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  • February 25, 2020
    3:00 pm
    Science Center 507

    HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR

    Speaker: Giovanni Inchiostro - Brown University   Title: Stable pairs with a twist
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  • 3:00 PMHARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR

    HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR

    3:00 PM-4:00 PM
    February 4, 2020

    1 Oxford Street, Cambridge, MA 02138 USA

    1 Oxford Street, Cambridge, MA 02138 USA

    I will construct LG mirrors for the Johnson-Kollár series of anticanonical del Pezzo surfaces in weighted projective 3-spaces. The main feature of these surfaces is that their anticanonical linear system is empty. Thus they fall outside of the range of the known mirror constructions. For each of these surfaces, the LG mirror is a pencil of hyperelliptic curves. I will exhibit the regularised I-function of the surface as a period of the pencil and I will sketch how to construct the pencil starting from a work of Beukers, Cohen, and Mellit on finite hypergeometric functions. This is joint work with Alessio Corti.

  • 4:15 PMDIFFERENTIAL GEOMETRY SEMINAR
    4:15 PM-5:15 PM
    February 4, 2020

    1 Oxford Street, Cambridge, MA 02138 USA

    1 Oxford Street, Cambridge, MA 02138 USA

    **CANCELED**

    Most 4-manifolds do not admit symplectic forms, but most admit 2-forms that are “nearly” symplectic. Just like the Seiberg-Witten (SW) invariants, there are Gromov invariants that are compatible with the near-symplectic form. Although (potentially exotic) 4-spheres don’t admit them, there is still a way to bring in near-symplectic techniques and I will describe my ongoing pseudo-holomorphic attempt(s) at analyzing them.

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  • 10:30 AMCMSA EVENT: CMSA Quantum Matter & Quantum Field Theory Seminar: A new theory for pseudogap metal in hole doped cuprates
    10:30 AM-12:00 PM
    February 5, 2020

    20 Garden Street, Cambridge, MA 02138

    20 Garden Street, Cambridge, MA 02138

    We provide a new parton theory for hole doped cuprates. We will describe both a pseudogap metal with small Fermi surfaces and the conventional Fermi liquid with large Fermi surfaces within mean field level of the same framework.  For the pseudogap metal,  “Fermi arc” observed in ARPES can be naturally reproduced.  We also provide a theory for a critical point across which the carrier density jumps from x to 1+x.   We will also discuss the generalization of the theory to Kondo breaking down transition in heavy fermion systems and  generic SU(N) Hubbard model.

  • 3:00 PMNUMBER THEORY SEMINAR
    3:00 PM-4:00 PM
    February 5, 2020

    1 Oxford Street, Cambridge, MA 02138 USA

    1 Oxford Street, Cambridge, MA 02138 USA

    There is a large literature about points of bounded height on varieties, and about number fields of bounded discriminant. We explain how to unify these two questions by means of a new definition of height for rational points on (certain) stacks over global fields. I talked about some aspects of this work at Barry’s birthday conference, and will try in this talk to emphasize different points, including a conjecture about the asymptotic counting function for points of bounded height on a stack X which simultaneously generalizes the Manin conjectures (the case where X is a variety) and the Malle conjectures (the case where X is a classifying stack BG.)

  • 4:30 PMCMSA EVENT: CMSA Colloquium Gentle Measurement of Quantum States and Differential Privacy
    4:30 PM-5:30 PM
    February 5, 2020

    20 Garden Street, Cambridge, MA 02138

    20 Garden Street, Cambridge, MA 02138

    I’ll discuss a recent connection between two seemingly unrelated
    problems: how to measure a collection of quantum states without
    damaging them too much (“gentle measurement”), and how to provide
    statistical data without leaking too much about individuals
    (“differential privacy,” an area of classical CS). This connection
    leads, among other things, to a new protocol for “shadow tomography”
    of quantum states (that is, answering a large number of questions
    about a quantum state given few copies of it).

  • 4:30 PMLOGIC COLLOQUIUM
    4:30 PM-5:30 PM
    February 5, 2020

    A ray in a graph G = (V, E) is a sequence X (possibly infinite) of distinct vertices x0, x1, . . . such that, for every i, E(xi , xi+1). A classical theorem of graph theory (Halin [1965]) states that if a graph has, for each k 2 N, a set of k many disjoint (say no vertices in common) infinite rays then there is an infinite set of disjoint infinite rays.

    The proof seems like an elementary argument by induction that uses the finite version of Menger’s theorem at each step. One would thus expect the theorem to follow by very elementary (even computable) methods plus a compactness argument (or equivalently arithmetic comprhension, ACA0). We show that this is not the case.

    Indeed, the construction of the infinite set of disjoint rays is much more complicated. It occupies a level of complexity previously inhabited by a number of logical principals and only one fact from the mathematical literature. Such theorems are called theorems of hyperarithmetic analysis. Formally this means that they imply (in !-models) that for every set A all transfinite iterations (through well-orderings computable from A) of the Turing jump beginning with A exist. On the other hand, they are true in the (!-model) consisting of the subsets of N generated from any single set A by these jump iterations.

    There are many variations of this theorem in the graph theory literature that inhabit the subject of ubiquity in graph theory. We discuss a number of them that also supply examples of theorems of hyperarithmetic analysis as well as classical variations that are proof theoretically even stronger.

    This work is joint with James Barnes and Jun Le Goh.

    If time permits we will also discuss a new class of theorems suggested by a “lemma” in one of the papers in the area. We call them almost theorems of hyperarithmetic analyisis. These are theorems that are proof theoretically very weak over Recursive Comprehension (RCA0) but become theorems of hyperarithmetic analysis once one assumes ACA0.

  • 4:30 PMOPEN NEIGHBORHOOD SEMINAR
    4:30 PM-5:30 PM
    February 5, 2020

    1 Oxford Street, Cambridge, MA 02138 USA

    1 Oxford Street, Cambridge, MA 02138 USA

    Imagine the universe is a periodic crystal. If gravity makes space negatively curved, the thin walls of the crystalline structure might trace out a pattern of circles in the sky, visible at night. In this talk we will describe how to generate pictures of these patterns and how to think like a hyperbolic astronomer. We also touch on the connection to knots and links and arithmetic groups. The lecture is accompanied by an exhibit of prints in the Science Center lobby. (This talk will be accessible to members of the department at all levels.)

