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  • 10:30 AMCMSA EVENT: CMSA Quantum Matter/Quantum Field Theory Seminar: Exploration on Deconfined Fractionalized Particles at Quantum Criticality — Fractional Chern Insulators and Shastry-Sutherland Quantum Magnets
    10:30 AM-12:00 PM
    April 1, 2020

    Speaker: Jong Yeon Lee – Harvard University

    via Zoom Video Conferencing: http://harvard.zoom.us/j/977347126

    One of the most exotic phenomena in condensed matter systems is the emergence of fractionalized particles. However, until now, only a few experimental systems are known to realize fractionalized excitations. This calls for more systematic ways to find and understand systems with fractionalization. One natural starting point is to look for an exotic quantum criticality, where the fundamental degrees of freedom become insufficient to describe the system accurately. Furthermore, understandings in exotic quantum critical phenomena would provide a unified perspective on nearby gapped phases, i.e. a guiding principle to engineer the system in a desirable direction that may host anyons. In this talk, I would present my works on two different types of quantum criticality: (1) Deconfined quantum critical point (DQCP) between plaquette valence-bond solids and Neel ordered state in Shastry-Sutherland lattice models [PRX 9, 041037 (2019)], where two distinct symmetry breaking order parameters become unified by the fractionalized degree of freedom. (2) Transitions between fractional Chern/Quantum Hall insulators tuned by the strength of lattice potential [PRX 8, 031015 (2018)]. Here, the low-lying excitations are already fractionalized; therefore, the deconfined fractional excitations follows more naturally, which is described by Chern-Simons quantum electrodynamics. The numerical results using iDMRG as well as theoretical analysis of their emergent critical properties would be presented. In the end, I would discuss their spectroscopic signatures, providing a full analysis of experimental verification.

  • 2:00 PMRANDOM MATRIX SEMINAR
    2:00 PM-3:00 PM
    April 1, 2020

    Speaker:  Ian Jauslin – Princeton University

    will speak on:

    A Simplified Approach to Interacting Bose Gases

    via Zoom Video Conferencing: http://harvard.zoom.us/j/147308224

    I will discuss some new results about an effective theory introduced by Lieb in 1963 to approximate the ground state energy of interacting Bosons at low density. In this regime, it agrees with the predictions of Bogolyubov. At high densities, Hartree theory provides a good approximation. In this talk, I will show that the ’63 effective theory is actually exact at both low and high densities, and numerically accurate to within a few percents in between, thus providing a new approach to the quantum many body problem that bridges the gap between low and high density.

  • 3:00 PMNUMBER THEORY SEMINAR
    3:00 PM-4:00 PM
    April 1, 2020

    Speaker: Shekhar Khare – UCLA

    via Zoom Video Conferencing: http://harvard.zoom.us/j/136830668

    In his work on modularity theorems, Wiles proved a numerical criterion for a map of rings R->T to be an isomorphism of complete intersections.  In addition to proving modularity theorems, this numerical criterion also implies a connection between the order of a certain Selmer group and a special value of an L-function.
    In this talk I will consider the case of a Hecke algebra acting on the cohomology a Shimura curve associated to  a quaternion algebra. In this case, one has an analogous map of rings R->T which is known to be an isomorphism, but in many cases the rings R and T fail to be complete intersections. This means that Wiles’s numerical criterion will fail to hold.

    I will describe a method for precisely computing the extent to which the numerical criterion fails (i.e. the ‘Wiles defect”) at a newform f which gives rise to an augmentation T -> Z_p. The defect turns out to be determined entirely by local information  of the newform f at the primes q dividing the discriminant of the quaternion algebra at which the mod p representation arising from f is “trivial”.  (For instance if
    f corresponds to a semistable elliptic curve, then the local defect at q is related to the
    “tame regulator” of the Tate period of the elliptic curve at q.)

    This is joint work with Gebhard Boeckle and Jeffrey Manning.

  • 4:00 PMINFORMAL GEOMETRY AND DYNAMICS SEMINAR

    INFORMAL GEOMETRY AND DYNAMICS SEMINAR

    4:00 PM-5:30 PM
    April 1, 2020

    Speaker: Curtis McMullen – Harvard University

    via Zoom Video Conferencing:  http://harvard.zoom.us/j/972495373

    We will describe how the problem of finding periodic trajectories in a regular pentagon can be solved using a new height on P^1 coming from real multiplication.

