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DTSTART;TZID=America/New_York:20220216T093000
DTEND;TZID=America/New_York:20220216T103000
DTSTAMP:20240425T182937Z
CREATED:20240213T112726Z
LAST-MODIFIED:20240425T182937Z
UID:10002499-1645003800-1645007400@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Kobayashi-Hitchin correspondences for harmonic bundles and monopoles
DESCRIPTION:Speaker: Takuro Mochizuki (Kyoto University) \nTitle: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles \nAbstract:  In 1960’s\, Narasimhan and Seshadri discovered the equivalence between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s\, Donaldson\, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles and stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then\, many interesting generalizations have been studied. \nIn this talk\, we would like to review a stream in the study of such correspondences for Higgs bundles\, integrable connections\, $D$-modules and periodic monopoles.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/2-16-2022-cmsa-colloquium/
LOCATION:Virtual
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Colloquium-02.16.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220215T093000
DTEND;TZID=America/New_York:20220215T103000
DTSTAMP:20240304T083319Z
CREATED:20230818T054001Z
LAST-MODIFIED:20240304T083319Z
UID:10001289-1644917400-1644921000@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Virtual Coulomb branch and quantum K-theory
DESCRIPTION:Abstract: In this talk\, I will introduce a virtual variant of the quantized Coulomb branch constructed by Braverman-Finkelberg-Nakajima\, where the convolution product is modified by a virtual intersection. The resulting virtual Coulomb branch acts on the moduli space of quasimaps into the holomorphic symplectic quotient T^*N//G. When G is abelian\, over the torus fixed points\, this representation is a Verma module. The vertex function\, a K-theoretic enumerative invariant introduced by A. Okounkov\, can be expressed as a Whittaker function of the algebra. The construction also provides a description of the quantum q-difference module. As an application\, this gives a proof of the invariance of the quantum q-difference module under variation of GIT.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/virtual-coulomb-branch-and-quantum-k-theory/
LOCATION:Virtual
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220210T093000
DTEND;TZID=America/New_York:20220210T110000
DTSTAMP:20240301T072127Z
CREATED:20240214T100805Z
LAST-MODIFIED:20240301T072127Z
UID:10002658-1644485400-1644490800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:The global structure of the Standard Model and new nonperturbative processes
DESCRIPTION:Speaker: Mohamed Anber (Durham University) \nTitle: The global structure of the Standard Model and new nonperturbative processes \nAbstract: It is well-established that the Standard Model (SM) of particle physics is based on su(3)Xsu(2)Xu(1) Lie-algebra. What is less appreciated\, however\, is that SM accommodates a Z_6 1-form global symmetry.  Gauging this symmetry\, or a subgroup of it\, changes the global structure of the SM gauge group and amounts to summing over sectors of instantons with fractional topological charges. After a brief review of the concept of higher-form symmetries\, I will explain the origin of the Z_6 1-form symmetry and construct the explicit fractional-instanton solutions on compact manifolds. The new instantons mediate baryon-number and lepton-number violating processes\, which can win over the weak BPST-instanton processes\, provided that SM accommodates extra hyper-charged particles above the TeV scale. I will also comment on the cosmological aspects of the new solutions.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/2-10-2022-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/jpeg:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-QMMP-02.10.2022-1544x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220209T200000
DTEND;TZID=America/New_York:20220209T213000
DTSTAMP:20240301T072509Z
CREATED:20240214T103129Z
LAST-MODIFIED:20240301T072509Z
UID:10002674-1644436800-1644442200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:On the absence of global anomalies of heterotic string theories