  • More events
    • 10:30 AMCMSA EVENT: CMSA Quantum Matter & Quantum Field Theory Seminar: A new theory for pseudogap metal in hole doped cuprates
      10:30 AM-12:00 PM
      February 5, 2020
      20 Garden Street, Cambridge, MA 02138
      20 Garden Street, Cambridge, MA 02138

      We provide a new parton theory for hole doped cuprates. We will describe both a pseudogap metal with small Fermi surfaces and the conventional Fermi liquid with large Fermi surfaces within mean field level of the same framework.  For the pseudogap metal,  “Fermi arc” observed in ARPES can be naturally reproduced.  We also provide a theory for a critical point across which the carrier density jumps from x to 1+x.   We will also discuss the generalization of the theory to Kondo breaking down transition in heavy fermion systems and  generic SU(N) Hubbard model.

    • 3:00 PMNUMBER THEORY SEMINAR
      NUMBER THEORY SEMINAR
      3:00 PM-4:00 PM
      February 5, 2020
      1 Oxford Street, Cambridge, MA 02138 USA
      1 Oxford Street, Cambridge, MA 02138 USA

      There is a large literature about points of bounded height on varieties, and about number fields of bounded discriminant. We explain how to unify these two questions by means of a new definition of height for rational points on (certain) stacks over global fields. I talked about some aspects of this work at Barry’s birthday conference, and will try in this talk to emphasize different points, including a conjecture about the asymptotic counting function for points of bounded height on a stack X which simultaneously generalizes the Manin conjectures (the case where X is a variety) and the Malle conjectures (the case where X is a classifying stack BG.)

    • 4:30 PMCMSA EVENT: CMSA Colloquium Gentle Measurement of Quantum States and Differential Privacy
      4:30 PM-5:30 PM
      February 5, 2020
      20 Garden Street, Cambridge, MA 02138
      20 Garden Street, Cambridge, MA 02138

      I’ll discuss a recent connection between two seemingly unrelated
      problems: how to measure a collection of quantum states without
      damaging them too much (“gentle measurement”), and how to provide
      statistical data without leaking too much about individuals
      (“differential privacy,” an area of classical CS). This connection
      leads, among other things, to a new protocol for “shadow tomography”
      of quantum states (that is, answering a large number of questions
      about a quantum state given few copies of it).

    • 4:30 PMLOGIC COLLOQUIUM
      4:30 PM-5:30 PM
      February 5, 2020

      A ray in a graph G = (V, E) is a sequence X (possibly infinite) of distinct vertices x0, x1, . . . such that, for every i, E(xi , xi+1). A classical theorem of graph theory (Halin [1965]) states that if a graph has, for each k 2 N, a set of k many disjoint (say no vertices in common) infinite rays then there is an infinite set of disjoint infinite rays.

      The proof seems like an elementary argument by induction that uses the finite version of Menger’s theorem at each step. One would thus expect the theorem to follow by very elementary (even computable) methods plus a compactness argument (or equivalently arithmetic comprhension, ACA0). We show that this is not the case.

      Indeed, the construction of the infinite set of disjoint rays is much more complicated. It occupies a level of complexity previously inhabited by a number of logical principals and only one fact from the mathematical literature. Such theorems are called theorems of hyperarithmetic analysis. Formally this means that they imply (in !-models) that for every set A all transfinite iterations (through well-orderings computable from A) of the Turing jump beginning with A exist. On the other hand, they are true in the (!-model) consisting of the subsets of N generated from any single set A by these jump iterations.

      There are many variations of this theorem in the graph theory literature that inhabit the subject of ubiquity in graph theory. We discuss a number of them that also supply examples of theorems of hyperarithmetic analysis as well as classical variations that are proof theoretically even stronger.

      This work is joint with James Barnes and Jun Le Goh.

      If time permits we will also discuss a new class of theorems suggested by a “lemma” in one of the papers in the area. We call them almost theorems of hyperarithmetic analyisis. These are theorems that are proof theoretically very weak over Recursive Comprehension (RCA0) but become theorems of hyperarithmetic analysis once one assumes ACA0.

    • 4:30 PMOPEN NEIGHBORHOOD SEMINAR
      4:30 PM-5:30 PM
      February 5, 2020
      1 Oxford Street, Cambridge, MA 02138 USA
      1 Oxford Street, Cambridge, MA 02138 USA

      Imagine the universe is a periodic crystal. If gravity makes space negatively curved, the thin walls of the crystalline structure might trace out a pattern of circles in the sky, visible at night. In this talk we will describe how to generate pictures of these patterns and how to think like a hyperbolic astronomer. We also touch on the connection to knots and links and arithmetic groups. The lecture is accompanied by an exhibit of prints in the Science Center lobby. (This talk will be accessible to members of the department at all levels.)

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  • 10:30 AMCMSA GENERAL RELATIVITY SEMINAR CMSA EVENT
    10:30 AM-11:30 AM
    February 7, 2020

    In this talk, we will introduce the concept of improvabilty of the dominant energy scalar and discuss strong consequences of non-improvability. We employ new, large families of deformations of the modified Einstein constraint operator and show that, generically, their adjoint linearizations are either injective, or else one can prove that kernel elements satisfy a “null-vector equation”. Combined with a conformal argument, we make significant progress toward Bartnik’s stationary conjecture. More specifically, we prove that a Bartnik minimizing initial data set can be developed into a spacetime that both satisfies the dominant energy condition and carries a global Killing field. We also show that this spacetime is vacuum near spatial infinity. This talk is based on the joint work with Dan Lee.

