Colloquia & Seminars

Speaker: Ruihua Fan, Harvard University

Title: Extracting the quantum Hall conductance from a single bulk wavefunction from the modular flow

Topological Quantum Matter Seminar Speaker: Ruihua Fan, Harvard University Title: Extracting the quantum Hall conductance from a single bulk wavefunction from the modular flow Abstract: One question in the study of topological phases is to identify the topological data from the ground state wavefunction without accessing the Hamiltonian. Since local measurement is not enough, entanglement becomes an indispensable tool. Here, we use modular Hamiltonian (entanglement Hamiltonian) and modular flow to rephrase previous studies on topological entanglement entropy and motivate a natural generalization, which we call the entanglement linear response. We will show how it embraces a previous work by Kim&Shi et al on the chiral central charge, and furthermore, inspires a new formula for the quantum Hall conductance....

Speaker: Dima Sinapova, Rutgers University

Title: The Tree Property and uncountable cardinals

Colloquium Speaker: Dima Sinapova (Rutgers University) Title: The Tree Property and uncountable cardinals Abstract: In the late 19th century Cantor discovered that there are different levels of infinity. More precisely he showed that there is no bijection between the natural numbers and the real numbers, meaning that the reals are uncountable. He then went on to discover a whole hierarchy of infinite cardinal numbers. It is natural to ask if finitary and countably infinite combinatorial objects have uncountable analogues. It turns out that the answer is yes. We will focus on one such key combinatorial property, the tree property. A classical result from graph theory (König's infinity lemma) shows the existence of this property for countable trees. We...

Speaker: Surya Ganguli, Stanford University

Title: Statistical mechanics of neural networks: From the geometry of high dimensional error landscapes to beating power law neural scaling

New Technologies in Mathematics Speaker: Surya Ganguli, Stanford University Title: Statistical mechanics of neural networks: From the geometry of high dimensional error landscapes to beating power law neural scaling Abstract: Statistical mechanics and neural network theory have long enjoyed fruitful interactions.  We will review some of our recent work in this area and then focus on two vignettes. First we will analyze the high dimensional geometry of neural network error landscapes that happen to arise as the classical limit of a dissipative many-body quantum optimizer.  In particular, we will be able to use the Kac-Rice formula and the replica method to calculate the number, location, energy levels, and Hessian eigenspectra of all critical points of any index.  Second we will review recent...

Speaker: Marcelo Disconzi, Vanderbilt University

Title: General-relativistic viscous fluids

General Relativity Seminar Speaker: Marcelo Disconzi, Vanderbilt University Title: General-relativistic viscous fluids Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with...

Speaker: Jie Wang, Harvard CMSA

Title: Kahler geometry in twisted materials

Member Seminar Speaker: Jie Wang Title: Kahler geometry in twisted materials Abstract: Flatbands are versatile platform for realizing exotic quantum phases due to the enhanced interactions. The canonical example is Landau level where fractional quantum Hall physics exists. Although interaction is strong, the fractional quantum Hall effect is relatively well understood thanks to its model wavefunction, exact parent Hamiltonian, conformal field theory analogous and other exact aspects. In generic flatbands, the interacting physics is controlled by the interplay between the interaction scale and intrinsic quantum geometries, in particular the Berry curvature and the Fubini-Study metric, which are in general spatially non-uniform. It is commonly believed that the non-uniform geometries destroy these exact properties of fractional quantum Hall physics, making...

Title: Title TBA

Quantum Matter Seminar

Title: Title TBA

Topological Quantum Matter Seminar

Speaker: Guy Gur-Ari, Google Brain

Title: Minerva: Solving Quantitative Reasoning Problems with Language Models

Title: Minerva: Solving Quantitative Reasoning Problems with Language Models Abstract: Quantitative reasoning tasks which can involve mathematics, science, and programming are often challenging for machine learning models in general and for language models in particular. We show that transformer-based language models obtain significantly better performance on math and science questions when trained in an unsupervised way on a large, math-focused dataset. Performance can be further improved using prompting and sampling techniques including chain-of-thought and majority voting. Minerva, a model that combines these techniques, achieves SOTA on several math and science benchmarks. I will describe the model, its capabilities and limitations.

Speaker: Subir Sachdev, Harvard

Title: Quantum statistical mechanics of charged black holes and strange metals

Colloquium Please note this colloquium will be held at a special time:  4:00-5:00 pm. Speaker: Subir Sachdev (Harvard) Title: Quantum statistical mechanics of charged black holes and strange metals Abstract: The Sachdev-Ye-Kitaev model was introduced as a toy model of interacting fermions without any particle-like excitations. I will describe how this toy model yields the universal low energy quantum theory of generic charged black holes in asymptotically 3+1 dimensional Minkowski space. I will also discuss how extensions of the SYK model yield a realistic theory of the strange metal phase of correlated electron systems.

Title:

Active Matter Seminar

Speaker: Zhigang Yau, Harvard CMSA

Title: Member Seminar: Title TBA

Speaker: Zhigang Yau

Title: Title TBA

Topological Quantum Matter Seminar

Title: Title TBA

New Technologies in Mathematics Seminar

Speaker: Leonid Rybnikov, Harvard CMSA

Title: Member Seminar: Title TBA

Speaker: Leonid Rybnikov

Title: Title TBA

Quantum Matter Seminar