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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220407T093000
DTEND;TZID=America/New_York:20220407T110000
DTSTAMP:20260507T080326
CREATED:20240214T102601Z
LAST-MODIFIED:20240301T063834Z
UID:10002669-1649323800-1649329200@cmsa.fas.harvard.edu
SUMMARY:Lattice Gauge Theory View of Toric Codes\, X-cube\, and More
DESCRIPTION:Youtube Video \n  \nAbstract: Exactly solvable spin models such as toric codes and X-cube model have heightened our understanding of spin liquids and topological matter in two and three dimensions. Their exact solvability\, it turns out\, is rooted in the existence of commuting generators in their parent lattice gauge theory (LGT). We can understand the toric codes as Higgsed descendants of the rank-1 U(1) LGT in two and three dimensions\, and the X-cube model as that of rank-2 U(1) LGT in three dimensions. Furthermore\, the transformation properties of the gauge fields in the respective LGT is responsible for\, and nearly determines the structure of the effective field theory (EFT) of the accompanying matter fields. We show how to construct the EFT of e and m particles in the toric codes and of fractons and lineons in the X-cube model by following such an idea. Recently we proposed some stabilizer Hamiltonians termed rank-2 toric code (R2TC) and F3 model (3D). We will explain what they are\, and construct their EFTs using the gauge principle as guidance. The resulting field theory of the matter fields are usually highly interacting and exhibit unusual conservation laws. Especially for the R2TC\, we demonstrate the existence of what we call the “dipolar braiding statistics” and outline the accompanying field theory which differs from the usual BF field theory of anyon braiding. \nReferences:\n[1] “Model for fractions\, fluxons\, and free verte excitations”\, JT Kim\, JH Han\, Phys. Rev. B 104\, 115128 (2021)\n[1] “Rank-2 toric code in two dimensions”\, YT Oh\, JT Kim\, EG Moon\, JH Han\, Phys. Rev. B 105\, 045128 (2022)\n[2] “Effective field theory for the exactly solvable stabilizer spin models”\, JT Kim\, YT Oh\, JH Han\, in preparation.\n[3] “Effective field theory of dipolar braiding statistics in two dimensions”\, YT Oh\, JT Kim\, JH Han\, in preparation.
URL:https://cmsa.fas.harvard.edu/event/4-7-2022-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-04.07.2022-1583x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220407T130000
DTEND;TZID=America/New_York:20220407T142600
DTSTAMP:20260507T080326
CREATED:20230824T173606Z
LAST-MODIFIED:20240304T082508Z
UID:10001310-1649336400-1649341560@cmsa.fas.harvard.edu
SUMMARY:Theories of branching morphogenesis
DESCRIPTION:Abstract:  The morphogenesis of branched tissues has been a subject of long-standing debate. Although much is known about the molecular pathways that control cell fate decisions\, it remains unclear how macroscopic features of branched organs\, including their size\, network topology and spatial pattern are encoded. Based on large-scale reconstructions of the mouse mammary gland and kidney\, we begin by showing that statistical features of the developing branched epithelium can be explained quantitatively by a local self-organizing principle based on a branching and annihilating random walk (BARW). In this model\, renewing tip-localized progenitors drive a serial process of ductal elongation and stochastic tip bifurcation that terminates when active tips encounter maturing ducts. Then\, based on reconstructions of the developing mouse salivary gland\, we propose a generalisation of BARW model in which tips arrested through steric interaction with proximate ducts reactivate their branching programme as constraints become alleviated through the expansion of the underlying mesenchyme. This inflationary branching-arresting random walk model offers a more general paradigm for branching morphogenesis when the ductal epithelium grows cooperatively with the tissue into which it expands.
URL:https://cmsa.fas.harvard.edu/event/theories-of-branching-morphogenesis/
CATEGORIES:Active Matter Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Active-Matter-Seminar-04.07.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220407T152200
DTEND;TZID=America/New_York:20220407T172200
DTSTAMP:20260507T080326
CREATED:20240214T113556Z
LAST-MODIFIED:20240301T103440Z
UID:10002702-1649344920-1649352120@cmsa.fas.harvard.edu
SUMMARY:The space of vector bundles on spheres: algebra\, geometry\, topology
DESCRIPTION:Abstract: Bott periodicity relates vector bundles on a topological space X to vector bundles on X “times a sphere”.   I’m not a topologist\, so I will try to explain an algebraic or geometric incarnation\, in terms of vector bundles on the Riemann sphere.   I will attempt to make the talk introductory\, and (for the most part) accessible to those in all fields\, at the expense of speaking informally and not getting far.   This relates to recent work of Hannah Larson\, as well as joint work with (separately) Larson and Jim Bryan.