  • 3:30 PMGAUGE-TOPOLOGY-SYMPLECTIC SEMINAR

    GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR

    3:30 PM-4:30 PM
    February 7, 2020

    1 Oxford Street, Cambridge, MA 02138 USA

    1 Oxford Street, Cambridge, MA 02138 USA

    I’ll discuss the Viterbo transfer functor from the (partially) wrapped Fukaya category of a Liouville domain to that of a subdomain. It is a localization when everything in sight is Weinstein, and I’ll explain how much of that survives if we drop the assumption that the cobordism is Weinstein. The result allows us to turn natural questions about exact Lagrangians into interesting questions in homotopical algebra.

     

    Future schedule is found here: http://scholar.harvard.edu/gerig/seminar

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  • 11:00 AMSEMINARS
    11:00 AM-12:30 PM
    February 11, 2020

    Motivic complexes of Voevodsky have no right to two properties (1) cohomological sparsity and (2) a relationship with differential forms. This is, however, true p-adically over characteristic p by a result of Geisser-Levine, relying on previous results of Bloch-Kato-Gabber. I will explain this result, including the cast of characters involved like the logarithmic de Rham-Witt sheaves, Bloch’s higher Chow groups and algebraic/Milnor K-theory.

  • 3:00 PMHARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR

    HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR

    3:00 PM-4:00 PM
    February 11, 2020

    1 Oxford Street, Cambridge, MA 02138 USA

    1 Oxford Street, Cambridge, MA 02138 USA

    The talk will revolve around combinatorial aspects Prym varieties, a class of Abelian varieties that occurs in the presence of double covers. Pryms have deep connections with torsion points of Jacobians, bi-tangent lines of curves, and spin structures. As I will explain, problems concerning Pryms may be reduced, via tropical geometry, to combinatorial games on graphs. As a consequence, we obtain new results concerning the geometry of special algebraic curves, and bounds on dimensions of certain Brill–Noether loci.

  • 3:30 PMMATHEMATICAL PICTURE LANGUAGE SEMINAR
    3:30 PM-4:30 PM
    February 11, 2020

    17 Oxford Street, Cambridge, MA 02138 USA

    17 Oxford Street, Cambridge, MA 02138 USA

    Sampling from a classical, thermal distribution is, in general, a computationally hard problem. In particular, standard Monte Carlo algorithms converge slowly close to a phase transition or in the presence of frustration. In this work, we explore whether a quantum computer can provide a speedup for problems of this type. The sampling problem can be reduced to the task of preparing a pure quantum state, the so-called Gibbs state [1]. Samples from the thermal distribution are obtained by performing projective measurements on this state. To prepare the Gibbs state, we exploit a mapping from a classical Monte Carlo algorithm to a quantum Hamiltonian whose ground state is the Gibbs state [2]. We demonstrate with concrete examples that a quantum speedup can be achieved by identifying optimal adiabatic trajectories in an extended parameter space of the quantum Hamiltonian. Our approach elucidates intimate connections between computational complexity and phase transitions. Finally, we propose a realistic implementation of the algorithm using Rydberg atoms suitable for near-term quantum devices.

    [1] R. D. Somma and C. D. Batista, Phys. Rev. Lett. 99, 030603 (2007).
    [2] F. Verstraete, M. M. Wolf, D. Perez-Garcia, and J. I. Cirac, Phys. Rev. Lett. 96, 220601 (2006).

  • 4:15 PMDIFFERENTIAL GEOMETRY SEMINAR
    4:15 PM-5:15 PM
    February 11, 2020

    1 Oxford Street, Cambridge, MA 02138 USA

    1 Oxford Street, Cambridge, MA 02138 USA

    In this talk, we discuss how to derive the equivariant SYZ mirror of toric manifolds by counting holomorphic discs. In the case of (semi-)Fano toric manifolds, those mirrors recover Givental’s equivariant mirrors, which compute the equivariant quantum cohomology. Also, we formulate and compute open Gromov-Witten invariants of singular SYZ fiber, which are closely related to the open Gromov-Witten invariants of Aganagic-Vafa branes. This talk is based on joint work with Hansol Hong, Siu-Cheong Lau, and Xiao Zheng.

    –Organized by Professor Shing-Tung Yau

  • More events
    • 11:00 AMSEMINARS
      11:00 AM-12:30 PM
      February 11, 2020

      Motivic complexes of Voevodsky have no right to two properties (1) cohomological sparsity and (2) a relationship with differential forms. This is, however, true p-adically over characteristic p by a result of Geisser-Levine, relying on previous results of Bloch-Kato-Gabber. I will explain this result, including the cast of characters involved like the logarithmic de Rham-Witt sheaves, Bloch’s higher Chow groups and algebraic/Milnor K-theory.

    • 3:00 PMHARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR
      HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR
      3:00 PM-4:00 PM
      February 11, 2020
      1 Oxford Street, Cambridge, MA 02138 USA
      1 Oxford Street, Cambridge, MA 02138 USA

      The talk will revolve around combinatorial aspects Prym varieties, a class of Abelian varieties that occurs in the presence of double covers. Pryms have deep connections with torsion points of Jacobians, bi-tangent lines of curves, and spin structures. As I will explain, problems concerning Pryms may be reduced, via tropical geometry, to combinatorial games on graphs. As a consequence, we obtain new results concerning the geometry of special algebraic curves, and bounds on dimensions of certain Brill–Noether loci.

    • 3:30 PMMATHEMATICAL PICTURE LANGUAGE SEMINAR
      3:30 PM-4:30 PM
      February 11, 2020
      17 Oxford Street, Cambridge, MA 02138 USA
      17 Oxford Street, Cambridge, MA 02138 USA

      Sampling from a classical, thermal distribution is, in general, a computationally hard problem. In particular, standard Monte Carlo algorithms converge slowly close to a phase transition or in the presence of frustration. In this work, we explore whether a quantum computer can provide a speedup for problems of this type. The sampling problem can be reduced to the task of preparing a pure quantum state, the so-called Gibbs state [1]. Samples from the thermal distribution are obtained by performing projective measurements on this state. To prepare the Gibbs state, we exploit a mapping from a classical Monte Carlo algorithm to a quantum Hamiltonian whose ground state is the Gibbs state [2]. We demonstrate with concrete examples that a quantum speedup can be achieved by identifying optimal adiabatic trajectories in an extended parameter space of the quantum Hamiltonian. Our approach elucidates intimate connections between computational complexity and phase transitions. Finally, we propose a realistic implementation of the algorithm using Rydberg atoms suitable for near-term quantum devices.