DESCRIPTION:Speaker: Yuji Tachikawa (Kavli IPMU\, U Tokyo) \nTitle: On the absence of global anomalies of heterotic string theories \nAbstract: Superstring theory as we know it started from the discovery by Green and Schwarz in 1984 that the perturbative anomalies of heterotic strings miraculously cancel. But the cancellation of global anomalies of heterotic strings remained an open problem for a long time. \nIn this talk\, I would like to report how this issue was finally resolved last year\, by combining two developments outside of string theory. Namely\, on one hand\, the study of topological phases in condensed matter theory has led to our vastly improved understanding of the general form of global anomalies. On the other hand\, the study of topological modular forms in algebraic topology allows us to constrain the data of heterotic worldsheet theories greatly\, as far as their contributions to the anomalies are concerned. Putting them together\, it is possible to show that global anomalies of heterotic strings are always absent. \nThe talk is based on https://arxiv.org/abs/2103.12211 and https://arxiv.org/abs/2108.13542 \, in collaboration with Mayuko Yamashita.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/2-9-2022-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/jpeg:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-QMMP-02.09.2022-1544x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220209T140000
DTEND;TZID=America/New_York:20220209T150000
DTSTAMP:20240517T193404Z
CREATED:20230808T181534Z
LAST-MODIFIED:20240517T193404Z
UID:10001204-1644415200-1644418800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Toward Demystifying Transformers and Attention
DESCRIPTION:Speaker: Ben Edelman\, Harvard Computer Science \nTitle: Toward Demystifying Transformers and Attention \nAbstract: Over the past several years\, attention mechanisms (primarily in the form of the Transformer architecture) have revolutionized deep learning\, leading to advances in natural language processing\, computer vision\, code synthesis\, protein structure prediction\, and beyond. Attention has a remarkable ability to enable the learning of long-range dependencies in diverse modalities of data. And yet\, there is at present limited principled understanding of the reasons for its success. In this talk\, I’ll explain how attention mechanisms and Transformers work\, and then I’ll share the results of a preliminary investigation into why they work so well. In particular\, I’ll discuss an inductive bias of attention that we call sparse variable creation: bounded-norm Transformer layers are capable of representing sparse Boolean functions\, with statistical generalization guarantees akin to sparse regression.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/2-9-2022-new-technologies-in-mathematics-seminar/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-NTM-Seminar-02.09.2022-1553x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220208T213000
DTEND;TZID=America/New_York:20220208T223000
DTSTAMP:20240501T205116Z
CREATED:20240214T041520Z
LAST-MODIFIED:20240501T205116Z
UID:10002524-1644355800-1644359400@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Tetrahedron instantons and M-theory indices
DESCRIPTION:Colloquium \nSpeaker: Wenbin Yan (Tsinghua University) \nTitle: Tetrahedron instantons and M-theory indices \nAbstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk\, we will review instanton moduli spaces\, explain the construction\, moduli space and partition functions of tetrahedron instantons. We will also point out possible relations with M-theory index which could be a generalization of Gupakuma-Vafa theory.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/tetrahedron-instantons-and-m-theory-indices/
LOCATION:Virtual
CATEGORIES:Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220208T093000
DTEND;TZID=America/New_York:20220208T103000
DTSTAMP:20240304T083416Z
CREATED:20230818T051427Z
LAST-MODIFIED:20240304T083416Z
UID:10001287-1644312600-1644316200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:SYZ Conjecture beyond Mirror Symmetry
DESCRIPTION:Abstract: Strominger-Yau-Zaslow conjecture is one of the guiding principles in mirror symmetry\, which not only predicts the geometric structures of Calabi-Yau manifolds but also provides a recipe for mirror construction. Besides mirror symmetry\, the SYZ conjecture itself is the holy grail in geometrical analysis and closely related to the behavior of the Ricci-flat metrics. In this talk\, we will explain how SYZ fibrations on log Calabi-Yau surfaces detect the non-standard semi-flat metric which generalized the semi-flat metrics of Greene-Shapere-Vafa-Yau. Furthermore\, we will use the SYZ fibration on log Calabi-Yau surfaces to prove the Torelli theorem of gravitational instantons of type ALH^*. This is based on the joint works with T. Collins and A. Jacob.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/syz-conjecture-beyond-mirror-symmetry/
LOCATION:Virtual
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220203T113000
DTEND;TZID=America/New_York:20220203T130000
DTSTAMP:20240301T073438Z
CREATED:20240301T073438Z
LAST-MODIFIED:20240301T073438Z
UID:10002886-1643887800-1643893200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Quantum Oscillations of Electrical Resistivity in an Insulator
