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

    Speaker: Keisuke Harigaya – IAS – CERN

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

    Speaker: Melanie Matchett Wood – Harvard University

    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: Prime numbers and Julia sets

    OPEN NEIGHBORHOOD SEMINAR
    Prime numbers and Julia sets

    Speaker: Laura DeMarco – Harvard University

    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

    Speaker: Shiraz Minwalla – Tata Institute of Fundamental Research

    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

    Speaker: Krishna Shrinivas – Harvard University

    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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  • CMSA EVENT: CMSA Interdisciplinary Science Seminar: The number of n-queens configurations

    Speaker: Michael Simkin – CMSA

    9:00 AM-10:00 AM
    September 23, 2021
    The n-queens problem is to determine Q(n), the number of ways to place n mutually non-threatening queens on an n x n board. The problem has a storied history and was studied by such eminent mathematicians as Gauss and Polya. The problem has also found applications in fields such as algorithm design and circuit development.
    Despite much study, until recently very little was known regarding the asymptotics of Q(n). We apply modern methods from probabilistic combinatorics to reduce understanding Q(n) to the study of a particular infinite-dimensional convex optimization problem. The chief implication is that (in an appropriate sense) for a~1.94, Q(n) is approximately (ne^(-a))^n. Furthermore, our methods allow us to study the typical “shape” of n-queens configurations.
    Zoom ID: 950 2372 5230 (Password: cmsa)
  • CMSA EVENT: CMSA Quantum Matter in Mathematics & Physics Seminar: Applications of instantons, sphalerons and instanton-dyons in QCD

    Speaker: Edward Shuryak – Stony Brook University

    10:30 AM-12:00 PM
    September 23, 2021

    I start with a general map of gauge topology, including monopoles, instantons and instanton-dyons. Then comes reminder of the “topological landscape”, the minimal energy gauge field configurations, as a function of Chern-Simons number Ncs and r.m.s. size. It includes “valleys” at integer Ncs separated by mountain ridges. The meaning of instantons,
    instanton-antiinstanton “streamlines” or thimbles, and sphalerons are reminded, together with some proposal to produce sphalerons at LHC and RHIC.

    Applications of instanton ensembles, as a model of QCD vacuum, are mostly related to their fermionic zero modes and t’Hooft effective Lagrangian, which explains explicit and spontaneous breaking of chiral symmetries. Recent applications are related with hadronic wave
    functions, at rest and in the light front (LFWFs). Two application would be spin-dependent forces and  the so called “flavor asymmetry of antiquark sea” of the nucleons. At temperatures comparable to deconfinement transition, instantons get split into constituents called instanton-dyons. Studies of their ensemble explains both deconfinement and chiral transitions, in ordinary and deformed QCD.

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

  • CMSA EVENT: CMSA Active Matter Seminar: The many phases of a cell

    Speaker: Krishna Shrinivas – Harvard University

    1:00 PM-2:00 PM
    September 23, 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.
    *rescheduled from 9/16/21
  • ALGEBRAIC DYNAMICS SEMINAR: Quantitative Logarithmic Equidistribution and S-Integrality

    Speaker: Jit Wu Yap – Harvard University

    4:00 PM-6:00 PM
    September 23, 2021

    Given a rational map defined over a number field, the Galois orbits of points with canonical height tending to zero will equidistribute to a measure supported on the Julia set. If one is able to extend the space of test functions to include those with certain logarithmic poles, then it is possible to obtain finiteness results on S-integral points. In this talk, we will study quantitative versions of logarithmic equidistribution in some special situations and their implications.

    http://people.math.harvard.edu/~demarco/AlgebraicDynamics/

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  • CMSA EVENT: CMSA Colloquium: Langlands duality for 3 manifolds

    Speaker: David Jordan – University of Edinburgh

    9:30 AM-10:30 AM
    September 29, 2021

    Langlands duality began as a deep and still mysterious conjecture in number theory, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten.  However to this day the Hilbert space attached to 3-manifolds, and hence the precise form of Langlands duality for them, remains a mystery.

    In this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi , and I will explain a Langlands duality in this setting, which we have conjectured with Ben-Zvi, Gunningham and Safronov.