      [1] R. D. Somma and C. D. Batista, Phys. Rev. Lett. 99, 030603 (2007).
      [2] F. Verstraete, M. M. Wolf, D. Perez-Garcia, and J. I. Cirac, Phys. Rev. Lett. 96, 220601 (2006).

    • 4:15 PMDIFFERENTIAL GEOMETRY SEMINAR
      4:15 PM-5:15 PM
      February 11, 2020
      1 Oxford Street, Cambridge, MA 02138 USA
      1 Oxford Street, Cambridge, MA 02138 USA

      In this talk, we discuss how to derive the equivariant SYZ mirror of toric manifolds by counting holomorphic discs. In the case of (semi-)Fano toric manifolds, those mirrors recover Givental’s equivariant mirrors, which compute the equivariant quantum cohomology. Also, we formulate and compute open Gromov-Witten invariants of singular SYZ fiber, which are closely related to the open Gromov-Witten invariants of Aganagic-Vafa branes. This talk is based on joint work with Hansol Hong, Siu-Cheong Lau, and Xiao Zheng.

      –Organized by Professor Shing-Tung Yau

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  • 10:30 AMCMSA EVENT: CMSA Quantum Matter/Quantum Field Theory Seminar: Monopoles in QED3 Dirac Spin Liquids
    10:30 AM-12:00 PM
    February 12, 2020

    20 Garden Street, Cambridge, MA 02138

    20 Garden Street, Cambridge, MA 02138

    No additional detail for this event.

  • 3:00 PMNUMBER THEORY SEMINAR
    3:00 PM-4:00 PM
    February 12, 2020

    1 Oxford Street, Cambridge, MA 02138 USA

    1 Oxford Street, Cambridge, MA 02138 USA

    Every Newton polygon satisfying the Kottwitz conditions occurs on Shimura varieties of PEL-type in positive characteristic (Viehmann/Wedhorn). In most cases, it is not known whether these Newton polygon strata contain points representing the Jacobians of smooth curves. In some cases, this is not even known for the mu-ordinary stratum. We provide a positive answer for the mu-ordinary and almost mu-ordinary strata in infinitely many cases. For base cases, we consider the arithmetic of some of Moonen’s families of cyclic covers of the projective line. As an application, we produce infinitely many new examples of unusual Newton polygons which occur for Jacobians of smooth curves. This is joint work with Li, Mantovan, and Tang.

  • 4:30 PMCMSA EVENT: CMSA Colloquium: A Compact, Logical Approach to Large-Market Analysis
    4:30 PM-5:30 PM
    February 12, 2020

    20 Garden Street, Cambridge, MA 02138

    20 Garden Street, Cambridge, MA 02138

    In game theory, we often use infinite models to represent “limit” settings, such as markets with a large number of agents or games with a long time horizon. Yet many game-theoretic models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. Here, we show how to extend key results from (finite) models of matching, games on graphs, and trading networks to infinite models by way of Logical Compactness, a core result from Propositional Logic. Using Compactness, we prove the existence of man-optimal stable matchings in infinite economies, as well as strategy-proofness of the man-optimal stable matching mechanism. We then use Compactness to eliminate the need for a finite start time in a dynamic matching model. Finally, we use Compactness to prove the existence of both Nash equilibria in infinite games on graphs and Walrasian equilibria in infinite trading networks.

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  • 10:30 AMCMSA EVENT: CMSA Condensed Matter/Math Seminar: Spontaneous symmetry breaking in SYK models
    10:30 AM-12:00 PM
    February 13, 2020

    20 Garden Street, Cambridge, MA 02138

    20 Garden Street, Cambridge, MA 02138

    No additional detail for this event.

  • 3:00 PMCOLLOQUIUMS
    3:00 PM-5:00 PM
    February 13, 2020

    1 Oxford Street, Cambridge, MA 02138 USA

    1 Oxford Street, Cambridge, MA 02138 USA

    No additional detail for this event.

  • 4:00 PMCOLLOQUIUMS
    4:00 PM-5:30 PM
    February 13, 2020

    1 Oxford Street, Cambridge, MA 02138

    1 Oxford Street, Cambridge, MA 02138

    will speak on: “Symplectic, or mirrorical, look at the Fargues-Fontaine curve”

    Homological mirror symmetry describes Lagrangian Floer theory on a torus in terms of vector bundles on the Tate elliptic curve.  A version of Lekili and Perutz’s works “over Z[[t]]”, where t is the Novikov parameter.  I will review this story and describe a modified form of it, which is joint work with Lekili, where the Floer theory is altered by a locally constant sheaf of rings on the torus. When the fiber of this sheaf of rings is perfectoid of characteristic p, and the holonomy around one of the circles in the torus is the pth power map, it is possible to specialize to t = 1, and the resulting theory there is described in terms of vector bundles on the equal-characteristic-version of the Fargues-Fontaine curve.

    Tea at 4:00 pm – Math Common Room, 4th Floor

    Talk at 4:30 pm – Hall A

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  • 10:30 AMCMSA GENERAL RELATIVITY SEMINAR CMSA EVENT

    CMSA GENERAL RELATIVITY SEMINAR CMSA EVENT

    10:30 AM-11:30 AM
    February 14, 2020

    Jang’s equation is a degenerate elliptic differential equation which plays an important role in the positive mass theorem. In this talk, we describe a high order WENO (Weighted Essentially Non-Oscillatory) scheme for the Jang’s equation. Some special solutions will be shown, such as those possessing spherical symmetry and axial symmetry.