DESCRIPTION:Speaker: Lu Li (U Michigan) \nTitle: Quantum Oscillations of Electrical Resistivity in an Insulator \nAbstract: In metals\, orbital motions of conduction electrons are quantized in magnetic fields\, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators\, in which all the electrons are localized. Here we report a notable exception in an insulator — ytterbium dodecaboride (YbB12). The resistivity of YbB12\, despite much larger than that of usual metals\, exhibits profound quantum oscillations under intense magnetic fields. This unconventional oscillation is shown to arise from the insulating bulk instead of conducting surface states. The large effective masses indicate strong correlation effects between electrons. Our result is the first discovery of quantum oscillations in the electrical resistivity of a strongly correlated insulator and will bring crucial insight into understanding the ground state in gapped Kondo systems.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/2-3-2022-quantum-matter-in-mathematics-and-physics-2/
LOCATION:Virtual
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220202T093000
DTEND;TZID=America/New_York:20220202T103000
DTSTAMP:20240304T075005Z
CREATED:20240214T041742Z
LAST-MODIFIED:20240304T075005Z
UID:10002525-1643794200-1643797800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Learning and inference from sensitive data
DESCRIPTION:Speaker: Adam Smith (Boston University) \nTitle: Learning and inference from sensitive data \nAbstract: Consider an agency holding a large database of sensitive personal information—say\,  medical records\, census survey answers\, web searches\, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records. \nI will discuss recent (and not-so-recent) results on this problem with a focus on the release of statistical models. I will first explain some of the fundamental limitations on the release of machine learning models—specifically\, why such models must sometimes memorize training data points nearly completely. On the more positive side\, I will present differential privacy\, a rigorous definition of privacy in statistical databases that is now widely studied\, and increasingly used to analyze and design deployed systems. I will explain some of the challenges of sound statistical inference based on differentially private statistics\, and lay out directions for future investigation.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/learning-and-inference-from-sensitive-data/
LOCATION:Virtual
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Colloquium-02.02.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220201T093000
DTEND;TZID=America/New_York:20220201T103000
DTSTAMP:20240304T064710Z
CREATED:20230818T053619Z
LAST-MODIFIED:20240304T064710Z
UID:10001288-1643707800-1643711400@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Curve-counting with fixed domain (“Tevelev degrees”)
DESCRIPTION:Abstract: We will consider the following problem: if (C\,x_1\,…\,x_n) is a fixed general pointed curve\, and X is a fixed target variety with general points y_1\,…\,y_n\, then how many maps f:C -> X in a given homology class are there\, such that f(x_i)=y_i? When considered virtually in Gromov-Witten theory\, the answer may be expressed in terms of the quantum cohomology of X\, leading to explicit formulas in some cases (Buch-Pandharipande). The geometric question is more subtle\, though in the presence of sufficient positivity\, it is expected that the virtual answers are enumerative. I will give an overview of recent progress on various aspects of this problem\, including joint work with Farkas\, Pandharipande\, and Cela\, as well as work of other authors.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/curve-counting-with-fixed-domain-tevelev-degrees/
LOCATION:Virtual
CATEGORIES:Algebraic Geometry in String Theory Seminar
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Algebraic-Geometry-in-String-Theory-02.01.2022-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220106T090000
DTEND;TZID=America/New_York:20220106T100000
DTSTAMP:20240529T175141Z
CREATED:20240215T093525Z
LAST-MODIFIED:20240529T175141Z
UID:10002721-1641459600-1641463200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:The smooth closing lemma for area-preserving surface diffeomorphisms
DESCRIPTION:Speaker: Boyu Zhang\, Princeton University \nTitle: The smooth closing lemma for area-preserving surface diffeomorphisms \nAbstract: In this talk\, I will introduce the smooth closing lemma for area-preserving diffeomorphisms on surfaces. The proof is based on a Weyl formula for PFH spectral invariants and a non-vanishing result of twisted Seiberg- Witten Floer homology. This is joint work with Dan Cristofaro-Gardiner and Rohil Prasad.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/1-6-2022-interdisciplinary-science-seminar/
LOCATION:Virtual
CATEGORIES:Interdisciplinary Science Seminar
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Interdisciplinary-Science-Seminar-01.06.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211215T140000
DTEND;TZID=America/New_York:20211215T150000
DTSTAMP:20240515T204057Z
CREATED:20230808T180208Z
LAST-MODIFIED:20240515T204057Z
UID:10001202-1639576800-1639580400@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Unreasonable effectiveness of the quantum complexity view on quantum many-body physics
