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March  March  March  1  CMSA EVENT: CMSA Quantum Matter/Quantum Field Theory Seminar: Exploration on Deconfined Fractionalized Particles at Quantum Criticality — Fractional Chern Insulators and ShastrySutherland Quantum Magnets
10:30 AM12:00 PM April 1, 2020 via Zoom Video Conferencing: https://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 valencebond solids and Neel ordered state in ShastrySutherland 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 lowlying excitations are already fractionalized; therefore, the deconfined fractional excitations follows more naturally, which is described by ChernSimons 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.  RANDOM MATRIX SEMINAR
2:00 PM3:00 PM April 1, 2020 will speak on: A Simplified Approach to Interacting Bose Gases via Zoom Video Conferencing: https://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.  NUMBER THEORY SEMINAR
3:00 PM4:00 PM April 1, 2020 via Zoom Video Conferencing: https://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 Lfunction. 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.  INFORMAL GEOMETRY AND DYNAMICS SEMINAR
INFORMAL GEOMETRY AND DYNAMICS SEMINAR Heights 4:00 PM5:30 PM April 1, 2020 via Zoom Video Conferencing: https://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.  CMSA EVENT: CMSA Colloquium: Datadriven machine learning approaches to monitor and predict events in healthcare. From populationlevel disease outbreaks to patientlevel monitoring
4:30 PM5:30 PM April 1, 2020 Online via Zoom Video Conferencing: https://harvard.zoom.us/meeting/977347126 I will describe datadriven machine learning methodologies that leverage Internetbased information from search engines, Twitter microblogs, crowdsourced disease surveillance systems, electronic medical records, and weather information to successfully monitor and forecast disease outbreaks in multiple locations around the globe in near realtime. I will also present datadriven machine learning methodologies that leverage continuousintime information coming from bedside monitors in Intensive Care Units (ICU) to help improve patients’ health outcomes and reduce hospital costs.
 2  THURSDAY SEMINAR SEMINAR
3:00 PM5:00 PM April 2, 2020 via Zoom Video Conferencing: https://harvard.zoom.us/j/140789806 We finish the computation of the automorphisms of rationalized E_noperads when n is at least 3, by verifying that the conditions of the GoldmanMillson theorem are satisfied for the map from the (dual) graph complex to the deformation complex of maps from the graphs cooperad to the cooperadic Wconstruction of the Poisson cooperad.
 3  CMSA GENERAL RELATIVITY SEMINAR CMSA EVENT
10:30 AM11:30 AM April 3, 2020 via Zoom Video Conferencing: https://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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5  6  7  MATHEMATICAL PICTURE LANGUAGE SEMINAR
10:00 AM11:00 AM April 7, 2020 via Zoom Video Conferencing: https://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 YangMills fields. Since the classical (hyperbolic) YangMills equation is a nonlinear 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 MaxwellPoisson equation. We will then replace the Maxwell Poisson equation by the YangMillsPoisson equation to find a decomposition of the YangMills configuration space into submanifolds arguably corresponding to positive and negative helicity. This is a report on the paper [1]. References [1] https://doi.org/10.1016/j.nuclphysb.2019.114685  DIFFERENTIAL GEOMETRY SEMINAR
4:15 PM5:15 PM April 7, 2020 via Zoom Video Conferencing: link TBA I will report on some recent progress on the problem of understanding the collapsing behavior of Ricciflat Kahler metrics on CalabiYau manifolds that admit a fibration structure, when the volume of the fibers shrinks to zero. Based on joint works with GrossZhang and with Hein.
 8  CMSA EVENT: CMSA Quantum Matter/Quantum Field Theory Seminar: Anomaly of the Electromagnetic Duality of Maxwell Theory
10:30 AM12:00 PM April 8, 2020 via Zoom Video Conferencing: https://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 allfermion electrodynamics—a version of the Maxwell theory where particles of odd (electric or magnetic) charge are fermions—discovered in the last few years.  NUMBER THEORY SEMINAR
3:00 PM4:00 PM April 8, 2020 via Zoom Video Conferencing: https://harvard.zoom.us/j/136830668 (joint w/ Arul Shankar) We discuss a new method to bound 5torsion in class groups of quadratic fields using the refined BSD conjecture for elliptic curves. The most natural “trivial” bound on the ntorsion is to bound it by the size of the entire class group, for which one has a global class number formula. We explain how to make sense of the ntorsion of a class group intrinsically as a selmer group of a Galois module. We may then similarly bound its size by the TateShafarevich group of an appropriate elliptic curve, which we can bound using the BSD conjecture. This fits into a general paradigm where one bounds selmer groups of finite Galois modules by embedding into global objects, and using class number formulas. If time permits, we explain how the function field picture yields unconditional results and suggests further generalizations.  INFORMAL GEOMETRY AND DYNAMICS SEMINAR
4:00 PM5:30 PM April 8, 2020 via Zoom Video Conferencing: https://harvard.zoom.us/j/972495373 The Oppenheim Conjecture, proved by Margulis, states that any irrational quadratic form, has values (at integer coordinates) that are dense on the real line. However, obtaining effective estimates for any given form is a very difficult problem. In this talk I will discuss recent results, where such effective estimates are obtained for generic forms using a combination of methods from dynamics and analytic number theory. I will also discuss some results on analogous problems for inhomogenous forms and more general higher degree polynomials.