    Intriguingly, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question, beyond the scope of the talk.

    Zoom link: https://harvard.zoom.us/j/95767170359 (Password: cmsa)

  • CMSA EVENT: CMSA JOINT QUANTUM MATTER IN MATH & PHYSICS and STRONGLY CORRELATED QUANTUM MATERIALS & HIGH-TEMPERATURE SUPERCONDUCTORS SEMINAR: Oscillations in the thermal conductivity of a spin liquid*

    Speaker: Nai Phuan Ong – Princeton University

    11:30 AM-1:00 PM
    September 29, 2021

    The layered honeycomb magnet alpha-RuCl3 orders below 7 K in a zigzag phase in zero field. An in-plane magnetic field H||a suppresses the zigzag order at 7 Tesla, leaving a spin-disordered phase widely believed to be a quantum spin liquid (QSL) that extends to ~12 T. We have observed oscillations in the longitudinal thermal conductivity Kxx vs. H from 0.4 to 4 K. The oscillations are periodic in 1/H (with a break-in-slope at 7 T). The amplitude function is maximal in the QSL phase (7 –11.5 T). I will describe a benchmark for crystalline disorder, the reproducibility and intrinsic nature of the oscillations, and discuss implications for the QSL state. I will also show detailed data on the thermal Hall conductivity Kxy measured from 0.4 K to 10 K and comment on recent half-quantization results.

    *Czajka et al., Nature Physics 17, 915 (2021).

    Collaborators: Czajka, Gao, Hirschberger, Lampen Kelley, Banerjee, Yan, Mandrus and Nagler.

     


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

  • NUMBER THEORY SEMINAR: Density of arithmetic Hodge loci

    NUMBER THEORY SEMINAR
    Density of arithmetic Hodge loci

    Speaker: Salim Tayou – Harvard University

    3:00 PM-4:00 PM
    September 29, 2021
    1 Oxford Street, Cambridge, MA 02138 USA

    I will explain a conjecture on density of arithmetic Hodge loci which includes and generalizes several recent density results of these loci in arithmetic geometry. This conjecture has also analogues over functions fields that I will survey. As a particular instance, I will outline the proof of the following result: a K3 surface over a number field admits infinitely many specializations where its Picard rank jumps. This last result is joint work with Ananth Shankar, Arul Shankar and Yunqing Tang.

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  • CMSA EVENT: CMSA Active Matter Seminar: Cytoskeletal Energetics and Energy Metabolism

    Speaker: Daniel Needleman – Harvard University

    1:00 PM-2:00 PM
    September 30, 2021
    Life is a nonequilibrium phenomenon. Metabolism provides a continuous flux of energy that dictates the form and function of many subcellular structures. These subcellular structures are active materials, composed of molecules which use chemical energy to perform mechanical work and locally violate detailed balance. One of the most dramatic examples of such a self-organizing structure is the spindle, the cytoskeletal based assembly which segregates chromosomes during cell division. Despite its central role, very little is known about the nonequilibrium thermodynamics of active subcellular matter, such as the spindle. In this talk, I will describe ongoing work from my lab aimed at understanding the flows of energy which drive the nonequilibrium behaviors of the cytoskeleton in vitro and in vivo.
    *rescheduled from 9/16/21
  • COLLOQUIUMS: Geometric Set Theory

    Speaker: Paul Larson – Miami University

    4:30 PM-5:30 PM
    September 30, 2021
    1 Oxford Street, Cambridge, MA 02138

    The field of Geometric Set Theory studies structures on sets of countable objects (typically Polish spaces) by considering virtual objects, typically uncountable sets representing members of the space under consideration in some larger model of set theory. This approach can be used to study analytic equivalence relations on Polish spaces, where the virtual objects represent equivalence classes. The representatives of the virtual classes can be used for instance to prove non-reducibility results between such equivalence relations. Another set of applications involves separating forms of the Axiom of Choice, specifically forms asserting the existence of a set of reals with certain first order properties. Typical examples include Vitali sets, Hamel bases, discontinuous homomorphisms on the real line or countable colorings of various graphs on Euclidean space. We will give a brief tour of some of the landmarks in the area, and discuss some directions for further research.

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