DESCRIPTION:Speaker: Anurag Anshu\, Department of EECS & Challenge Institute for Quantum Computation\, UC Berkeley \nTitle: Unreasonable effectiveness of the quantum complexity view on quantum many-body physics \nAbstract: A central challenge in quantum many-body physics is to estimate the properties of natural quantum states\, such as the quantum ground states and Gibbs states. Quantum Hamiltonian complexity offers a computational perspective on this challenge and classifies these natural quantum states using the language of quantum complexity classes. This talk will provide a gentle introduction to the field and highlight its success in pinning down the hardness of a wide variety of quantum states. In particular\, we will consider the gapped ground states and Gibbs states on low dimensional lattices\, which are believed to exhibit ‘low complexity’ due to the widely studied area law behaviour. Here\, we will see the crucial role of complexity-theoretic methods in progress on the ‘area law conjecture’ and in the development of efficient algorithms to classically simulate quantum many-body systems.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/12-15-21-new-technologies-in-mathematics/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-NTM-Seminar-12.15.21-2.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211209T093000
DTEND;TZID=America/New_York:20211209T143000
DTSTAMP:20250328T200233Z
CREATED:20230705T082223Z
LAST-MODIFIED:20250328T200233Z
UID:10000072-1639042200-1639060200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:CMSA Math-Science Literature Lecture - Karen Uhlenbeck
DESCRIPTION:Karen Uhlenbeck (Institute for Advanced Study) \nTitle: The Noether Theorems in Geometry: Then and Now \nAbstract: The 1918 Noether theorems were a product of the general search for energy and momentum conservation in Einstein’s newly formulated theory of general relativity. Although widely referred to as the connection between symmetry and conservation laws\, the theorems themselves are often not understood properly and hence have not been as widely used as they might be. In the first part of the talk\, I outline a brief history of the theorems\, explain a bit of the language\, translate the first theorem into coordinate invariant language and give a few examples. I will mention only briefly their importance in physics and integrable systems. In the second part of the talk\, I describe why they are still relevant in geometric analysis: how they underlie standard techniques and why George Daskalopoulos and I came to be interested in them for our investigation into the best Lipschitz maps of Bill Thurston. Some applications to integrals on a domain a hyperbolic surface leave open possibilities for applications to integrals on domains which are locally symmetric spaces of higher dimension. The talk finishes with an example or two from the literature. \nTalk Chair: Laura DeMarco \nVIDEO
URL:https://live-hu-cmsa-222.pantheonsite.io/event/12-9-21-math-science-literature-lecture-karen-uhlenbeck/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/Lecture_Uhlenbeck_12921.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211208T140000
DTEND;TZID=America/New_York:20211208T150000
DTSTAMP:20240515T203917Z
CREATED:20230808T175752Z
LAST-MODIFIED:20240515T203917Z
UID:10001201-1638972000-1638975600@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Hierarchical Transformers are More Efficient Language Models
DESCRIPTION:Speaker: Piotr Nawrot\, University of Warsaw \nTitle: Hierarchical Transformers are More Efficient Language Models \nAbstract: Transformer models yield impressive results on many NLP and sequence modeling tasks. Remarkably\, Transformers can handle long sequences which allows them to produce long coherent outputs: full paragraphs produced by GPT-3 or well-structured images produced by DALL-E. These large language models are impressive but also very inefficient and costly\, which limits their applications and accessibility. We postulate that having an explicit hierarchical architecture is the key to Transformers that efficiently handle long sequences. To verify this claim\, we first study different ways to upsample and downsample activations in Transformers so as to make them hierarchical. We use the best performing upsampling and downsampling layers to create Hourglass – a hierarchical Transformer language model. Hourglass improves upon the Transformer baseline given the same amount of computation and can yield the same results as Transformers more efficiently. In particular\, Hourglass sets new state-of-the-art for Transformer models on the ImageNet32 generation task and improves language modeling efficiency on the widely studied enwik8 benchmark.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/12-8-21-new-technologies-in-mathematics/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-NTM-Seminar-12.08.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211208T103000
