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May  May  1  MATHEMATICAL PICTURE LANGUAGE SEMINAR
MATHEMATICAL PICTURE LANGUAGE SEMINAR TBD 10:00 AM11:00 AM June 1, 2021  COLLOQUIUMS
3:00 PM4:00 PM June 1, 2021 Title: From Ramanujan to Rokhlin, via quantum groups Abstract: In this talk, intended for a broad audience, I will describe recent work on new qseries invariants of 3manifolds labeled by SpinC structures. While the original motivation for studying these invariants is rooted in topology, they exhibit a number of unexpected properties and connections to other areas of mathematics, e.g. turn out to be characters of logarithmic vertex algebras. Registration is required to receive the Zoom information. Please go here to register.
 2  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Ultra Unification: Quantum Fields Beyond the Standard Model
10:30 AM12:00 PM June 2, 2021 Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). Here I propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly cancellation and cobordism constraints (especially from the baryon minus lepton number B – L, the electroweak hypercharge Y, and the mixed gaugegravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension, whose low energy contains unitary Lorentz invariant topological quantum field theories (TQFTs): either 3+1d noninvertible TQFT (longrange entangled gapped phase), or 4+1d invertible or noninvertible TQFT (shortrange or longrange entangled gapped phase). Alternatively, there could also be righthanded neutrinos, or gapless unparticle conformal field theories, or their combinations to altogether cancel the anomaly. We propose that a new highenergy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects, etc., whose open ends carry deconfined fractionalized particle or anyonic string excitations). I will also fill in the dictionary between math, QFT, and condensed matter terminology, and elaborate on the global anomalies of Z2, Z4, Z16 classes useful for beyond SM. Work is based on arXiv:2012.15860, arXiv:2008.06499, arXiv:2006.16996, arXiv:1910.14668. Zoom: https://harvard.zoom.us/j/977347126
 3  CMSA EVENT: CMSA Interdisciplinary Science Seminar: Navigating Seas of Change – the Role and Significance of CrossDisciplinary Research
9:00 AM10:00 AM June 3, 2021 As atmospheric CO2 levels continue to rise and global and coastal ocean become warmer and more eutrophic as a result of human activities, we need better ways to detect and understand how marine ecosystems are responding to these changes. Until recently, most biological oceanographers relied on shipboard measurements that were limited in their coverage and inadequate to investigate changes at large spatial and temporal scales. With the advent of satellites, autonomous platforms and numerical methods, biological oceanographers are turning to empirical and semianalytical algorithms to scale limited shipboard measurements from local scales to regional, basin and global scales. While progress has been interdisciplinary research involving collaborations between biological, physical and methodical scientists could help us make rapid advances and mitigate impacts on the livelihoods of coastal communities which are at greatest risk. This presentation will cover a case study from the Arabian Sea in the Indian Ocean and describe the promise and potential of interdisciplinary research in advancing climate change and ecosystem research for societal benefit. Zoom: https://harvard.zoom.us/j/98248914765?pwd=Q01tRTVWTVBGT0lXek40VzdxdVVPQT09 (Password: 419419)  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Higher Dimensional Topological Order, Higher Category and A Classification in 3+1D
10:30 AM12:00 PM June 3, 2021 Topological orders are gapped quantum liquid states without any symmetry. Most of their properties can be captured by investigating topological defects and excitations of various dimensions. Topological defects in n dimensions naturally form a (weak) ncategory. In particular, anomalous topological order (boundary theory) is described by fusion ncategory and anomalyfree topological order (bulk) is described by nondegenerate braided fusion ncategory. Holographic principle works for topological orders: boundary always has a unique bulk. Another important property in 3+1D or higher is that pointlike excitations must have trivial statistics; they must carry representations of a certain group. Such a “gauge group” is hidden in every higher dimensional topological order. In 3+1D, condensing pointlike excitations leads to a canonical boundary which in turn determines the bulk topological order. By studying this boundary, a rather simple classification is obtained: 3+1D topological orders are classified by the above “gauge group” together with some cocycle twists. These ideas would also play an important role in dimensions higher than 3+1D and in the study of higher categories, topological quantum field theories and other related subjects. Zoom: https://harvard.zoom.us/j/977347126
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3:00 PM4:00 PM June 8, 2021 Title: The twodimensional Ising model revisited Abstract: I will describe joint work with Constantin Teleman, in which we cast topological eyes on a wellstudied system in condensed matter physics. In particular, we use the symmetry in a strong form and apply the technology of extended topological field theory. We obtain a proof of duality, construct a new dual theory for models based on a nonabelian group, and make dynamical predictions. The lecture will not assume any physics background. Registration is required to receive the Zoom information. Please go here to register.