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  • 3:00 PMMATHEMATICAL PICTURE LANGUAGE SEMINAR
    3:00 PM-4:00 PM
    February 18, 2020

    The out-of-time-ordered correlation (OTOC) and entanglement are two physically motivated and widely used probes of the “scrambling” of quantum information, a phenomenon that has drawn great interest recently in quantum gravity and many-body physics. We argue that the corresponding notions of scrambling can be fundamentally different, by proving an asymptotic separation between the time scales of the saturation of OTOC and that of entanglement entropy in a random quantum circuit model defined on graphs with a tight bottleneck, such as tree graphs connected at the roots. Our result counters the intuition that a random quantum circuit mixes in time proportional to the diameter of the underlying graph of interactions. It also provides a more rigorous justification for an argument of arXiv:1807.04363, that black holes may be slow information scramblers. Such observations may be of fundamental importance in the understanding of the black hole information problem. The bounds we obtained for OTOC are interesting in their own right in that they generalize previous studies of OTOC on lattices to the geometries on graphs in a rigorous and general fashion.

  • 4:15 PMDIFFERENTIAL GEOMETRY SEMINAR

    DIFFERENTIAL GEOMETRY SEMINAR

    4:15 PM-5:15 PM
    February 18, 2020

    1 Oxford Street, Cambridge, MA 02138 USA

    1 Oxford Street, Cambridge, MA 02138 USA

    In 2008, Christodoulou achieved a major breakthrough in the context of mathematical general relativity in being able to form trapped surfaces dynamically from initial data for the Einstein vacuum system. The results and methods which he lays out in his 600+ page manuscript has led to a flurry of activity in the last decade. I will give a rough overview of the basic ideas, describe how far theorems have come, and describe some recent progress – joint with Nikos Athanasiou – in this direction.

    –Organized by Professor Shing-Tung Yau

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  • 10:30 AMCMSA EVENT: CMSA Quantum Matter/Quantum Field Theory Seminar:Modeling the pseudogap state in cuprates: quantum disordered pair density wave
    10:30 AM-12:00 PM
    February 19, 2020

    20 Garden Street, Cambridge, MA 02138

    20 Garden Street, Cambridge, MA 02138

    I will briefly review the pseudogap phenomenology in high Tc cuprate superconductors, especially recent experiments related to charge density waves and pair density waves, and propose a simple theory of the pseudogap. By quantum disordering a pair density wave, we found a state composed of insulating antinodal pairs and a nodal electron pocket. We compare the theoretical predictions with ARPES results, optical conductivity, quantum oscillation and other experiments.

  • 3:00 PMNUMBER THEORY SEMINAR
    3:00 PM-4:00 PM
    February 19, 2020

    1 Oxford Street, Cambridge, MA 02138 USA

    1 Oxford Street, Cambridge, MA 02138 USA

    We consider the family of normal octic fields with Galois group $D_4$, ordered by their discriminant. In forthcoming joint work with Arul Shankar, we verify the strong form of Malle’s conjecture for this family of number fields, obtaining the order of growth as well as the constant of proportionality. In this talk, we will discuss and review the combination of techniques from analytic number theory and geometry-of-numbers methods used to prove this and related results.

  • 4:00 PMSEMINARS
    4:00 PM-6:00 PM
    February 19, 2020

    Can you use the homotopy type of the space of knots in a simply-connected 4-manifold to distinguish smooth structures? The answer is no, using embedding calculus. I will also give some examples which show that embedding calculus does distinguish smooth structures in high dimensions. This is joint with Ben Knudsen.

  • 4:30 PMOPEN NEIGHBORHOOD SEMINAR

    OPEN NEIGHBORHOOD SEMINAR

    4:30 PM-5:30 PM
    February 19, 2020

    1 Oxford Street, Cambridge, MA 02138 USA

    1 Oxford Street, Cambridge, MA 02138 USA

    Max Dehn made many remarkable contributions to mathematics, and his name pops up in lots of places, most often in topology, where we have “Dehn surgery”, the “Dehn twist”, and “Dehn’s lemma”. Famously, Dehn supplied an incorrect proof of the lemma that bears his name. The mistake wasn’t noticed for nearly a decade, and took nearly another four decades to fix. In this talk, I won’t mention the lemma, but I will say a few words about Dehn himself, a few more about his early work on “scissors congruences”, and then yet more on the Dehn twist, closing with a recent result about Dehn twists in four dimensions. (This talk will be accessible to members of the department at all levels.)

  • 5:15 PMCMSA EVENT: CMSA Colloquium: Quantum Money from Lattices
    5:15 PM-6:15 PM
    February 19, 2020

    20 Garden Street, Cambridge, MA 02138

    20 Garden Street, Cambridge, MA 02138

    Quantum money is a cryptographic protocol for quantum computers. A quantum money protocol consists of a quantum state which can be created (by the mint) and verified (by anybody with a quantum computer who knows what the “serial number” of the money is), but which cannot be duplicated, even by somebody with a copy of the quantum state who knows the verification protocol. Several previous proposals have been made for quantum money protocols. We will discuss the history of quantum money and give a protocol which cannot be broken unless lattice cryptosystems are insecure.

  • More events
    • 10:30 AMCMSA EVENT: CMSA Quantum Matter/Quantum Field Theory Seminar:Modeling the pseudogap state in cuprates: quantum disordered pair density wave
      10:30 AM-12:00 PM
      February 19, 2020
      20 Garden Street, Cambridge, MA 02138
      20 Garden Street, Cambridge, MA 02138

      I will briefly review the pseudogap phenomenology in high Tc cuprate superconductors, especially recent experiments related to charge density waves and pair density waves, and propose a simple theory of the pseudogap. By quantum disordering a pair density wave, we found a state composed of insulating antinodal pairs and a nodal electron pocket. We compare the theoretical predictions with ARPES results, optical conductivity, quantum oscillation and other experiments.

    • 3:00 PMNUMBER THEORY SEMINAR
      3:00 PM-4:00 PM
      February 19, 2020
      1 Oxford Street, Cambridge, MA 02138 USA
      1 Oxford Street, Cambridge, MA 02138 USA

      We consider the family of normal octic fields with Galois group $D_4$, ordered by their discriminant. In forthcoming joint work with Arul Shankar, we verify the strong form of Malle’s conjecture for this family of number fields, obtaining the order of growth as well as the constant of proportionality. In this talk, we will discuss and review the combination of techniques from analytic number theory and geometry-of-numbers methods used to prove this and related results.