  • 4:30 PMCMSA EVENT: CMSA Colloquium: Data-driven machine learning approaches to monitor and predict events in healthcare. From population-level disease outbreaks to patient-level monitoring
    4:30 PM-5:30 PM
    April 1, 2020

    Speaker: Mauricio Santillana – Harvard University

    Online via Zoom Video Conferencing: http://harvard.zoom.us/meeting/977347126

     I will describe data-driven machine learning methodologies that leverage Internet-based information from search engines, Twitter microblogs, crowd-sourced disease surveillance systems, electronic medical records, and weather information to successfully monitor and forecast disease outbreaks in multiple locations around the globe in near real-time. I will also present data-driven machine learning methodologies that leverage continuous-in-time information coming from bedside monitors in Intensive Care Units (ICU) to help improve patients’ health outcomes and reduce hospital costs.
  • More events
    • 10:30 AMCMSA EVENT: CMSA Quantum Matter/Quantum Field Theory Seminar: Exploration on Deconfined Fractionalized Particles at Quantum Criticality — Fractional Chern Insulators and Shastry-Sutherland Quantum Magnets
      10:30 AM-12:00 PM
      April 1, 2020
      Speaker: Jong Yeon Lee - Harvard University

      via Zoom Video Conferencing: http://harvard.zoom.us/j/977347126

      One of the most exotic phenomena in condensed matter systems is the emergence of fractionalized particles. However, until now, only a few experimental systems are known to realize fractionalized excitations. This calls for more systematic ways to find and understand systems with fractionalization. One natural starting point is to look for an exotic quantum criticality, where the fundamental degrees of freedom become insufficient to describe the system accurately. Furthermore, understandings in exotic quantum critical phenomena would provide a unified perspective on nearby gapped phases, i.e. a guiding principle to engineer the system in a desirable direction that may host anyons. In this talk, I would present my works on two different types of quantum criticality: (1) Deconfined quantum critical point (DQCP) between plaquette valence-bond solids and Neel ordered state in Shastry-Sutherland lattice models [PRX 9, 041037 (2019)], where two distinct symmetry breaking order parameters become unified by the fractionalized degree of freedom. (2) Transitions between fractional Chern/Quantum Hall insulators tuned by the strength of lattice potential [PRX 8, 031015 (2018)]. Here, the low-lying excitations are already fractionalized; therefore, the deconfined fractional excitations follows more naturally, which is described by Chern-Simons quantum electrodynamics. The numerical results using iDMRG as well as theoretical analysis of their emergent critical properties would be presented. In the end, I would discuss their spectroscopic signatures, providing a full analysis of experimental verification.

    • 2:00 PMRANDOM MATRIX SEMINAR
      2:00 PM-3:00 PM
      April 1, 2020
      Speaker:  Ian Jauslin - Princeton University

      will speak on:

      A Simplified Approach to Interacting Bose Gases

      via Zoom Video Conferencing: http://harvard.zoom.us/j/147308224

      I will discuss some new results about an effective theory introduced by Lieb in 1963 to approximate the ground state energy of interacting Bosons at low density. In this regime, it agrees with the predictions of Bogolyubov. At high densities, Hartree theory provides a good approximation. In this talk, I will show that the ’63 effective theory is actually exact at both low and high densities, and numerically accurate to within a few percents in between, thus providing a new approach to the quantum many body problem that bridges the gap between low and high density.

    • 3:00 PMNUMBER THEORY SEMINAR
      3:00 PM-4:00 PM
      April 1, 2020
      Speaker: Shekhar Khare - UCLA

      via Zoom Video Conferencing: http://harvard.zoom.us/j/136830668

      In his work on modularity theorems, Wiles proved a numerical criterion for a map of rings R->T to be an isomorphism of complete intersections.  In addition to proving modularity theorems, this numerical criterion also implies a connection between the order of a certain Selmer group and a special value of an L-function.
      In this talk I will consider the case of a Hecke algebra acting on the cohomology a Shimura curve associated to  a quaternion algebra. In this case, one has an analogous map of rings R->T which is known to be an isomorphism, but in many cases the rings R and T fail to be complete intersections. This means that Wiles’s numerical criterion will fail to hold.

      I will describe a method for precisely computing the extent to which the numerical criterion fails (i.e. the ‘Wiles defect”) at a newform f which gives rise to an augmentation T -> Z_p. The defect turns out to be determined entirely by local information  of the newform f at the primes q dividing the discriminant of the quaternion algebra at which the mod p representation arising from f is “trivial”.  (For instance if
      f corresponds to a semistable elliptic curve, then the local defect at q is related to the
      “tame regulator” of the Tate period of the elliptic curve at q.)

      This is joint work with Gebhard Boeckle and Jeffrey Manning.

    • 4:00 PMINFORMAL GEOMETRY AND DYNAMICS SEMINAR
      INFORMAL GEOMETRY AND DYNAMICS SEMINAR
      4:00 PM-5:30 PM
      April 1, 2020
      Speaker: Curtis McMullen - Harvard University

      via Zoom Video Conferencing:  http://harvard.zoom.us/j/972495373

      We will describe how the problem of finding periodic trajectories in a regular pentagon can be solved using a new height on P^1 coming from real multiplication.