DTEND;TZID=America/New_York:20211208T120000
DTSTAMP:20240301T083428Z
CREATED:20240214T094451Z
LAST-MODIFIED:20240301T083428Z
UID:10002644-1638959400-1638964800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Defects\, link invariants and exact WKB
DESCRIPTION:Speaker: Fei Yan (Rutgers) \nTitle: Defects\, link invariants and exact WKB \nAbstract: I will describe some of my recent work on defects in supersymmetric field theories. The first part of my talk is focused on line defects in certain large classes of 4d N=2 theories and 3d N=2 theories. I will describe geometric methods to compute the ground states spectrum of the bulk-defect system\, as well as implications on the construction of link invariants. In the second part I will talk about some perspectives of surface defects in 4d N=2 theories and related applications on the exact WKB method for ordinary differential equations. This talk is based on past joint work with A. Neitzke\, various work in progress with D. Gaiotto\, S. Jeong\, A. Khan\, G. Moore\, as well as work by myself.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/12-8-2021-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-QMMP-12.08.21-1544x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211207T093000
DTEND;TZID=America/New_York:20211207T103000
DTSTAMP:20240122T054102Z
CREATED:20230818T050741Z
LAST-MODIFIED:20240122T054102Z
UID:10001286-1638869400-1638873000@live-hu-cmsa-222.pantheonsite.io
SUMMARY:2d N=(0\,1) gauge theories\, Spin(7) orientifolds and triality
DESCRIPTION:
URL:https://live-hu-cmsa-222.pantheonsite.io/event/12-7-21-algebraic-geometry-in-string-theory/
LOCATION:Virtual
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211201T140000
DTEND;TZID=America/New_York:20211201T143000
DTSTAMP:20240515T203641Z
CREATED:20230808T175251Z
LAST-MODIFIED:20240515T203641Z
UID:10001200-1638367200-1638369000@live-hu-cmsa-222.pantheonsite.io
SUMMARY:The Principles of Deep Learning Theory
DESCRIPTION:Speaker: Dan Roberts\, MIT & Salesforce \nTitle: The Principles of Deep Learning Theory \nAbstract: Deep learning is an exciting approach to modern artificial intelligence based on artificial neural networks. The goal of this talk is to provide a blueprint — using tools from physics — for theoretically analyzing deep neural networks of practical relevance. This task will encompass both understanding the statistics of initialized deep networks and determining the training dynamics of such an ensemble when learning from data. \nIn terms of their “microscopic” definition\, deep neural networks are a flexible set of functions built out of many basic computational blocks called neurons\, with many neurons in parallel organized into sequential layers. Borrowing from the effective theory framework\, we will develop a perturbative 1/n expansion around the limit of an infinite number of neurons per layer and systematically integrate out the parameters of the network. We will explain how the network simplifies at large width and how the propagation of signals from layer to layer can be understood in terms of a Wilsonian renormalization group flow. This will make manifest that deep networks have a tuning problem\, analogous to criticality\, that needs to be solved in order to make them useful. Ultimately we will find a “macroscopic” description for wide and deep networks in terms of weakly-interacting statistical models\, with the strength of the interactions between the neurons growing with depth-to-width aspect ratio of the network. Time permitting\, we will explain how the interactions induce representation learning. \nThis talk is based on a book\, The Principles of Deep Learning Theory\, co-authored with Sho Yaida and based on research also in collaboration with Boris Hanin. It will be published next year by Cambridge University Press.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/12-1-21-new-technologies-in-mathematics-seminar-series/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-NTM-Seminar-12.01.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211130T093000
DTEND;TZID=America/New_York:20211130T103000
DTSTAMP:20240122T053703Z
CREATED:20230818T050118Z
LAST-MODIFIED:20240122T053703Z
UID:10001285-1638264600-1638268200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:K_2 and Quantum Curves
DESCRIPTION:
URL:https://live-hu-cmsa-222.pantheonsite.io/event/k_2-and-quantum-curves/
LOCATION:Virtual
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211124T103000
DTEND;TZID=America/New_York:20211124T120000
DTSTAMP:20240301T084626Z
CREATED:20240214T100439Z
LAST-MODIFIED:20240301T084626Z
UID:10002655-1637749800-1637755200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Multipartitioning topological phases and quantum entanglement