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12  13  CMSA EVENT: CMSA Mathematical Physics Seminar: Comments on the latticecontinuum correspondence
12:00 PM1:00 PM April 13, 2020 will speak on: The goal of this talk is to precisely describe how certain operator properties of continuum QFT (e.g. operator product expansions, current algebras, vertex operator algebras) emerge from an underlying lattice theory. The main lesson will be that a “continuum limit” must always involve two or more cutoffs being taken to zero in a specific order. In other words, the naive statement that continuum theories are obtained from lattice ones by letting a “lattice spacing” go to zero is never sufficient to describe the latticecontinuum correspondence. Using these insights, I will show in detail how the KacMoody algebra arises from a nonperturbatively well defined, fully regularized model of free fermions, and I will comment on generalizations and applications to bosonization. Time permitting, I will describe more intricate examples involving scalar fields, and I will discuss several open questions. via Zoom Video Conferencing: https://harvard.zoom.us/j/837429475
 14  MATHEMATICAL PICTURE LANGUAGE SEMINAR
10:00 AM11:00 AM April 14, 2020 via Zoom Video Conferencing: https://harvard.zoom.us/j/779283357 We study the nonlinear Schroedinger equation (NLS) with bounded initial data which does not vanish at infinity. Examples include periodic, quasiperiodic and random initial data. On the lattice we prove that solutions are polynomially bounded in time for any bounded data. In the continuum, local existence is proved for real analytic data by a Newton iteration scheme. Global existence for NLS with a regularized nonlinearity follows by analyzing a local energy norm. This is joint work with B. Dodson and A. Soffer.  DIFFERENTIAL GEOMETRY SEMINAR
4:15 PM5:15 PM April 14, 2020 via Zoom Video Conferencing: link TBA The anisotropic Calderon inverse problem consists in recovering the metric of a compact connected Riemannian manifold with boundary from the knowledge of the DirichlettoNeumann map at fixed energy. A fundamental result due to Lee and Uhlmann states that there is uniqueness in the analytic case. We shall present counterexamples to uniqueness in cases when: 1) The metric smooth in the interior of the manifold, but only Holder continuous on one connected component of the boundary, with the Dirichlet and Neumann data being measured on the same proper subset of the boundary. 2) The metric is smooth everywhere and Dirichlet and Neumann data are measured on disjoint subsets of the boundary. This is joint work with Thierry Daude (CergyPontoise) and Francois Nicoleau (Nantes).
 15  CMSA EVENT: CMSA Quantum Matter/Quantum Field Theory Seminar: Introduction to Categorical Approach to Topological Phases in Arbitrary Dimensions
10:30 AM12:00 PM April 15, 2020 I will talk about some ideas that are essential to build a general framework for topological phases in arbitrary dimensions. I will also discuss how these ideas are applied when global symmetry or higher symmetry is present, and how to understand and classify such higher SET/SPT orders. via Zoom Video Conferencing: https://harvard.zoom.us/j/977347126  INFORMAL GEOMETRY AND DYNAMICS SEMINAR
4:00 PM5:30 PM April 15, 2020 via Zoom Video Conferencing: https://harvard.zoom.us/j/972495373 Strata of abelian differentials have long been of interest for their dynamical and algebrogeometric properties, but relatively little is understood about their topology. I will describe a project aimed at understanding the (orbifold) fundamental groups of nonhyperelliptic 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.  CMSA EVENT: CMSA Colloquium: Stability of spacetimes with supersymmetric compactifications
4:30 PM5:30 PM April 15, 2020 will speak on: Spacetimes with compact directions, which have special holonomy such as CalabiYau spaces, play an important role in supergravity and string theory. In this talk I will discuss the global, nonlinear stability for the vacuum Einstein equations on a spacetime which is a cartesian product of a high dimensional Minkowski space with a compact Ricci flat internal space with special holonomy. I will start by giving a brief overview of related stability problems which have received a lot of attention recently, including the black hole stability problem. This is based on joint work with Pieter Blue, Zoe Wyatt and ShingTung Yau. *via Zoom Video Conferencing: https://harvard.zoom.us/j/952543678
 16  CMSA EVENT: CMSA Condensed Matter/Math Seminar: Spectral Gaps in Quantum Spin Systems
10:30 AM12:00 PM April 16, 2020 via Zoom Video Conferencing: https://harvard.zoom.us/j/977347126 Quantum spin systems are manybody models which are of wide interest in modern physics and at the same time amenable to rigorous mathematical analysis. A central question about a quantum spin system is whether its Hamiltonian exhibits a spectral gap above the ground state. The existence of such a spectral gap has farreaching consequences, e.g., for the ground state complexity. In this talk, we survey recent progress regarding spectral gaps for frustrationfree quantum spin systems in dimensions greater than 1 such as the antiferromagnetic models of AffleckKennedyLiebTasaki (AKLT).
