Colloquia & Seminars

Title: Twisted D-branes and TQFTs valued in Calabi-Yau categories

Quantum Field Theory and Physical Mathematics Seminar Speaker: Surya Raghavendran, Yale University Title: Twisted D-branes and TQFTs valued in Calabi-Yau categories Abstract: Recently, Bozec–Calaque–Scherotzke have articulated a noncommutative version of the AKSZ construction, which associates to a smooth Calabi–Yau category a fully extended TQFT valued in a category of iterated Calabi–Yau cospans. In this talk, I will study a class of examples of such theories which arise in the context of conjectures of Costello and Li, which describe Type II strings in certain Ramond–Ramond backgrounds as topological strings. These TQFTs capture structural features of the BPS physics of D-branes that are universal in Chan–Paton factors. Conjecturally commutative limits of the values of such theories on closed manifolds can...

Title: Dynamics as intersection problem

Colloquium Speaker: Nikita Nekrasov, Simons Center Title: Dynamics as intersection problem Abstract: Most classical and quantum field theories are based on an action principle. However, there are important exceptions to this --- hydrodynamics and the theory of self-dual fields. In this talk we formulate the covariant relativistic fluid dynamics, with or without magnetic fields, as well as the theory of chiral boson in 1+1 dimensions, self-dual tensor in 1+5 dimensions, and self-dual four-form of IIB supergravity, in terms of intersection theory of an auxiliary phase space. This provides a common covariant geometric framework for systems without a conventional action, while at the same time laying the groundwork for quantization via the Kontsevich approach. Joint work with Paul Wiegmann....

Title: New directions in synthetic data

New Technologies in Mathematics Seminar Speaker: Tatsunori Hashimoto, Stanford Title: New directions in synthetic data Abstract: Synthetic data has been an effective, if boring set of techniques: prompt some language model to restructure your corpus to match some downstream task, with occasionally some distillation. In this talk, we will take a more expansive view of synthetic data as a general algorithmic tool for generative modeling, arguing that the design space and possibilities of synthetic data are much bigger than it might seem. Through a few recent works, we will show that synthetic data has major benefits beyond transforming the data - improving in-domain perplexities, and enabling unique algorithmic primitives, such as neighborhood smoothing and concatenated ‘mega’ documents. With...

Title: Quantum Field Theory and Physical Mathematics

Quantum Field Theory and Physical Mathematics Seminar  

Title: Statistical Shape Analysis of Complex Natural Structures

Colloquium Speaker: Anuj Srivastava, Johns Hopkins University Title: Statistical Shape Analysis of Complex Natural Structures Abstract: Statistical modeling and analysis of structured data is a fast-growing field in Statistics and Data Science. Rapid advances in imaging techniques have led to tremendous amounts of data for analyzing imaged objects across several scientific disciplines. Examples include shapes of cancer cells, botanical trees, human biometrics, 3D genome, brain anatomical structures, crowd videos, nano-manufacturing, and so on. Shapes are relevant even in non-imaging data contexts, e.g., the shapes of COVID rate curves or the shapes of activity cycles in lifestyle data. Imposing statistical models and inferences on shapes seems daunting because the shape is an abstract notion and one requires precise mathematical...

Title: Polynomial invariants of conjugation over finite fields

Algebra Seminar Speaker: Aryaman Maithani, University of Utah Title: Polynomial invariants of conjugation over finite fields Abstract: Consider the conjugation action of GL₂(K) on the polynomial ring K[X₂ₓ₂]. When K is an infinite field, the ring of invariants is a polynomial ring generated by the trace and the determinant. We describe the ring of invariants when K is a finite field, and show that it is a hypersurface.    

Title: Quantum Field Theory and Physical Mathematics

Quantum Field Theory and Physical Mathematics Seminar  

Title: Separation of timescales controls feature learning and overfitting in large neural networks

New Technologies in Mathematics Seminar Speaker: Pierfrancesco Urbani, Universite Paris-Saclay, CNRS, CEA, Institut de physique theorique Title: Separation of timescales controls feature learning and overfitting in large neural networks Abstract: To understand the inductive bias and generalization capabilities of large, overparameterized machine learning models, it is essential to analyze the dynamics of their training algorithms. Using dynamical mean field theory we investigate the learning dynamics of large two-layer neural networks. Our findings reveal that, for networks with a large width, the training process exhibits a separation of timescales phenomenon. This leads to several key observations: 1. The emergence of a slow timescale linked to the growth in Gaussian/Rademacher complexity of the network; 2. An inductive bias favoring low...

Title: CMSA Q&A Seminar: Hugh Woodin, Harvard

CMSA Q&A Seminar Speaker: Hugh Woodin, Harvard Title: Truth, proof, and AI