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  • CMSA Condensed Matter/Math Seminar: Deconfined metallic quantum criticality-I
    9:00 AM-10:30 AM
    July 9, 2020

    A number of strongly correlated electronic materials exhibit quantum criticality that does not fit into the conventional Landau-Ginzburg-Wilson paradigm of continuous phase transitions. Inspired by these experimental examples, I will discuss a new class of quantum phase transitions that describe a continuous transition between a Fermi liquid metal with a generic electronic Fermi surface and electrical insulators without Fermi surface of neutral excitations. Such phase transitions are described in terms of a finite density of fractionalized excitations coupled to emergent gauge fields. I will discuss various concrete examples of such gauge theories and describe their associated phase transitions using a renormalization group framework.  Remarkably, we find examples of continuous phase transitions between Landau Fermi liquid metals and insulators, where the quantum critical point hosts a non-Fermi liquid with a sharp Fermi surface but no long-lived quasiparticles. I will comment on the relevance of this new theoretical framework for some of the most pressing questions in the field of quantum matter.

    Zoom: https://harvard.zoom.us/j/977347126

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  • Integrability and Braided Tensor Categories
    10:00 AM-11:00 AM
    July 14, 2020

    Many integrable critical classical statistical mechanical models and the corresponding quantum spin chains possess a fractional-spin conserved current. Such currents have been constructed by utilizing quantum-group algebras, fermionic and parafermionic operators, and ideas from “discrete holomorphicity”. I define them generally and naturally using a braided tensor category, a topological structure familiar from the study of knot invariants, anyons and conformal field theory.  I derive simple constraints on the Boltzmann weights necessary and sufficient for such a current to exist, generalizing those found using quantum-group algebras. I find many solutions, in both geometric and local models. In all cases, the resulting weights are those of an integrable lattice model, giving a linear construction for “Baxterising”, i.e. building a solution of the Yang-Baxter equation out of topological data.

    Zoom: https://harvard.zoom.us/j/779283357

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  • CMSA Quantum Matter/Quantum Field Theory Seminar: Interplay between two boundary effects
    10:30 AM-12:00 PM
    July 15, 2020

    We study the interplay between two nontrivial boundary effects: (1) the d-1 dimensional edge states of d-dimensional strongly interacting symmetry protected topological states, and (2) the boundary fluctuations of d-dimensional bulk quantum criticality. We also discuss states localized at an interface in a higher dimensional bulk, when the bulk undergoes a quantum phase transition. Using controlled analytical methods, we demonstrate that the interplay between the two different boundary effects leads to rich physics at the d-1 dimensional boundary, including new stable fixed points, and also an exotic quantum phase transition which cannot happen in a local d-1 dimensional system alone. Our analytical calculation is qualitatively consistent with recent numerical works on nonlocal quantum many body systems.

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  • CMSA Condensed Matter/Math Seminar: Deconfined metallic quantum criticality – II
    10:30 AM-12:00 PM
    July 16, 2020

    The main goal of this talk is to discuss in detail a concrete setup for deconfined metallic quantum criticality. In particular, we propose that certain quantum Hall bilayers can host examples of a deconfined metal-insulator transition (DMIT), where a Fermi liquid (FL) metal with a generic electronic Fermi surface evolves into a gapped insulator (or, an insulator with Goldstone modes) through a continuous quantum phase transition. The transition can be accessed by tuning a single parameter, and its universal critical properties can be understood using a controlled framework. At the transition, the two layers are effectively decoupled, where each layer undergoes a continuous transition from a FL to a generalized composite Fermi liquid (gCFL). The thermodynamic and transport properties of the gCFL are similar to the usual CFL, while its spectral properties are qualitatively different. The FL-gCFL quantum critical point hosts a sharply defined Fermi surface without long-lived electronic quasiparticles. Immediately across the transition, the two layers of gCFL are unstable to forming an insulating phase. We discuss the topological properties of the insulator and various observable signatures associated with the DMIT. Some key ingredients of this proposal include Dirac-Chern-Simons theory, color superconductivity, dimensional decoupling, etc.

    Zoom: https://harvard.zoom.us/j/977347126

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  • Applied von Neumann Algebra
    10:00 AM-11:00 AM
    July 21, 2020

    We are interested in mathematical results which are stated entirely without reference to von Neumann algebras but whose proofs use von Neumann algebras in an essential way. The first stunning example is the Kaplansky result that ab=1 iff ba=1 in a group algebra over a field of characteristic zero. Connes’ noncommutative integration theory yields other examples. We will concentrate on a new example in the theory of zero sets of Bergman spaces where we are able to calculate a certain density of orbits of Fuchsian groups.

    Zoom: https://harvard.zoom.us/j/779283357

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  • 2020 Big Data Conference
    All day
    July 24, 2020-July 25, 2020

    Please note: the 2020 Big Data Conference will take place virtually. More information to follow.

    On August 24-25, 2020 the CMSA will be hosting our sixth annual Conference on Big Data. The Conference will feature many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.

    Organizers: 

    Shing-Tung Yau, William Caspar Graustein Professor of Mathematics, Harvard University

    Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business

    Horng-Tzer Yau, Professor of Mathematics, Harvard University

    Sergiy Verstyuk, CMSA, Harvard University

    Speakers:

    Sanjeev Arora, Princeton University

    Joseph Dexter, Dartmouth University

    Nicole Immorlica, Microsoft

    Amin Saberi, Stanford University

    Vira Semenova, University of California, Berkeley

    Varda Shalev, Tel Aviv University

    Elizabeth Sibert, Harvard University

    Information about last year’s conference can be found here: cmsa.fas.harvard.edu/2019-big-data/

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  • 2020 Big Data Conference
    All day
    July 25, 2020-July 25, 2020

    Please note: the 2020 Big Data Conference will take place virtually. More information to follow.

    On August 24-25, 2020 the CMSA will be hosting our sixth annual Conference on Big Data. The Conference will feature many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.

    Organizers: 

    Shing-Tung Yau, William Caspar Graustein Professor of Mathematics, Harvard University

    Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business

    Horng-Tzer Yau, Professor of Mathematics, Harvard University

    Sergiy Verstyuk, CMSA, Harvard University

    Speakers:

    Sanjeev Arora, Princeton University

    Joseph Dexter, Dartmouth University

    Nicole Immorlica, Microsoft

    Amin Saberi, Stanford University

    Vira Semenova, University of California, Berkeley

    Varda Shalev, Tel Aviv University

    Elizabeth Sibert, Harvard University

    Information about last year’s conference can be found here: cmsa.fas.harvard.edu/2019-big-data/

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