 9  10  CMSA EVENT: CMSA Interdisciplinary Science Seminar: The deformation space of geodesic triangulations and Tutte’s embedding
9:00 AM10:00 AM June 10, 2021 In 1984, Bloch, Connelly, and Henderson proved that the space of geodesic triangulations of a convex polygon is contractible. It was found that Tutte’s embedding theorem could give a very simple proof to BlochConnellyHenderson’s theorem, and provides an elegant algorithm for image morphing on convex polygons. We recently generalize Tutte’s embedding theorem, and prove that the deformation space of geodesic triangulations of a closed Riemannian surface of negative curvature is contractible. This confirms a conjecture by Connelly, Henderson, Ho, Starbird in 1983, and also indicates a method for image morphing on closed surfaces. Zoom: https://harvard.zoom.us/j/98248914765?pwd=Q01tRTVWTVBGT0lXek40VzdxdVVPQT09 (Password: 419419)  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Minimal nondegenerate extensions and an anomaly indicator
10:30 AM12:00 PM June 10, 2021 Braided fusion categories arise as the Ginvariant (extended) observables in a 2+1D topological order, for some (generalized) symmetry group G. A minimal nondegenerate extension exists when the Gsymmetry can be gauged. I will explain what this has to do with the classification of 3+1D topological orders. I will also explain a resolution to a 20yearold question in mathematics, which required inventing an indicator for a specific particularly problematic anomaly, and a clever calculation of its value. Based on arXiv:2105.15167, joint with David Reutter. Zoom: https://harvard.zoom.us/j/977347126
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3:00 PM4:00 PM June 14, 2021 Title: Topics in computers and mathematics Abstract: Advances in computation and machine learning are changing the way we do pure mathematics and theoretical physics. Using examples from differential geometry, finite group theory and other fields, I will survey some directions which I believe will have major impact during the coming decade: machine learning, ML inspired numerical methods, computer assisted proofs and interactive theorem proving. Registration is required to receive the Zoom information. Please go here to register.
 15  MATHEMATICAL PICTURE LANGUAGE SEMINAR
MATHEMATICAL PICTURE LANGUAGE SEMINAR TBD 10:00 AM11:00 AM June 15, 2021  CMSA EVENT: CMSA Math Science Literature Lecture Series
11:00 AM12:30 PM June 15, 2021 TITLE: Nonlinear stability of Kerr black holes for small angular momentum ABSTRACT: According to a wellknown conjecture, initial data sets, for the Einstein vacuum equations, sufficiently close to a Kerr solution with parameters $a, m$, $a/m <1$, have maximal developments with complete future null infinity and with domain of outer communication (i.e complement of a future event horizon) which approaches (globally) a nearby Kerr solution. I will describe the main ideas in my recent joint work with Jeremie Szeftel concerning the resolution of the conjecture for small angular momentum, i.e. $, $a/m $ sufficiently small. The work, ArXiv:2104.11857v1, also depends on forthcoming work on solutions of nonlinear wave equations in realistic perturbations of Kerr, with Szeftel and Elena Giorgi, which I will also describe. Talk char: Lydia Bieri Please register here Visit the website here
 16  ANNOUNCEMENTS
10:00 AM1:15 PM June 16, 2021 In solidarity with Azat Miftakhov *Starting at 4pm Central European Summer Time (UTC+2)* It will be organized online by the Azat Miftakhov committee in solidarity with Azat Miftakhov, a graduate student from Moscow State University who has been arbitrarily detained by Russian state authorities for almost two years and a half. 4:00 pm Cédric Villani (Member of the French National Assembly) Opening speech 4:15 pm Maryna Viazovska (École Polytechnique Fédérale de Lausanne, Switzerland) tba 5:15 pm Alexander Bufetov (CNRS & Institut de Mathématiques de Marseille, France & Steklov, IITP RAS, Russia) Determinantal point processes: quasisymmetries, minimality and interpolation 6:15 pm Peter Scholze (Universität Bonn, Germany) Condensed Mathematics * Tokyo at 11pm, Moscow at 5pm, Bonn, Paris and Warsaw at 4pm, London at 3pm, New York at 10am, San Francisco at 7am The webinar will be broadcast live on several websites whose addresses will be announced a few days before. Further the information available at caseazatmiftakhov.org  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Uses of Wilson Operator Expansion in Gauge Theories
