Calendar

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  • CMSA EVENT: Computational Biology Symposium
    10:00 AM-3:50 PM
    May 3, 2021

    On Monday, May 3rd the Harvard CMSA will be hosting a Computational Biology Symposium virtually on Zoom. Please visit the event webpage for the schedule and more information. The event poster is attached.

    Registration is free but required. Register here. Details on how to join the webinar will be sent to registered participants before the event.

    The speakers will be:
    Uri Alon, Weizmann Institute
    Elana Fertig, Johns Hopkins
    Martin Hemberg, Brigham and Women’s Hospital
    Peter Kharchenko, Harvard University
    Smita Krishnaswamy, Yale University
    John Marioni, EMBL-EBI
    Eran Segal, Weizmann Institute
    Meromit Singer, Harvard Medical School

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  • MATHEMATICAL PICTURE LANGUAGE SEMINAR
    10:00 AM-11:00 AM
    May 4, 2021

    Lieb-Thirring inequalities are a mathematical expression of the uncertainty and exclusion principles in quantum mechanics. They were introduced by Lieb and Thirring in 1975 in their proof of stability of matter and have since played an important role in several areas of analysis and mathematical physics. We provide a gentle introduction to classical aspects of this subject and we also present some newer developments, concerning extensions of several inequalities in harmonic analysis to the setting of families of orthonormal functions.

    Zoom: https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09

  • CMSA EVENT: CMSA Computer Science for Mathematicians: Rank-Based Independence Testing in Near Linear Time
    11:30 AM-12:30 PM
    May 4, 2021

    In 1948 Hoeffding proposed a nonparametric test that detects dependence between two continuous random variables (X,Y), based on the ranking of n paired samples (Xi,Yi). The computation of this commonly-used test statistic requires O(n log n) time. Hoeffding’s test is consistent against any dependent probability density f(x,y), but can be fooled by other bivariate distributions with continuous margins. Variants of this test with stronger consistency have been considered in works by Blum, Kiefer, and Rosenblatt, Yanagimoto, and Bergsma and Dassios, and others. The so far best known algorithms to compute them have required quadratic time.

    We present an algorithm that computes these improved tests in time O(n log n). It is based on a new combinatorial approach for counting pattern occurrences in a given permutation, which we call corner tree formulas, and will be explained in the talk.

    Joint work with Calvin Leng.

    Zoom: https://harvard.zoom.us/j/98231541450

  • HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR

    HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR
    Refined unramified cohomology

    3:00 PM-4:00 PM
    May 4, 2021

    We introduce refined unramified cohomology and prove some
    general comparison theorems to cycle groups. Our approach has several applications. For instance, it allows to construct the first example of a smooth complex projective variety whose Griffiths group has infinite torsion subgroup.

    Zoom: https://harvard.zoom.us/j/91794282895?pwd=VFZxRWdDQ0VNT0hsVTllR0JCQytoZz09

  • DIFFERENTIAL GEOMETRY SEMINAR
    9:00 PM-10:00 PM
    May 4, 2021

    We are interested in smoothing of a degenerate Calabi-Yau variety or a pair (degenerate CY, sheaf). I will explain an algebraic framework for solving such smoothability problems. The idea is to glue local dg Lie algebras (or dg Batalin-Vilkovisky algebras), coming from suitable local models, to get a global object. The key observation is that while this object is only an almost dg Lie algebra (or pre-dg Lie algebra), it is sufficient to prove unobstructedness of the associated Maurer-Cartan equation (a kind of Bogomolov-Tian-Todorov theorem) under suitable assumptions, so the former can be regarded as a singular version of the Kodaira-Spencer DGLA. Our framework applies to degenerate CY varieties previously studied by Kawamata-Namikawa and Gross-Siebert, as well as a more general class of varieties called toroidal crossing spaces (by the recent work of Felten-Filip-Ruddat). This talk is based on joint works with Conan Leung, Ziming Ma and Y.-H. Suen.

    Zoom: https://harvard.zoom.us/j/96709211410?pwd=SHJyUUc4NzU5Y1d0N2FKVzIwcmEzdz09

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  • CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Anomalies and Supersymmetry
    8:00 PM-9:30 PM
    May 5, 2021

    Diffeomorphisms and supersymmetry transformations act on all local quantum field theory operators, including on the Noether currents associated with other continuous symmetries, such as flavor or R-symmetry. I will discuss how quantum anomalies in these symmetries produce the local Bardeen-Zumino terms that ensure that the corresponding consistent Noether currents in the diffeomorphism and supersymmetry Ward identities are replaced by their covariant form. An important difference between diffeomorphisms and supersymmetry is that, while the effective action remains invariant under diffeomorphisms in the absence of a gravitational anomaly, the local terms in the supersymmetry Ward identity generated by quantum anomalies in other symmetries generally result in the non-invariance of the effective action under supersymmetry. In certain cases, however, supersymmetry invariance may be restored by suitably enlarging the multiplet that contains the anomalous Noether current. The structure of all local terms in the Ward identities due to quantum anomalies can be determined by solving the Wess-Zumino consistency conditions, which can be reformulated as a BRST cohomology problem. I will present a generalization of the standard BRST algebra for gauge theories and the associated anomaly descent procedure that is necessary for accommodating diffeomorphisms and supersymmetry transformations. I will also discuss how, in some cases, the solution of the Wess-Zumino consistency conditions in the presence of supersymmetry can be efficiently determined from a supersymmetric Chern-Simons action in one dimension higher through anomaly inflow. I will conclude with a brief discussion of the implications of the local terms in the supersymmetry Ward identity for the dependence of supersymmetric partition functions on backgrounds that admit Killing spinors.