URL:https://cmsa.fas.harvard.edu/event/4-7-2022-interdisciplinary-science-seminar/
CATEGORIES:Interdisciplinary Science Seminar
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-Interdisciplinary-Science-Seminar-04.07.2022-1583x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220408T084500
DTEND;TZID=America/New_York:20220408T101500
DTSTAMP:20260507T080326
CREATED:20240214T084325Z
LAST-MODIFIED:20240301T105121Z
UID:10002595-1649407500-1649412900@cmsa.fas.harvard.edu
SUMMARY:Synthetic Regression Discontinuity: Estimating Treatment Effects using Machine Learning
DESCRIPTION:Speaker: Jörn Boehnke \nTitle: Synthetic Regression Discontinuity: Estimating Treatment Effects using Machine Learning \nAbstract:  In the standard regression discontinuity setting\, treatment assignment is based on whether a unit’s observable score (running variable) crosses a known threshold.  We propose a two-stage method to estimate the treatment effect when the score is unobservable to the econometrician while the treatment status is known for all units.  In the first stage\, we use a statistical model to predict a unit’s treatment status based on a continuous synthetic score.  In the second stage\, we apply a regression discontinuity design using the predicted synthetic score as the running variable to estimate the treatment effect on an outcome of interest.  We establish conditions under which the method identifies the local treatment effect for a unit at the threshold of the unobservable score\, the same parameter that a standard regression discontinuity design with known score would identify. We also examine the properties of the estimator using simulations\, and propose the use machine learning algorithms to achieve high prediction accuracy.  Finally\, we apply the method to measure the effect of an investment grade rating on corporate bond prices by any of the three largest credit ratings agencies.  We find an average 1% increase in the prices of corporate bonds that received an investment grade as opposed to a non-investment grade rating.
URL:https://cmsa.fas.harvard.edu/event/4-8-2022-member-seminar/
LOCATION:Virtual
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220411T100000
DTEND;TZID=America/New_York:20220411T110000
DTSTAMP:20260507T080326
CREATED:20230730T181035Z
LAST-MODIFIED:20240301T072853Z
UID:10001148-1649671200-1649674800@cmsa.fas.harvard.edu
SUMMARY:Type IIB flux compactifications with $h^{1\,1}=0$
DESCRIPTION:Abstract: We revisit type IIB flux compactification that are mirror dual to type IIA on rigid Calabi-Yau manifolds. We find a variety of interesting new solutions\, like fully stabilized Minkowski vacua and infinite families of AdS$_4$ solutions with arbitrarily large numbers of spacetime filling D3 branes. We discuss how these solutions fit into the web of swampland conjectures.
URL:https://cmsa.fas.harvard.edu/event/4-11-2021-swampland-seminar/
LOCATION:Virtual
CATEGORIES:Swampland Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220412T093000
DTEND;TZID=America/New_York:20220412T103000
DTSTAMP:20260507T080326
CREATED:20240214T065956Z
LAST-MODIFIED:20240304T060444Z
UID:10002553-1649755800-1649759400@cmsa.fas.harvard.edu
SUMMARY:BCFW recursion relations and non-planar positive geometry
DESCRIPTION:Abstract: There is a close connection between the scattering amplitudes in planar N=4 SYM theory and the cells in the positive Grassmannian. In the context of BCFW recursion relations the tree-level S-matrix is represented as a sum of planar on-shell diagrams (aka plabic graphs) and associated with logarithmic forms on the Grassmannian cells of certain dimensionality. In this talk\, we explore non-adjacent BCFW shifts which naturally lead to non-planar on-shell diagrams and new interesting subspaces inside the real Grassmannian. \n**This talk will be hybrid. Talk will be held at CMSA (20 Garden St) Room G10. \nAll non-Harvard affiliated visitors to the CMSA building will need to complete this covid form prior to arrival. \nLINK TO FORM
URL:https://cmsa.fas.harvard.edu/event/4-12-2022-combinatorics-physics-and-probability-seminar/
CATEGORIES:Combinatorics Physics and Probability
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-Combinatorics-Physics-and-Probability-Seminar-04.12.22-1583x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220412T115800
DTEND;TZID=America/New_York:20220412T125800
DTSTAMP:20260507T080326
CREATED:20230825T080118Z
LAST-MODIFIED:20240304T061648Z
UID:10001294-1649764680-1649768280@cmsa.fas.harvard.edu
SUMMARY:Applications of Higher Determinant Map
DESCRIPTION:Abstract: In this talk I will explain the construction of a determinant map for Tate objects and two applications: (i) to construct central extensions of iterated loop groups and (ii) to produce a determinant theory on certain ind-schemes. For that I will introduce some aspects of the theory of Tate objects in a couple of contexts.