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19  20  CMSA EVENT: CMSA Mathematical Physics Seminar: Fourier–Mukai equivalences arising from Cremona transformations I: K3 surfaces
12:00 PM1:00 PM April 20, 2020 will speak on: The derived equivalences of K3 surfaces and the K3 categories of certain cubic fourfolds are known to be realizable as Hodge isometries, i.e. lattice isometries preserving Hodge structures. On the other hand, Hodge isometries are also known to appear when one factorizes a birational map between varieties and tracks the actions on the middle cohomologies. When does a Hodge isometry induced from the derived equivalence of K3 surfaces/categories arise from a birational map? This is the first of two related talks discussing this question. In this talk, I will exhibit such examples for general K3 surfaces of degree 12. As a corollary, I will introduce how the construction gives an interesting relation in the Grothendieck ring of algebraic varieties. This is joint work with Brendan Hassett. via Zoom Video Conferencing: https://harvard.zoom.us/j/837429475
 21  MATHEMATICAL PICTURE LANGUAGE SEMINAR
10:00 AM11:00 AM April 21, 2020 Work of Ernst Specker (1960), Simon Kochen and Ernst Specker (1967), and John Bell (1964) concerning the nonexistence of a hiddenvariables theory reproducing the predictions of Quantum Mechanics is reviewed. Subsequently, a novel approach to Quantum Mechanics yielding – among other things – a solution of the measurement problem is outlined. via Zoom Video Conferencing: https://harvard.zoom.us/j/779283357  DIFFERENTIAL GEOMETRY SEMINAR
3:00 PM4:00 PM April 21, 2020 In this talk I’ll discuss work in preparation on the unknottedness of asymptotically conical self shrinkers in R^3. via Zoom Video Conferencing: if you would like to attend, please email spicard@math.harvard.edu
 22  CMSA EVENT: CMSA Quantum Matter/Quantum Field Theory Seminar: Global anomalies in the Standard Model(s) and Beyond
10:30 AM12:00 PM April 22, 2020 Global anomalies in gauge theories are detected by the exponentiated etainvariant, which becomes a cobordism invariant when perturbative anomalies vanish. We analyse global anomalies in four distinct (but equally valid) versions of the Standard Model of particle physics by computing the appropriate cobordism groups. In two cases we find that there are no global anomalies beyond the Witten anomaly associated with the SU(2) factor, while in the other cases we show that there are no global anomalies at all. This uncovers a subtle interplay between local and global anomalies in closely related gauge theories. We will then discuss a more subtle version of this `anomaly interplay’ occurring in a U(2) gauge theory defined without a spin structure. via Zoom Video Conferencing: https://harvard.zoom.us/j/977347126  RANDOM MATRIX SEMINAR
2:00 PM3:00 PM April 22, 2020 We introduce a class of UVregularized twobody interactions for fermions in $\R^d$ and prove a LiebRobinson estimate for the dynamics of this class of manybody systems. As a step towards this result, we also prove a propagation bound of LiebRobinson type for continuum oneparticle Schr\“odinger operators. We apply the propagation bound to prove the existence of a strongly continuous infinitevolume dynamics on the CAR algebra. via Zoom Video Conferencing: https://harvard.zoom.us/j/147308224  INFORMAL GEOMETRY AND DYNAMICS SEMINAR
4:00 PM5:30 PM April 22, 2020 We give a construction of a pseudoAnosov map of a surface starting from (and almost isomorphic to) a hyperbolic automorphism of an ntorus. The construction arises from a peano curve based on an invariant spacefilling tree. This construction allows to confirm (for degree 3) a conjecture of Fried regarding stretch factors of pseudoAnosov maps. via Zoom Video Conferencing: https://harvard.zoom.us/j/972495373
 23  CMSA EVENT: CMSA Condensed Matter/Math Seminar: Linear in temperature resistivity in the limit of zero temperature from the time reparameterization soft mode
