Calendar

< 2021 >
September
  • 01
    September 1, 2021

    CMSA Quantum Matter in Mathematics and Physics Seminar: Naturalness and muon anomalous magnetic moment

    10:10 AM-11:40 AM
    September 1, 2021
    We study a model for explaining the apparent deviation of the muon anomalous magnetic moment, (g-2), from the Standard Model expectation. There are no new scalars and hence no new hierarchy puzzles beyond those associated with the Standard model Higgs; the only new particles that are relevant for (g-2) are vector-like singlet and doublet leptons. Interestingly, this simple model provides a calculable example violating the Wilsonian notion of naturalness: despite the absence of any symmetries prohibiting its generation, the coefficient of the naively leading dimension-six operator for (g−2) vanishes at one-loop. While effective field theorists interpret this either as a surprising UV cancellation of power divergences, or as a delicate cancellation between matching UV and calculable IR corrections to (g−2) from parametrically separated scales, there is a simple explanation in the full theory: the loop integrand is a total derivative of a function vanishing in both the deep UV and IR. The leading contribution to (g−2) arises from dimension-eight operators, and thus the required masses of new fermions are lower than naively expected, with a sizable portion of parameter space already covered by direct searches at the LHC. All of the viable parameter can be probed by the LHC and planned future colliders.

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

  • 02
    September 2, 2021

    CMSA Quantum Matter in Mathematics and Physics Seminar: Exotic quantum matter: From lattice gauge theory to hyperbolic lattices

    10:30 AM-12:00 PM
    September 2, 2021

    This talk, in two parts, will discuss two (unrelated) instances of exotic quantum matter. In the first part, I will discuss quantum critical points describing possible transitions out of the Dirac spin liquid, towards either symmetry-breaking phases or topologically ordered spin liquids. I will also comment on the role of instanton zero modes for symmetry breaking in parton gauge theories. In the second part, I will propose an extension of Bloch band theory to hyperbolic lattices, such as those recently realized in circuit QED experiments, based on ideas from algebraic geometry and Riemann surface theory.

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

  • 08
    September 8, 2021

    The average size of 3-torsion in class groups of 2-extensions

    3:00 PM-4:00 PM
    September 8, 2021
    Science Center 507
    1 Oxford Street, Cambridge, MA 02138 USA

    The p-torsion in the class group of a number field K is conjectured to be small: of size at most |Disc K|^epsilon, and to have constant average size in families with a given Galois closure group (when p doesn’t divide the order of the group).  In general, the best upper bound we have is |Disc K|^{1/2+epsilon}, and previously the only two cases known with constant average were for 3-torsion in quadratic fields (Davenport and Heilbronn, 1971) and 2-torsion in non-Galois cubic fields (Bhargava, 2005).  We prove that the 3-torsion is constant on average for fields with Galois closure group any 2-group with a transposition, including, e.g. quartic D_4 fields.  We will discuss the main inputs into the proof with an eye towards giving an introduction to the tools in the area.  This is joint work with Robert Lemke Oliver and Jiuya Wang.

  • 08
    September 8, 2021

    Prime numbers and Julia sets

    4:30 PM-5:30 PM
    September 8, 2021
    Science Center 507
    1 Oxford Street, Cambridge, MA 02138 USA
    Interesting patterns of prime numbers can arise in recursively defined sequences (such as the Fibonacci sequence). For non-linear recursions, there are intriguing connections with complex dynamics and the Mandelbrot set. This is just one of the many ways that Number Theory and Chaotic Dynamical Systems come together. I’ll present a few examples and a glimpse into some of my own research in this direction.
  • 09
    September 9, 2021

    On the dynamical Bogomolov conjecture

    4:00 PM-6:00 PM
    September 9, 2021

    Motivated by the Manin-Mumford and the Bogomolov conjecture for abelian varieties, Zhang conjectured that an analogous statement holds in a more general dynamical setting. In this talk we discuss various Bogomolov-type problems in the dynamical setting.

    On Zoom. Go to http://people.math.harvard.edu/~demarco/AlgebraicDynamics/ for more information