DESCRIPTION:Speaker: Shinsei Ryu (Princeton University) \nTitle: Multipartitioning topological phases and quantum entanglement \nAbstract: We discuss multipartitions of the gapped ground states of (2+1)-dimensional topological liquids into three (or more) spatial regions that are adjacent to each other and meet at points. By considering the reduced density matrix obtained by tracing over a subset of the regions\, we compute various correlation measures\, such as entanglement negativity\, reflected entropy\, and associated spectra. We utilize the bulk-boundary correspondence to achieve such multipartitions and construct the reduced density matrix near the entangling boundaries. We find the fingerprints of topological liquid in these quantities\, such as (universal pieces in) the scaling of the entanglement negativity\, and a non-trivial distribution of the spectrum of the partially transposed density matrix.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/11-24-2021-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-QMMP-11.24.21-1583x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211118T143000
DTEND;TZID=America/New_York:20211118T160000
DTSTAMP:20240301T090528Z
CREATED:20240214T100731Z
LAST-MODIFIED:20240301T090528Z
UID:10002657-1637245800-1637251200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Exact Eigenstates in Non-Integrable Systems: A violation of the ETH
DESCRIPTION:Speaker: B. Andrei Bernevig (Princeton University) \nTitle: Exact Eigenstates in Non-Integrable Systems: A violation of the ETH \nAbstract: We find that several non-integrable systems exhibit some exact eigenstates that span the energy spectrum from lowest to the highest state. In the AKLT Hamiltonian and in several others “special” non-integrable models\, we are able to obtain the analytic expression of states exactly and to compute their entanglement spectrum and entropy to show that they violate the eigenstate thermalization hypothesis. This represented the first example of ETH violation in a non-integrable system; these types of states have gained notoriety since then as quantum Scars in the context of Rydberg atoms experiments. We furthermore show that the structure of these states\, in most models where they are found is that of an almost spectrum generating algebra which we call Restricted Spectrum Generating Algebra. This includes the (extended) Hubbard model\, as well as some thin-torus limits of Fractional Quantum Hall states. Yet in other examples\, such as the recently found chiral non-linear Luttinger liquid\, their structure is more complicated and not understood.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/11-18-2021-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Quantum-Matter-in-Mathematics-and-Physics-11.18.21-1583x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211116T150000
DTEND;TZID=America/New_York:20211116T163000
DTSTAMP:20240301T090706Z
CREATED:20240214T101038Z
LAST-MODIFIED:20240301T090706Z
UID:10002660-1637074800-1637080200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Quantum Geometric Aspects of Chiral Twisted Graphene Models
DESCRIPTION:Speaker: Jie Wang (Simons Foundation) \nTitle: Quantum Geometric Aspects of Chiral Twisted Graphene Models \nAbstract: “Moire” materials produced by stacking monolayers with small relative twist angles are of intense current interest for the range of correlated electron phenomena they exhibit. The quench of the kinetic energy means that the interacting physics is controlled by the interplay between the interaction scale and intrinsic quantum geometries of the flat band states\, in particular the Berry curvature and the Fubini-Study metric\, which are in general spatially non-uniform. We show that the analytical solution of the twisted bilayer graphene wavefunction in the chiral limit has a special band geometry\, endowing the Brillouin zone with a complex structure. This talk focus on the origin of the momentum space complex structure\, concrete models that realize it\, and its implications to electron-electron interactions. We first show the momentum space complex structure in Chern number C=1 flatbands implies the Bloch wavefunction to exhibit an exact correspondence to the lowest Landau level in the dual momentum space [2]. We present a generalization of the Haldane pseudopotential concept to deal with interacting problems in these bands and discuss experimental implications [2]. We also present an analytically solvable multi-layer generalized chiral graphene model\, which exhibits arbitrarily high Chern number and ideal quantum geometries [3]. Numerical studies of interacting particles indicate model fractional Chern insulators without Landau level analogues\, characterized by exact degeneracies and infinite particle entanglement spectra gaps [3]. References: \n[1] Jie Wang\, Yunqin Zheng\, Andrew J. Millis\, Jennifer Cano (Phys. Rev. Research 3\, 023155)\n[2] Jie Wang\, Jennifer Cano\, Andrew J. Millis\, Zhao Liu\, Bo Yang (arXiv: 2105.07491\, to appear in PRL)\n[3] Jie Wang\, Zhao Liu (arXiv: 2109.10325)
URL:https://live-hu-cmsa-222.pantheonsite.io/event/11-16-2021-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211112T143000