10:30 AM12:00 PM April 23, 2020 The most puzzling aspect of the `strange metal’ behavior of correlated electron compounds is that the linear in temperature resistivity often extends down to low temperatures, lower than natural microscopic energy scales. We consider recently proposed deconfined critical points (or phases) in models of electrons in large dimension lattices with random nearestneighbor exchange interactions. The criticality is in the class of SachdevYeKitaev models, and exhibits a time reparameterization soft mode representing quantum gravity in dual holographic theories. We compute the low temperature resistivity in a large $M$ limit of models with SU($M$) spin symmetry, and find that the dominant temperature dependence arises from this soft mode. The resistivity is linear in temperature down to zero temperature at the critical point, with a coefficient universally proportional to the product of the residual resistivity and the coefficient of the linear in temperature specific heat. We argue that the time reparameterization soft mode offers a promising and generic mechanism for resolving the strange metal puzzle. via Zoom Video Conferencing: https://harvard.zoom.us/j/977347126
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26  27  28  MATHEMATICAL PICTURE LANGUAGE SEMINAR
10:00 AM11:00 AM April 28, 2020 Experimentalists are getting better and better at building qubits, but no matter how hard they try, their qubits will never be perfect. In order to build a large quantum computer, we will almost certainly need to encode the qubits using quantum errorcorrecting codes and encode the quantum circuits using faulttolerant protocols. The central result of the theory of fault tolerance is the threshold theorem, which states that arbitrarily long and reliable quantum computations are possible if the error rate per gate or time step is below some constant threshold value. Fault tolerance can be nicely defined using graphical techniques, allowing for a relatively straightforward proof of the threshold theorem. via Zoom: https://harvard.zoom.us/j/779283357  DIFFERENTIAL GEOMETRY SEMINAR
3:00 PM4:00 PM April 28, 2020 The SYZ conjecture predicts that for polarised CalabiYau manifolds undergoing the large complex structure limit, there should be a special Lagrangian torus fibration. A weak version asks if this fibration can be found in the generic region. I will discuss my recent work proving this weak SYZ conjecture for the degenerating hypersurfaces in the Fermat family. Although these examples are quite special, this is the first construction of generic SYZ fibrations that works uniformly in all complex dimensions. If you would like to attend, please email spicard@math.harvard.edu
 29  CMSA EVENT: CMSA Quantum Matter/Quantum Field Theory Seminar: If the Weak were Strong and the Strong were Weak
10:30 AM12:00 PM April 29, 2020 I will give an account of the work ArXiv:1907.08221 where we explore the phase structure of the Standard Model as the relative strengths of the SU(2) weak force and SU(3) strong force are varied. With a single generation of fermions, the structure of chiral symmetry breaking suggests that there is no phase transition as we interpolate between the SU(3)confining phase and the SU(2)confining phase. Remarkably, the massless lefthanded neutrino, familiar in our world, morphs smoothly into a massless righthanded downquark. With multiple generations, a similar metamorphosis occurs, but now proceeding via a phase transition. via Zoom Video Conferencing: https://harvard.zoom.us/j/977347126  RANDOM MATRIX SEMINAR
2:00 PM3:00 PM April 29, 2020 Spin wave theory suggests that low temperature properties of the Heisenberg model can be described in terms of noninteracting quasiparticles called magnons. In my talk I will review the basic concepts and predictions of spin wave approximation and report on recent rigorous results in that direction. Based on joint work with Robert Seiringer.
via Zoom Video Conferencing: https://harvard.zoom.us/j/147308224  INFORMAL GEOMETRY AND DYNAMICS SEMINAR
4:00 PM5:30 PM April 29, 2020 Triangulated surfaces are compact (hyperbolic) Riemann surfaces that admit a conformal triangulation by equilateral triangles. Brooks and Makover started the study of the geometry of random large genus triangulated surfaces. Mirzakhani later proved analogous results for random hyperbolic surfaces. These results, along with many others, suggest that the geometry of triangulated surfaces mirrors the geometry of arbitrary hyperbolic surfaces especially in the case of large genus asymptotics. In this talk, I will describe an approach to show that triangulated surfaces are asymptotically welldistributed in moduli space. via Zoom: https://harvard.zoom.us/j/972495373
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