    • 4:30 PMCMSA EVENT: CMSA Colloquium: Data-driven machine learning approaches to monitor and predict events in healthcare. From population-level disease outbreaks to patient-level monitoring
      4:30 PM-5:30 PM
      April 1, 2020
      Speaker: Mauricio Santillana - Harvard University

      Online via Zoom Video Conferencing: http://harvard.zoom.us/meeting/977347126

       I will describe data-driven machine learning methodologies that leverage Internet-based information from search engines, Twitter microblogs, crowd-sourced disease surveillance systems, electronic medical records, and weather information to successfully monitor and forecast disease outbreaks in multiple locations around the globe in near real-time. I will also present data-driven machine learning methodologies that leverage continuous-in-time information coming from bedside monitors in Intensive Care Units (ICU) to help improve patients’ health outcomes and reduce hospital costs.
2
  • 3:00 PMTHURSDAY SEMINAR SEMINAR
    3:00 PM-5:00 PM
    April 2, 2020

    Speaker: Sander Kupers – Harvard University

    via Zoom Video Conferencing: http://harvard.zoom.us/j/140789806

    We finish the computation of the automorphisms of rationalized E_n-operads when n is at least 3, by verifying that the conditions of the Goldman-Millson theorem are satisfied for the map from the (dual) graph complex to the deformation complex of maps from the graphs cooperad to the cooperadic W-construction of the Poisson cooperad.

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  • 10:30 AMCMSA GENERAL RELATIVITY SEMINAR CMSA EVENT
    10:30 AM-11:30 AM
    April 3, 2020

    Speaker: Hyun Chul Jang – University of Connecticut

    via Zoom Video Conferencing: http://harvard.zoom.us/j/635180669

    In this talk, we will discuss the rigidity of positive mass theorem for asymptotically hyperbolic manifolds. That is, if the mass equality holds, then the manifold is isometric to hyperbolic space. The proof used a variational approach with the scalar curvature constraint. It also involves an investigation on a type of Obata’s equations, which leads to recent splitting results with Galloway. This talk is based on the joint works with L.-H. Huang and D. Martin, and with G. J. Galloway.

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  • 10:00 AMMATHEMATICAL PICTURE LANGUAGE SEMINAR
    10:00 AM-11:00 AM
    April 7, 2020

    Speaker: Leonard Gross – Cornell University

    via Zoom Video Conferencing: http://harvard.zoom.us/j/779283357

    Circularly polarized light (i.e. helicity) is a concept defined in terms of
    plane wave expansions of solutions to Maxwell’s equations.  We wish to find  an analogous concept for classical and quantized Yang-Mills fields. Since the classical (hyperbolic) Yang-Mills equation is a non-linear equation, a gauge invariant  plane wave expansion does not exist.  We will first
    show, in electromagnetism,  an equivalence between the usual plane wave characterization  of helicity and a characterization in terms of (anti-)self  duality of a gauge potential on a half space of Euclidean R^4. The transition from Minkowski space to Euclidean space is implemented by the
    Maxwell-Poisson equation. We will then replace the Maxwell- Poisson equation by the Yang-Mills-Poisson equation to find a decomposition of the Yang-Mills configuration space into submanifolds arguably corresponding to positive and negative helicity. This is a report on the paper [1].
    References
    [1] http://doi.org/10.1016/j.nuclphysb.2019.114685

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  • 10:30 AMCMSA EVENT: CMSA Quantum Matter/Quantum Field Theory Seminar: Anomaly of the Electromagnetic Duality of Maxwell Theory
    10:30 AM-12:00 PM
    April 8, 2020

    Speaker: Chang-Tse Hsieh – IPMU and U Tokyo

    via Zoom Video Conferencing: http://harvard.zoom.us/j/977347126

    Every physicist knows that the classical electromagnetism is described by Maxwell’s equations and that it is invariant under the electromagnetic duality S: (E, B) → (B, −E). However, the properties of the electromagnetic duality in the quantum theory might not be as well known to physicists in general, and in fact are not very well understood in the literature. This is particularly true when going around a nontrivial path in the spacetime results in a duality transformation. In our recent work, we uncovered a feature of the Maxwell theory and its duality symmetry in such a situation, namely that it has a quantum anomaly. We found that the anomaly of this system in a particular formulation is 56 times that of a Weyl fermion. Our result reproduces, as a special case, the known anomaly of the all-fermion electrodynamics—a version of the Maxwell theory where particles of odd (electric or magnetic) charge are fermions—discovered in the last few years.

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  • 4:00 PMINFORMAL GEOMETRY AND DYNAMICS SEMINAR
    4:00 PM-5:30 PM
    April 15, 2020

    Speaker: Nick Salter – Columbia University

    via Zoom Video Conferencing: http://harvard.zoom.us/j/972495373

    Strata of abelian differentials have long been of interest for their dynamical and algebro-geometric properties, but relatively little is understood about their topology. I will describe a project aimed at understanding the (orbifold) fundamental groups of non-hyperelliptic stratum components. The centerpiece of this is the monodromy representation valued in the mapping class group of the surface relative to the zeroes of the differential. For g \ge 5, we give a complete description of this as the stabilizer of the framing of the (punctured) surface arising from the flat structure associated to the differential. This is joint work with Aaron Calderon.

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news

Gabriel Goldberg Awarded Sacks Prize

Gabriel Goldberg, 2019 Harvard Mathematics Doctoral recipient, has been awarded the 2019 Sacks Prize by the Association for Symbolic Logic, an international organization supporting research...
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