    • 4:00 PMSEMINARS
      4:00 PM-6:00 PM
      February 19, 2020

      Can you use the homotopy type of the space of knots in a simply-connected 4-manifold to distinguish smooth structures? The answer is no, using embedding calculus. I will also give some examples which show that embedding calculus does distinguish smooth structures in high dimensions. This is joint with Ben Knudsen.

    • 4:30 PMOPEN NEIGHBORHOOD SEMINAR
      OPEN NEIGHBORHOOD SEMINAR
      4:30 PM-5:30 PM
      February 19, 2020
      1 Oxford Street, Cambridge, MA 02138 USA
      1 Oxford Street, Cambridge, MA 02138 USA

      Max Dehn made many remarkable contributions to mathematics, and his name pops up in lots of places, most often in topology, where we have “Dehn surgery”, the “Dehn twist”, and “Dehn’s lemma”. Famously, Dehn supplied an incorrect proof of the lemma that bears his name. The mistake wasn’t noticed for nearly a decade, and took nearly another four decades to fix. In this talk, I won’t mention the lemma, but I will say a few words about Dehn himself, a few more about his early work on “scissors congruences”, and then yet more on the Dehn twist, closing with a recent result about Dehn twists in four dimensions. (This talk will be accessible to members of the department at all levels.)

    • 5:15 PMCMSA EVENT: CMSA Colloquium: Quantum Money from Lattices
      5:15 PM-6:15 PM
      February 19, 2020
      20 Garden Street, Cambridge, MA 02138
      20 Garden Street, Cambridge, MA 02138

      Quantum money is a cryptographic protocol for quantum computers. A quantum money protocol consists of a quantum state which can be created (by the mint) and verified (by anybody with a quantum computer who knows what the “serial number” of the money is), but which cannot be duplicated, even by somebody with a copy of the quantum state who knows the verification protocol. Several previous proposals have been made for quantum money protocols. We will discuss the history of quantum money and give a protocol which cannot be broken unless lattice cryptosystems are insecure.

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  • 10:30 AMCMSA EVENT: CMSA Condensed Matter/Math Seminar: Lattice models that realize $Z_n$ 1-symmetry-protected topological states for even $n$
    10:30 AM-12:00 PM
    February 20, 2020

    20 Garden Street, Cambridge, MA 02138

    20 Garden Street, Cambridge, MA 02138

    Higher symmetries can emerge at low energies in a topologically ordered state with no symmetry, when some topological excitations have very high energy scales while other topological excitations have low energies.  The low energy properties of topological orders in this limit, with the emergent higher symmetries, may be described by higher symmetry protected topological order. This motivates us, as a simplest example, to study a lattice model of $Z_n$-1-symmetry protected topological (1-SPT) states in 3+1D for even $n$. We write down an exactly solvable lattice model and study its boundary transformation. On the boundary, we show the existence of anyons with non-trivial self-statistics.  For the $n=2$ case, where the bulk classification is given by an integer $m$ mod 4, we show that the boundary can be gapped with double semion topological order for $m=1$ and toric code for $m=2$. The bulk ground state wavefunction amplitude is given in terms of the linking numbers of loops in the dual lattice.  Our construction can be generalized to arbitrary 1-SPT protected by finite unitary symmetry.

  • 3:00 PMTHURSDAY SEMINAR SEMINAR
    3:00 PM-5:00 PM
    February 20, 2020

    1 Oxford Street, Cambridge, MA 02138 USA

    1 Oxford Street, Cambridge, MA 02138 USA

    No additional detail for this event.

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  • 10:30 AMCMSA GENERAL RELATIVITY SEMINAR CMSA EVENT

    CMSA GENERAL RELATIVITY SEMINAR CMSA EVENT

    10:30 AM-11:30 AM
    February 21, 2020

    The Event Horizon Telescope image of the supermassive black hole in the galaxy M87 is dominated by a bright, unresolved ring.  General relativity predicts that embedded within this image lies a thin “photon ring,” which is itself composed of an infinite sequence of self-similar subrings.  Each subring is a lensed image of the main emission, indexed by the number of photon orbits executed around the black hole.  I will review recent theoretical advances in our understanding of lensing by Kerr black holes, based on arXiv:1907.04329, 1910.12873, and 1910.12881.  In particular, I will describe the critical parameters γ, δ, and τ that respectively control the demagnification, rotation, and time delay of successive lensed images of a source.  These observable parameters encode universal effects of general relativity, which are independent of the details of the emitting matter and also produce strong, universal signatures on long interferometric baselines.  These signatures offer the possibility of precise measurements of black hole mass and spin, as well as tests of general relativity, using only a sparse interferometric array such as a future extension of the EHT to space

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  • 12:00 PMCMSA EVENT: CMSA Mathematical Physics Seminar: Coisotropic branes on symplectic tori and homological mirror symmetry
    12:00 PM-1:00 PM
    February 24, 2020

    20 Garden Street, Cambridge, MA 02138

    20 Garden Street, Cambridge, MA 02138

    Homological mirror symmetry (HMS) asserts that the Fukaya category of a symplectic manifold is derived equivalent to the category of coherent sheaves on the mirror complex manifold. Without suitable enlargement (split closure) of the Fukaya category, certain objects of it are missing to prevent HMS from being true. Kapustin and Orlov conjecture that coisotropic branes should be included into the Fukaya category from a physics view point. In this talk, I will construct for linear symplectic tori a version of the Fukaya category including coisotropic branes and show that the usual Fukaya category embeds fully faithfully into it. I will also explain the motivation of the construction through the perspective of Homological mirror symmetry.