10:30 AM12:00 PM June 16, 2021 I discuss some, now quite old, applications of Wilson Operator Product Expansion in gauge theories which were developed by Valentin Zakharov, Mikhail Shifman and me. It includes a penguin mechanism of enhancement in weak nonleptonic decays, gluon condensate and QCD sum rules, Wilsonian action in supersymmetric gauge theories and exact beta functions. Zoom: https://harvard.zoom.us/j/977347126
 17  CMSA EVENT: CMSA Interdisciplinary Science Seminar: Molecular mechanisms of Taxane resistance in prostate cancer
9:00 AM10:00 AM June 17, 2021 Taxanes act by stabilizing microtubules (MTs) and prolong survival in men with prostate cancer (PCa), but biomarkers predictive of responses and clinically actionable mechanism(s) of resistance have yet to be identified. We recently reported that a decrease or absence of MT bundling, despite high levels of intratumoral taxanes, is a basis and a potential pharmacodynamic biomarker of taxane resistance. To determine the molecular basis for this impaired MT bundling, we treated docetaxel sensitive PCa models in vivo for multiple cycles until resistance, and found upregulation of FOXJ1 (a master transcription factor regulating tubulin associated proteins), as well as one of its downstream effector protein, TPPP3, in the resistant tumors. Moreover, mining of patient databases showed that amplification of the FOXJ1 gene is also associated with taxane exposure. Together these data implicate the FOXJ1TPPP3 regulatory network in taxane resistance. In parallel with these in vivo studies, we have carried in vitro drug screens for agents that enhance responses to docetaxel in 3D/organoid culture. A prominent agent that emerged is a histone methyltransferase inhibitor. Our overall goals are to identify clinically meaningful mechanisms of taxane resistance, to develop therapeutic combinations that enhance efficacy and/or target these resistance mechanisms, and to identify biomarkers indicative of specific mechanisms. Our hypotheses, which are based on our published and preliminary data, are that one major mechanism for taxane resistance is upregulation of the FOXJ1TPPP3 pathway, and that combination therapies can be developed that enhance taxane efficacy and delay or prevent the emergence of resistance. The specific aims are 1) Determine the effect of FOXJ1TPPP3 regulatory network on microtubule dynamics, stability and targetengagement by taxanes in vitro and in vivo and 2) Identify effective combination therapies to enhance docetaxel responses and overcome taxane resistance. Zoom: https://harvard.zoom.us/j/98248914765?pwd=Q01tRTVWTVBGT0lXek40VzdxdVVPQT09 (Password: 419419)  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: What can supersymmetry do that other field theories cannot
10:30 AM12:00 PM June 17, 2021
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20  21  22  MATHEMATICAL PICTURE LANGUAGE SEMINAR
10:00 AM11:00 AM June 22, 2021 The commutative graph complex, defined by contracting edges in graphs, was introduced by Kontsevich in 1993. Recently, ChanGalatiusPayne have shown that its cohomology can be identified with a piece of the cohomology of moduli spaces of curves, and Willwacher showed that graph cohomology in degree zero it is related to the GrothendieckTeichmuller Lie algebra. Nevertheless, the cohomology of the graph complex remains mysterious, and little is known explicitly. In this talk I will explain how to use invariant trace forms to construct differential forms on a moduli space of metric graphs. By integrating these forms, one can canonically assign integrals to graphs, which are very closely related to Feynman integrals in perturbative quantum field theory, but have the property that they always converge. A Stokes formula enables us to deduce some information about the cohomology of the graph complex, and leads to new predictions about its structure, and its relation to physics. Zoom: https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09
 23  24  CMSA EVENT: CMSA Interdisciplinary Science Seminar: 3D Smectic Liquid Crystals
9:00 AM10:00 AM June 24, 2021 Liquid crystals are an intermediate state of matter which flow like liquids but retain molecular ordering similar to that of crystals. Their physical properties make them ideal for a wide range of technological applications. The molecules in smectic liquid crystals form welldefined layers which slide across one another. In this talk we will discuss a model for smectics from the physics literature based on the minimization of a suitable energy and present recent results obtained jointly with Xiaodong Yan. No prior knowledge of liquid crystals or the relevant mathematics will be assumed.
Zoom: https://harvard.zoom.us/j/98248914765?pwd=Q01tRTVWTVBGT0lXek40VzdxdVVPQT09 (Password: 419419)
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