DTEND;TZID=America/New_York:20211112T160000
DTSTAMP:20240301T090838Z
CREATED:20240214T101408Z
LAST-MODIFIED:20240301T090838Z
UID:10002663-1636727400-1636732800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:A degeneracy bound for homogeneous topological order
DESCRIPTION:Speaker: Jeongwan Haah (Microsoft) \nTitle: A degeneracy bound for homogeneous topological order
URL:https://live-hu-cmsa-222.pantheonsite.io/event/11-12-2021-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211103T140000
DTEND;TZID=America/New_York:20211103T153000
DTSTAMP:20240301T091205Z
CREATED:20240214T102259Z
LAST-MODIFIED:20240301T091205Z
UID:10002667-1635948000-1635953400@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Non-Invertible Duality Defects in 3+1 Dimensions
DESCRIPTION:Speaker: Clay Cordova (U Chicago) \nTitle: Non-Invertible Duality Defects in 3+1 Dimensions \nAbstract:  For any quantum system invariant under gauging a higher-form global symmetry\, we construct a non-invertible topological defect by gauging in only half of spacetime. This generalizes the Kramers-Wannier duality line in 1+1 dimensions to higher spacetime dimensions. We focus on the case of a one-form symmetry in 3+1 dimensions and determine the fusion rule. From modular invariance and a direct analysis of one-form symmetry-protected topological phases\, we show that the existence of certain kinds of duality defects is intrinsically incompatible with a trivially gapped phase. By further assuming time-reversal symmetry\, we find that the presence of certain duality defects implies that the low-energy phase has to be gapless unless the one-form symmetry is spontaneously broken. We give an explicit realization of this duality defect in the free Maxwell theory where the duality defect is realized by a Chern-Simons coupling between the gauge fields from the two sides.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/11-3-3021-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211029T120000
DTEND;TZID=America/New_York:20211029T130000
DTSTAMP:20240301T091452Z
CREATED:20240214T102641Z
LAST-MODIFIED:20240301T091452Z
UID:10002670-1635508800-1635512400@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Anomaly resolution via decomposition
DESCRIPTION:Speaker: Eric Sharpe (Virginia Tech) \nTitle: Anomaly resolution via decomposition \nAbstract: In this talk we will discuss a method of anomaly resolution due to Wang-Wen-Witten in the special case of (1+1) dimensional theories. Briefly\, for our purposes\, Wang-Wen-Witten argued that an ill-defined anomalous orbifold [X/G] could be resolved by extending G to a larger group and adding suitable phases.  We analyze this process from the perspective of decomposition\, a property of (1+1)-dimensional theories with “one-form symmetries” first described in 2006.  Examples of such theories include orbifolds with trivially-acting subgroups\, of which the extensions of [X/G] are examples.  After a review of decomposition\, we will see that decomposition implies that in (1+1) dimensions\, the Wang-Wen-Witten procedure results in orbifolds that are equivalent to disjoint unions of orbifolds of X by explicitly nonanomalous subgroups of G.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/10-29-2021-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211021T153000
DTEND;TZID=America/New_York:20211021T170000
DTSTAMP:20240301T091902Z
CREATED:20240214T102900Z
LAST-MODIFIED:20240301T091902Z
UID:10002672-1634830200-1634835600@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Electric-magnetic duality and the Geometric Langlands duality
DESCRIPTION:Title: Electric-magnetic duality and the Geometric Langlands duality \nAbstract: I will give a pedagogical review of the connection between electric-magnetic duality and the Geometric Langlands duality.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/10-21-2021-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211020T093000
DTEND;TZID=America/New_York:20211020T103000
DTSTAMP:20240507T193206Z
CREATED:20240214T043359Z
LAST-MODIFIED:20240507T193206Z
UID:10002530-1634722200-1634725800@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Categorification and applications
DESCRIPTION:Speaker: Peng Shan (Tsinghua University)\n\n\n\nTitle: Categorification and applications \nAbstract: I will give a survey of the program of categorification for quantum groups\, some of its recent development and applications to representation theory.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/categorification-and-applications/
LOCATION:Virtual
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Colloquium-10.20.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211014T090000
DTEND;TZID=America/New_York:20211014T100000
DTSTAMP:20240529T180858Z
CREATED:20240214T082843Z
LAST-MODIFIED:20240529T180858Z
UID:10002588-1634202000-1634205600@live-hu-cmsa-222.pantheonsite.io
SUMMARY:D3C: Reducing the Price of Anarchy in Multi-Agent Learning