  • 3:00 PMCMSA EVENT: CMSA Special Seminar: How will we do Mathematics in 2030?
    3:00 PM-4:00 PM
    February 24, 2020

    20 Garden Street, Cambridge, MA 02138

    20 Garden Street, Cambridge, MA 02138

    We make the case that over the coming decade, computer assisted reasoning will become far more widely used in the mathematical sciences. This includes interactive and automatic theorem verification, symbolic algebra, and emerging technologies such as formal knowledge repositories, semantic search and intelligent textbooks.

    After a short review of the state of the art, we survey directions where we expect progress, such as mathematical search and formal abstracts, developments in computational mathematics, integration of computation into textbooks, and organizing and verifying large calculations and proofs. For each we try to identify the barriers and potential solutions.

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  • 3:00 PMHARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR

    HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR

    3:00 PM-4:00 PM
    February 25, 2020

    1 Oxford Street, Cambridge, MA 02138 USA

    1 Oxford Street, Cambridge, MA 02138 USA

    It is well known that, for pointed nodal curves, considering flat and proper families of pairs (X,D) leads to a proper moduli space. Still, while the notion of stable pairs is a higher dimensional analogue of pointed nodal curves, the right definition of a family of stable pairs is far from obvious. In this work, building on an idea of Kollár and the work of Abramovich and Hassett, we give an alternative definition of a family of stable pairs, in the case where the divisor D is reduced. This definition is more amenable to the tools of deformation theory. As an application we produce functorial gluing morphisms on the moduli spaces of surfaces, generalizing the clutching and gluing morphisms that describe the boundary strata of the moduli of curves. This is joint work with D. Bejleri.
  • 3:30 PMMATHEMATICAL PICTURE LANGUAGE SEMINAR
    3:30 PM-4:30 PM
    February 25, 2020

    17 Oxford Street, Cambridge, MA 02138 USA

    17 Oxford Street, Cambridge, MA 02138 USA

    In this work, we propose a systematical framework to construct Bell inequalities from stabilizers which are maximally violated by general stabilizer states. We show that the constructed Bell inequalities can self-test any stabilizer state which is essentially device-independent, if and only if these stabilizers can uniquely determine the state in a device-dependent manner. This bridges the gap between device-independent and device-dependent verification methods. Our framework can not only inspire more fruitful multipartite Bell inequalities from conventional verification methods, but also pave the way for their practical applications.

    Joint work with Qi Zhao, arXiv:2002.01843

  • 4:15 PMDIFFERENTIAL GEOMETRY SEMINAR
    4:15 PM-5:15 PM
    February 25, 2020

    1 Oxford Street, Cambridge, MA 02138 USA

    1 Oxford Street, Cambridge, MA 02138 USA

    Let $M$ be a complete Ricci-flat manifold with Euclidean
    volume growth. A theorem of Colding-Minicozzi states that if a tangent
    cone at infinity of $M$ is smooth, then it is the unique tangent cone.
    The key component in their proof is an infinite dimensional
    Lojasiewicz-Simon inequality, which implies rapid decay of the
    $L^2$-norm of the trace-free Hessian of the Green function. In this
    talk we discuss how this inequality can be exploited to identify two
    arbitrarily far apart scales in $M$ in a natural manner through a
    diffeomorphism. We also prove a pointwise Hessian estimate for the
    Green function when there is an additional condition on sectional
    curvature, which is an analogue of various matrix Harnack inequalities
    obtained by Hamilton and Li-Cao in different time-dependent settings.

    — Organized by Prof. Shing-Tung Yau

26
  • 10:30 AMCMSA EVENT: CMSA Quantum Matter/Quantum Field Theory Seminar: Jordan-Wigner dualities for translation-invariant Hamiltonians in any dimension
    10:30 AM-12:00 PM
    February 26, 2020

    20 Garden Street, Cambridge, MA 02138

    20 Garden Street, Cambridge, MA 02138

    Inspired by recent constructions of Jordan-Wigner transformations in higher dimensions by Kapustin et. al., I will present a framework for an exact bosonization, which locally maps a translation-invariant model of spinless fermions to a gauge theory of Pauli spins. I will show that the duality exists for an arbitrary number of (possibly many-body) “hopping” operators in any dimension and provide an explicit construction. The duality can be concisely stated in terms of an algebraic formalism of translation-invariant Hamiltonians proposed by Haah.
    I will then present two interesting applications. First, bosonizing Majorana stabilizer codes, such as the Majorana color code or the checkerboard model, into Pauli stabilizer codes. Second, bosonizing fermionic systems where fermion parity is conserved on submanifolds such as higher-form, line, planar or fractal symmetry. In 3+1D, the latter two can give rise to fracton models where emergent particles are immobile, but yet can be “fermionic”. This may give rise to new non-relativistic ‘t Hooft anomalies.
  • 2:00 PMRANDOM MATRIX SEMINAR
    2:00 PM-3:00 PM
    February 26, 2020

    20 Garden Street, Cambridge, MA 02138

    20 Garden Street, Cambridge, MA 02138

    I will describe how certain recursive distributional equations can be solved by importing rigorous results on the convergence of approximation schemes for degenerate PDEs, from numerical analysis. This project is joint work with Luc Devroye, Hannah Cairns, Celine Kerriou, and Rivka Maclaine Mitchell.

  • 3:00 PMNUMBER THEORY SEMINAR
    3:00 PM-4:00 PM
    February 26, 2020

    1 Oxford Street, Cambridge, MA 02138 USA

    1 Oxford Street, Cambridge, MA 02138 USA

    One of the fundamental challenges in number theory is to understand the intricate way in which the additive and multiplicative structures in the integers intertwine. We will explore a dynamical approach to this topic. After introducing a new dynamical framework for treating questions in multiplicative number theory, we will present an ergodic theorem which
    contains various classical number-theoretic results, such as the Prime Number Theorem, as special cases. This naturally leads to a formulation of an extended form of Sarnak’s conjecture, which deals with the disjointness of actions of (N,+) and (N,*). This talk is based on joint work with Vitaly Bergelson.

