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  • September 21, 2021
    3:00 pm
    Science Center 507

    HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR

    Speaker: Christopher Eur - Harvard University   Title: Tautological classes of matroids
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  • CMSA EVENT: 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

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  • NUMBER THEORY SEMINAR
    3:00 PM-4:00 PM
    September 8, 2021
    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.

  • OPEN NEIGHBORHOOD SEMINAR

    OPEN NEIGHBORHOOD SEMINAR
    Prime numbers and Julia sets

    4:30 PM-5:30 PM
    September 8, 2021
    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.
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  • CMSA EVENT: CMSA Quantum Matter in Mathematics & Physics Seminar: The Hilbert Space of large N Chern-Simons matter theories
    10:30 AM-12:00 PM
    September 16, 2021
    We demonstrate that all known formulae for the thermal partition function for large N Chern Simons matter theory admit a simple Hilbert Space interpretation. In each case this quantity equals the partition function of an associated ungauged large $N$ matter theory with a particular local Lagrangian with one additional element: the Fock Space of  this associated theory is projected down to the subspace of its WZW singlets. This projection, in particular,  implies the previously encountered `Bosonic Exclusion Principle’, namely that no single particle state can be occupied by more than $k_B$ particles ($k_B$ is the Chern Simons level). Unlike its Gauss Law counterpart, the WZW constraint does not trivialize in the large volume limit. However thermodynamics does simplify in this limit;  the final partition function reduces to  a product of partition functions associated with each single particle state. These individual single particle state partition functions are a one parameter generalizations of their free boson and free fermion counterparts, and reduce to the later at extreme values of the ‘t Hooft coupling. At generic values of the rank and the level the occupation statistics of each energy level is given by a $q$ deformation of the usual free formulae of Bose and Fermi statistics.

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

  • CMSA EVENT: CMSA Active Matter Seminar: The many phases of a cell
    1:00 PM-2:00 PM
    September 16, 2021
    I will begin by introducing an emerging paradigm of cellular organization – the dynamic compartmentalization of biochemical pathways and molecules by phase separation into distinct and multi-phase condensates. Motivated by this, I will discuss two largely orthogonal problems, united by the theme of phase separation in multi-component and chemically active fluid mixtures.
    1. I will propose a theoretical model based on Random-Matrix Theory, validated by phase-field simulations, to characterizes the rich emergent dynamics, compositions, and steady-state properties that underlie multi-phase coexistence in fluid mixtures with many randomly interacting components.
    2. Motivated by puzzles in gene-regulation and nuclear organization, I will propose a role for how liquid-like nuclear condensates can be organized and regulated by the active process of RNA synthesis (transcription) and RNA-protein coacervation. Here, I will describe theory and simulations based on a Landau formalism and recent experimental results from collaborators.
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