URL:https://cmsa.fas.harvard.edu/event/applications-of-higher-determinant-map/
LOCATION:Virtual
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220413T093000
DTEND;TZID=America/New_York:20220413T103000
DTSTAMP:20260507T080326
CREATED:20240214T035353Z
LAST-MODIFIED:20240304T073600Z
UID:10002516-1649842200-1649845800@cmsa.fas.harvard.edu
SUMMARY:Quantisation in monoidal categories and quantum operads
DESCRIPTION:Abstract: The standard definition of symmetries of a structure given on a set S (in the sense of Bourbaki) is the group of bijective maps S to S\, compatible with this structure. But in fact\, symmetries of various structures related to storing and transmitting information (such as information spaces) are naturally embodied in various classes of loops such as Moufang loops\, – nonassociative analogs of groups. The idea of symmetry as a group is closely related to classical physics\, in a very definite sense\, going back at least to Archimedes. When quantum physics started to replace classical\, it turned out that classical symmetries must also be replaced by their quantum versions\, e.g. quantum groups. \nIn this talk we explain how to define and study quantum versions of symmetries\, relevant to information theory and other contexts.
URL:https://cmsa.fas.harvard.edu/event/quantisation-in-monoidal-categories-and-quantum-operads/
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-04.13.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220413T203000
DTEND;TZID=America/New_York:20220413T220000
DTSTAMP:20260507T080326
CREATED:20240214T102340Z
LAST-MODIFIED:20240301T063645Z
UID:10002668-1649881800-1649887200@cmsa.fas.harvard.edu
SUMMARY:Why is the mission impossible? Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
DESCRIPTION:Youtube Video \nAbstract: It has been known that the four-dimensional abelian chiral gauge theories of an anomaly-free set of Wely fermions can be formulated on the lattice preserving the exact gauge invariance and the required locality property in the framework of the Ginsparg- Wilson relation. This holds true in two dimensions. However\, in the related formulation including the mirror Ginsparg-Wilson fermions\, it has been argued that the mirror fermions do not decouple: in the 3450 model with Dirac- and Majorana-Yukawa couplings to XY-spin field\, the two- point vertex function of the (external) gauge field in the mirror sector shows a singular non-local behavior in the so-called ParaMagnetic Strong-coupling(PMS) phase. \nWe re-examine why the attempt seems a “Mission: Impossible” in the 3450 model. We point out that the effective operators to break the fermion number symmetries (’t Hooft operators plus others) in the mirror sector do not have sufficiently strong couplings even in the limit of large Majorana-Yukawa couplings. We also observe that the type of Majorana-Yukawa term considered there is singular in the large limit due to the nature of the chiral projection of the Ginsparg-Wilson fermions\, but a slight modification without such singularity is allowed by virtue of the very nature. \nWe then consider a simpler four-flavor axial gauge model\, the 14(-1)4 model\, in which the U(1)A gauge and Spin(6)( SU(4)) global symmetries prohibit the bilinear terms\, but allow the quartic terms to break all the other continuous mirror-fermion symmetries. This model in the weak gauge-coupling limit is related to the eight-flavor Majorana Chain with a reduced SO(6)xSO(2) symmetry in Euclidean path-integral formulation. We formulate the model so that it is well-behaved and simplified in the strong-coupling limit of the quartic operators. Through Monte-Carlo simulations in the weak gauge-coupling limit\, we show a numerical evidence that the two-point vertex function of the gauge field in the mirror sector shows a regular local behavior. \nFinally\, by gauging a U(1) subgroup of the U(1)A× Spin(6)(SU(4)) of the previous model\, we formulate the 21(−1)3 chiral gauge model and argue that the induced effective action in the mirror sector satisfies the required locality property. This gives us “A New Hope” for the mission to be accomplished.