DESCRIPTION:Speaker: Ian Gemp\, DeepMind \nTitle: D3C: Reducing the Price of Anarchy in Multi-Agent Learning \nAbstract: In multi-agent systems the complex interaction of fixed incentives can lead agents to outcomes that are poor (inefficient) not only for the group but also for each individual agent. Price of anarchy is a technical game theoretic definition introduced to quantify the inefficiency arising in these scenarios– it compares the welfare that can be achieved through perfect coordination against that achieved by self-interested agents at a Nash equilibrium. We derive a differentiable upper bound on a price of anarchy that agents can cheaply estimate during learning. Equipped with this estimator agents can adjust their incentives in a way that improves the efficiency incurred at a Nash equilibrium. Agents adjust their incentives by learning to mix their reward (equiv. negative loss) with that of other agents by following the gradient of our derived upper bound. We refer to this approach as D3C. In the case where agent incentives are differentiable D3C resembles the celebrated Win-Stay Lose-Shift strategy from behavioral game theory thereby establishing a connection between the global goal of maximum welfare and an established agent-centric learning rule. In the non-differentiable setting as is common in multiagent reinforcement learning we show the upper bound can be reduced via evolutionary strategies until a compromise is reached in a distributed fashion. We demonstrate that D3C improves outcomes for each agent and the group as a whole on several social dilemmas including a traffic network exhibiting Braess’s paradox a prisoner’s dilemma and several reinforcement learning domains.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/10-14-2021-interdisciplinary-science-seminar/
LOCATION:Virtual
CATEGORIES:Interdisciplinary Science Seminar
ATTACH;FMTTYPE=image/png:https://live-hu-cmsa-222.pantheonsite.io/media/CMSA-Interdisciplinary-Science-Seminar-10.14.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211007T115400
DTEND;TZID=America/New_York:20211007T135400
DTSTAMP:20240301T092837Z
CREATED:20240214T090253Z
LAST-MODIFIED:20240301T092837Z
UID:10002604-1633607640-1633614840@live-hu-cmsa-222.pantheonsite.io
SUMMARY:A tour of categorical symmetry
DESCRIPTION:Title: A tour of categorical symmetry \nAbstract: I will discuss some perspectives on symmetry coming from the study of topological defects in quantum field theory. I will argue that we should take topological defects themselves to define the symmetries of QFT. This gives us a view of the “category of QFTs”. I will describe some examples of these “categorical symmetries”\, their applications\, and some open problems.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/10-7-2021-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211006T114900
DTEND;TZID=America/New_York:20211006T134900
DTSTAMP:20240301T093241Z
CREATED:20240214T090718Z
LAST-MODIFIED:20240301T093241Z
UID:10002606-1633520940-1633528140@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Line defects in CFTs: Renormalization group flows and semiclassical limits
DESCRIPTION:Title: Line defects in CFTs: Renormalization group flows and semiclassical limits \nAbstract: I will discuss line defects in d-dimensional Conformal Field Theories (CFTs). In the first part of the talk\, I will argue that the ambient CFT places nontrivial constraints on Renormalization Group (RG) flows on such line defects. I will show that the flow on line defects is consequently irreversible and furthermore a canonical decreasing entropy function exists. This construction generalizes the g theorem to line defects in arbitrary dimensions.  In the second part of the talk\, I will present some applications. In particular\, I will discuss impurities with large isospin S for some O(3) symmetric theories in the epsilon expansion.  For sufficiently large S diagrammatic perturbation theory breaks down\, and these are studied in a semiclassical expansion at fixed epsilon S.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/10-6-2021-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211006T093000
DTEND;TZID=America/New_York:20211006T103000
DTSTAMP:20240501T205719Z
CREATED:20240214T044013Z
LAST-MODIFIED:20240501T205719Z
UID:10002532-1633512600-1633516200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Strings\, knots and quivers
DESCRIPTION:Speaker: Piotr Sułkowski (University of Warsaw) \nTitle: Strings\, knots and quivers \nAbstract: I will discuss a recently discovered relation between quivers and knots\, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence\, and it states that various invariants of a given knot are captured by characteristics of a certain quiver\, which can be associated to this knot. Among others\, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver\, it provides a new insight on knot categorification\, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/strings-knots-and-quivers/
LOCATION:Virtual
CATEGORIES:Colloquium
END:VEVENT
END:VCALENDAR