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

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  • MATHEMATICAL PICTURE LANGUAGE SEMINAR

    MATHEMATICAL PICTURE LANGUAGE SEMINAR
    The Energy-Based Learning Model

    10:00 AM-11:00 AM
    May 18, 2021

    One of the hottest sub-topics of machine learning in recent times has been Self-Supervised Learning (SSL). In SSL, a learning machine captures the dependencies between input variables, some of which may be observed, denoted X, and others not always observed, denoted Y. SSL pre-training has revolutionized natural language processing and is making very fast progress in speech and image recognition. SSL may enable machines to learn predictive models of the world through observation, and to learn representations of the perceptual world, thereby reducing the number of labeled samples or rewarded trials to learn a downstream task. In the Energy-Based Model framework (EBM), both X and Y are inputs, and the model outputs a scalar energy that measures the degree of incompatibility between X and Y. EBMs are implicit functions that can represent complex and multimodal dependencies between X and Y. EBM architectures belong to two main families: joint embedding architectures and latent-variable generative architectures. There are two main families of methods to train EBMs: contrastive methods, and volume regularization methods. Much of the underlying mathematics of EBM is borrowed from statistical physics, including concepts of partition function, free energy, and variational approximations thereof.

    Zoom: https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09

  • CMSA EVENT: CMSA Computer Science for Mathematicians: Optimization Methods in AI and Machine Learning: Submodularity and Beyond
    11:30 AM-12:30 PM
    May 18, 2021

    Several optimization problems in AI Machine Learning can be solved with the maximization of functions that exhibit natural diminishing returns. Examples include feature selection for Generalized Linear Models, Data Summarization, and Bayesian experimental design. By leveraging diminishing returns, it is possible to design efficient approximation algorithms for these problems.One of the simplest notions of diminishing returns is submodularity. Submodular functions are particularly interesting, because they admit simple, yet non-trivial, polynomial-time approximation algorithms. In recent years, several definitions have been proposed, to generalize the notion of submodularity. A study of these generalized functions lead to the design of efficient approximation algorithms for non-convex problems.In this talk, I will discuss the notion of submodularity, and illustrate relevant results on this topic, including new interesting combinatorial algorithms. I will also talk about generalizations of this notion to continuous domains, and how they translate into first- and second-order conditions. I will discuss how these notions pertain interesting problems in AI Machine Learning.

    Zoom: https://harvard.zoom.us/j/98231541450

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  • CMSA EVENT: CMSA Math Science Literature Lecture Series
    9:00 AM-10:30 AM
    May 25, 2021

    TITLE: K-theory and characteristic classes in topology and complex geometry (a tribute to Atiyah and Hirzebruch)

    ABSTRACT: We will discuss the K-theory of complex vector bundles on
    topological spaces and of holomorphic vector bundles on complex
    manifolds. A central question is the relationship between K-theory
    and cohomology. This is done in topology by constructing
    characteristic classes, but other constructions appear in the

    holomorphic or algebraic context. We will discuss the Hirzebruch-
    Riemann-Roch formula, the Atiyah-Hirzebruch spectral sequence, the

    role of complex cobordism, and other tools developed later on, like
    the Bloch-Ogus spectral sequence.

    Talk chair: Baohua Fu

    Written articles will accompany each lecture in this series and be available as part of the publication “History and Literature of Mathematical Science.”

    For more information, please visit the event page.

    Register here to attend.
  • MATHEMATICAL PICTURE LANGUAGE SEMINAR

    MATHEMATICAL PICTURE LANGUAGE SEMINAR
    Rigorous results about Relative entropy in QFT

    10:00 AM-11:00 AM
    May 25, 2021

    We will present some rigorous results about Relative entropy in QFT, motivated in part by recent physicists’ work which however depends on heuristic arguments such as introducing cut off and using path integrals. In the particular case of CFT, we will discuss interesting relations between relative entropy, central charge and global dimension of conformal net

    Zoom: https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09

  • COLLOQUIUMS

    COLLOQUIUMS
    Special Colloquium

    3:00 PM-4:00 PM
    May 25, 2021

    Title: New Structures in Gravitational Waves

    Abstract: Mathematical General Relativity (GR) explores the structures and resulting dynamics of gravitational systems. These are described by the Einstein equations, which can be written as a system of nonlinear, hyperbolic partial differential equations. Recent years have seen fruitful interactions between physical questions and geometric analysis, sparking new breakthroughs, in particular related to gravitational radiation. Gravitational waves transport information from faraway regions of the Universe. They were observed for the first time by Advanced LIGO in 2015. So far, most studies in GR have been devoted to sources like binary black hole mergers or generally to sources that are stationary outside of a compact set. However, when extended neutrino halos are present, the situation changes.  Mathematically, we describe these systems by asymptotically-flat manifolds solving the Einstein equations. In this talk, I will present new results on gravitational radiation for sources that are not stationary outside of a compact set, but whose gravitational fields fall off more slowly towards infinity. A panorama of new gravitational effects opens up when delving deeper into these more general spacetimes. In particular, whereas the former sources produce memory effects (permanent change of the spacetime) that are finite and of purely electric parity, the latter in addition generate memory of magnetic type, and both types grow. These new effects emerge naturally from the Einstein equations.

    Registration is required to receive the Zoom information.

    Please go here to register.

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