  • 4:30 PMCMSA EVENT: CMSA Colloquium: The Cubical Route to Understanding Groups
    4:30 PM-5:30 PM
    February 26, 2020

    20 Garden Street, Cambridge, MA 02138

    20 Garden Street, Cambridge, MA 02138

    Cube complexes have come to play an increasingly central role within geometric group theory, as their connection to right-angled Artin groups provides a powerful combinatorial bridge between geometry and algebra. This talk will introduce nonpositively curved cube complexes, and then describe the developments that culminated in  the resolution of the virtual Haken conjecture for 3-manifolds and  simultaneously dramatically extended our understanding of many  infinite groups.
  • More events
    • 10:30 AMCMSA EVENT: CMSA Quantum Matter/Quantum Field Theory Seminar: Jordan-Wigner dualities for translation-invariant Hamiltonians in any dimension
      10:30 AM-12:00 PM
      February 26, 2020
      20 Garden Street, Cambridge, MA 02138
      20 Garden Street, Cambridge, MA 02138
      Inspired by recent constructions of Jordan-Wigner transformations in higher dimensions by Kapustin et. al., I will present a framework for an exact bosonization, which locally maps a translation-invariant model of spinless fermions to a gauge theory of Pauli spins. I will show that the duality exists for an arbitrary number of (possibly many-body) “hopping” operators in any dimension and provide an explicit construction. The duality can be concisely stated in terms of an algebraic formalism of translation-invariant Hamiltonians proposed by Haah.
      I will then present two interesting applications. First, bosonizing Majorana stabilizer codes, such as the Majorana color code or the checkerboard model, into Pauli stabilizer codes. Second, bosonizing fermionic systems where fermion parity is conserved on submanifolds such as higher-form, line, planar or fractal symmetry. In 3+1D, the latter two can give rise to fracton models where emergent particles are immobile, but yet can be “fermionic”. This may give rise to new non-relativistic ‘t Hooft anomalies.
    • 2:00 PMRANDOM MATRIX SEMINAR
      2:00 PM-3:00 PM
      February 26, 2020
      20 Garden Street, Cambridge, MA 02138
      20 Garden Street, Cambridge, MA 02138

      I will describe how certain recursive distributional equations can be solved by importing rigorous results on the convergence of approximation schemes for degenerate PDEs, from numerical analysis. This project is joint work with Luc Devroye, Hannah Cairns, Celine Kerriou, and Rivka Maclaine Mitchell.

    • 3:00 PMNUMBER THEORY SEMINAR
      3:00 PM-4:00 PM
      February 26, 2020
      1 Oxford Street, Cambridge, MA 02138 USA
      1 Oxford Street, Cambridge, MA 02138 USA

      One of the fundamental challenges in number theory is to understand the intricate way in which the additive and multiplicative structures in the integers intertwine. We will explore a dynamical approach to this topic. After introducing a new dynamical framework for treating questions in multiplicative number theory, we will present an ergodic theorem which
      contains various classical number-theoretic results, such as the Prime Number Theorem, as special cases. This naturally leads to a formulation of an extended form of Sarnak’s conjecture, which deals with the disjointness of actions of (N,+) and (N,*). This talk is based on joint work with Vitaly Bergelson.

    • 4:30 PMCMSA EVENT: CMSA Colloquium: The Cubical Route to Understanding Groups
      4:30 PM-5:30 PM
      February 26, 2020
      20 Garden Street, Cambridge, MA 02138
      20 Garden Street, Cambridge, MA 02138
      Cube complexes have come to play an increasingly central role within geometric group theory, as their connection to right-angled Artin groups provides a powerful combinatorial bridge between geometry and algebra. This talk will introduce nonpositively curved cube complexes, and then describe the developments that culminated in  the resolution of the virtual Haken conjecture for 3-manifolds and  simultaneously dramatically extended our understanding of many  infinite groups.
27
  • 4:30 PMHARVARD-MIT-BU-BRANDEIS-NORTHEASTERN COLLOQUIUM

    HARVARD-MIT-BU-BRANDEIS-NORTHEASTERN COLLOQUIUM

    4:30 PM-5:30 PM
    February 27, 2020

    1 Oxford Street, Cambridge, MA 02138

    1 Oxford Street, Cambridge, MA 02138

    The groups of homeomorphisms or diffeomorphisms of a manifold have many striking parallels with finite dimensional Lie groups. In this talk, I’ll describe some of these, and explain new work, joint with Lei Chen, that gives an orbit classification theorem and a structure theorem for actions of homeomorphism and diffeomorphism groups on other spaces, analogous to some classical results for actions of locally compact Lie groups. As applications, we answer many concrete questions towards classifying all actions of Diff(M) on other manifolds (many of which are nontrivial, for instance Diff(M) acts naturally on the unit tangent bundle of M…) and resolve several threads in a research program initiated by Ghys. I’ll aim to give both a broad overview and several toy applications in the talk.

    Tea at 4:00 pm – Math Common Room

    Talk at 4:30 pm – Hall A

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  • 3:30 PMGAUGE-TOPOLOGY-SYMPLECTIC SEMINAR

    GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR

    3:30 PM-4:30 PM
    February 28, 2020

    1 Oxford Street, Cambridge, MA 02138 USA

    1 Oxford Street, Cambridge, MA 02138 USA

    We give the first examples of codimension-1 knotting in the 4-sphere, i.e. there is a 3-ball B_1 with boundary the standard linear 2-sphere, which is not isotopic rel boundary to the standard linear 3-ball B_0. Actually, there is an infinite family of distinct isotopy classes of such balls. This implies that there exist inequivalent fiberings of the unknot in 4-sphere, in contrast to the situation in dimension-3. Also, that there exists diffeomorphisms of S^1 x B^3 homotopic rel boundary to the identity, but not isotopic rel boundary to the identity. Joint work with Ryan Budney.

    Future schedule is found here: http://scholar.harvard.edu/gerig/seminar

29

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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JDG Conference
May 1, 2020 - May 3, 2020     

Confirmed speakers: Toby Colding, MIT Tristan Collins, MIT Simon Donaldson, Stony Brook University Hélène Esnault, Freie Universität Berlin Kenji Fukaya, Stony Brook University Pengfei Guan,...
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