah-Bott formula for Artin stacks.  In the Deligne-Mumford case our methods allow us to remove the global resolution hypothesis for the virtual normal bundle.

https://harvard.zoom.us/j/97335783449?pwd=S3U0eVdyODFEdzNaRXVEUTF3R3NwZz09

We will present some rigorous results about entropy and  relative entropy in QFT, motivated in part by recent physicists’ work which however depends on heuristic arguments such as introducing cut off and using path integrals.

https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09

I will explain a notion of rank for the relations amongst the equations of a projective variety, generalizing the classical notion of rank of a quadric. I will then explain a result telling us that, for a general canonical curve, all syzygies are linear combinations of syzygies of minimal rank. This is a sweeping generalization of old results of Andreotti-Mayer, Harris-Arbarello and Green, which tell us that canonical curves are defined by quadrics of rank four. As a special case, this perspective gives us a new, and simpler, proof of Green’s conjecture for general curves.

https://harvard.zoom.us/j/91082896381?pwd=TmJCanRPVlM4VGR2L1RzZGVGbHRVQT09

The SYZ proposal suggests that mirror symmetry is T-duality. It is a folklore that locally free sheaves are mirror to a Lagrangian multi-section of the SYZ fibration. In this talk, I will introduce the notion of tropical Lagrangian multi-sections and discuss how to obtain from such object to a class of locally free sheaves on the log Calabi-Yau spaces that Gross-Siebert have considered. I will also discuss a joint work with Kwokwai Chan and Ziming Ma, where we proved the smoothability of a class of locally free sheaves on some log Calabi-Yau surfaces by using combinatorial data obtained from tropical Lagrangian multi-sections.

Zoom Link: https://cuhk.zoom.us/j/95804207557

Meeting ID: 958 0420 7557; Passcode: 20220302

We construct infinitely many new exactly solvable local commuting projector lattice Hamiltonian models for general bosonic beyond group cohomology invertible topological phases of order two and four in any spacetime dimensions, whose boundaries are characterized by gravitational anomalies. Examples include the beyond group cohomology invertible phase “w2w3” in (4+1)D that has an anomalous boundary topological order with fermionic particle and fermionic loop excitations that have mutual statistics. Finally, we will demonstrate a few examples of fermionic loop excitations.

https://harvard.zoom.us/j/977347126
Password: cmsa

Scaling laws and associated downstream trends can be used as an organizing principle when thinking about current and future ML progress.  I will briefly review scaling laws for generative models in a number of domains, emphasizing language modeling.  Then I will discuss scaling results for transfer from natural language to code, and results on python programming performance from “codex” and other models.  If there’s time I’ll discuss prospects for the future — limitations from dataset sizes, and prospects for RL and other techniques.

Inspired by an analogy between torsion and preperiodic points, Zhang has proposed a dynamical generalization of the classical Manin-Mumford and Bogomolov conjectures. A special case of these conjectures, for `split’ maps, has recently been established by Nguyen, Ghioca and Ye. In particular, they show that two rational maps have at most finitely many common preperiodic points, unless they are `related’. Recent breakthroughs by Dimitrov, Gao, Habegger and Kühne have established that the classical Bogomolov conjecture holds uniformly across curves of given genus.

In this talk we discuss uniform versions of the dynamical Bogomolov conjecture across 1-parameter families of split maps and curves. To this end, we establish instances of a ‘relative dynamical Bogomolov conjecture’. This is joint work with Harry Schmidt (University of Basel).

The Newell-Littlewood numbers are defined in terms of the  Littlewood-Richardson coefficients. Both arise as tensor product  multiplicities for a classical Lie group. A. Klyachko connected  eigenvalues of sums of Hermitian matrices to the saturated LR-cone and  established defining linear inequalities. We prove analogues for the  saturated NL-cone. This is based on work with Gidon Orelowitz, Nicolas  Ressayre and Alexander Yong.

We will explore the fascinating history of counting shapes, starting with counting dots (you can have no dots or one dot or two dots…) and then moving on to counting shapes of higher dimension. Hopefully you will see some connections to interesting questions in geometry, physics, homotopy theory, and number theory.

While over-parameterization is widely believed to be crucial for the success of optimization for the neural networks, most existing theories on over-parameterization do not fully explain the reason — they either work in the Neural Tangent Kernel regime where neurons don’t move much, or require an enormous number of neurons. In this talk I will describe our recent works towards understanding training dynamics that go beyond kernel regimes with only polynomially many neurons (mildly overparametrized). In particular, we first give a local convergence result for mildly overparametrized two-layer networks. We then analyze the global training dynamics for a related overparametrized tensor model. For both works, we rely on a key intuition that neurons in overparametrized models work in groups and it’s important to understand the behavior of an average neuron in the group. Based on two works: https://arxiv.org/abs/2102.02410 and https://arxiv.org/abs/2106.06573.

Professor Rong Ge is Associate Professor of Computer Science at Duke University. He received his Ph.D. from the Computer Science Department of Princeton University, supervised by Sanjeev Arora. He was a post-doc at Microsoft Research, New England. In 2019, he received both a Faculty Early Career Development Award from the National Science Foundation and the prestigious Sloan Research Fellowship. His research interest focus on theoretical computer science and machine learning. Modern machine learning algorithms such as deep learning try to automatically learn useful hidden representations of the data. He is interested in formalizing hidden structures in the data and designing efficient algorithms to find them. His research aims to answer these questions by studying problems that arise in analyzing text, images, and other forms of data, using techniques such as non-convex optimization and tensor decompositions.

Zoom ID: 950 2372 5230 (Password: cmsa)

In this talk we will discuss the interaction between magnetic monopoles and massless fermions. In the 1980’s Callan and Rubakov showed that in the simplest example and that fermion-monopole interactions catalyze proton decay in GUT completions of the standard model. Here we will explain how fermions in general representations interact with general spherically symmetric monopoles and classify the types of symmetries that are broken: global symmetries with ABJ-type anomalies.

https://harvard.zoom.us/j/977347126
Password: cmsa