URL:https://cmsa.fas.harvard.edu/event/4-13-2022-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-Seminar-04.13.22-1583x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220414T090000
DTEND;TZID=America/New_York:20220414T100000
DTSTAMP:20260507T080326
CREATED:20240214T113429Z
LAST-MODIFIED:20240301T103314Z
UID:10002701-1649926800-1649930400@cmsa.fas.harvard.edu
SUMMARY:SIMPLEs: a single-cell RNA sequencing imputation strategy preserving gene modules and cell clusters variation
DESCRIPTION:Abstract: A main challenge in analyzing single-cell RNA sequencing (scRNA-seq) data is to reduce technical variations yet retain cell heterogeneity. Due to low mRNAs content per cell and molecule losses during the experiment (called ‘dropout’)\, the gene expression matrix has a substantial amount of zero read counts. Existing imputation methods treat either each cell or each gene as independently and identically distributed\, which oversimplifies the gene correlation and cell type structure. We propose a statistical model-based approach\, called SIMPLEs (SIngle-cell RNA-seq iMPutation and celL clustErings)\, which iteratively identifies correlated gene modules and cell clusters and imputes dropouts customized for individual gene module and cell type. Simultaneously\, it quantifies the uncertainty of imputation and cell clustering via multiple imputations. In simulations\, SIMPLEs performed significantly better than prevailing scRNA-seq imputation methods according to various metrics. By applying SIMPLEs to several real datasets\, we discovered gene modules that can further classify subtypes of cells. Our imputations successfully recovered the expression trends of marker genes in stem cell differentiation and can discover putative pathways regulating biological processes.
URL:https://cmsa.fas.harvard.edu/event/4-14-2022-interdisciplinary-science-seminar/
CATEGORIES:Interdisciplinary Science Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Interdisciplinary-Science-Seminar-04.14.22-1583x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220414T093000
DTEND;TZID=America/New_York:20220414T103000
DTSTAMP:20260507T080326
CREATED:20240214T083016Z
LAST-MODIFIED:20240301T112943Z
UID:10002589-1649928600-1649932200@cmsa.fas.harvard.edu
SUMMARY:Global existence and stability of de Sitter-like solutions to the Einstein-Yang-Mills equations in spacetime dimensions n≥4
DESCRIPTION:Abstract: In this talk\, we briefly introduce our recent work on establishing the global existence and stability to the future of non-linear perturbation of de Sitter-like solutions to the Einstein-Yang-Mills system in n≥4 spacetime dimension. This generalizes Friedrich’s (1991) Einstein-Yang-Mills stability results in dimension n=4 to all higher dimensions. This is a joint work with Todd A. Oliynyk and Jinhua Wang.
URL:https://cmsa.fas.harvard.edu/event/4-14-2022-general-relativity-seminar/
LOCATION:Virtual
CATEGORIES:General Relativity Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220414T093000
DTEND;TZID=America/New_York:20220414T110000
DTSTAMP:20260507T080326
CREATED:20240214T102053Z
LAST-MODIFIED:20240813T162915Z
UID:10002666-1649928600-1649934000@cmsa.fas.harvard.edu
SUMMARY:Cancellation of the vacuum energy and Weyl anomaly in the standard model\, and a two-sheeted\, CPT-symmetric universe
DESCRIPTION:Youtube video \n  \n\n\nAbstract: I will explain a mechanism to cancel the vacuum energy and both terms in the Weyl anomaly in the standard model of particle physics\, using conformally-coupled dimension-zero scalar fields.  Remarkably\, given the standard model gauge group SU(3)xSU(2)xU(1)\, the cancellation requires precisely 48 Weyl spinors — i.e. three generations of standard model fermions\, including right-handed neutrinos.  Moreover\, the scalars possess a scale-invariant power spectrum\, suggesting a new explanation for the observed primordial density perturbations in cosmology (without the need for inflation). \nAs context\, I will also introduce a related cosmological picture in which this cancellation mechanism plays an essential role.  Our universe seems to be dominated by radiation at early times\, and positive vacuum energy at late times.  Taking the symmetry and analyticity properties of such a universe seriously suggests a picture in which spacetime has two sheets\, related by a symmetry that\, in turn\, selects a preferred (CPT-symmetric) vacuum state for the quantum fields that live on the spacetime.  This line of thought suggests new explanations for a number of observed properties of the universe\, including: its homogeneity\, isotropy and flatness; the arrow of time; several properties of the primordial perturbations; and the nature of dark matter (which\, in this picture\, is a right-handed neutrino\, radiated from the early universe like Hawking radiation from a black hole).  It also makes a number of testable predictions. \n(Based on recent\, and ongoing\, work with Neil Turok: arXiv:1803.08928\, arXiv:2109.06204\, arXiv:2110.06258\, arXiv:2201.07279.)
URL:https://cmsa.fas.harvard.edu/event/4-14-2022-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-Seminar-04.14.22-1583x2048-1-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220415T090000
DTEND;TZID=America/New_York:20220415T130000
DTSTAMP:20260507T080326
CREATED:20230705T083343Z
LAST-MODIFIED:20240229T102446Z
UID:10000088-1650013200-1650027600@cmsa.fas.harvard.edu
SUMMARY:Workshop on Machine Learning and Mathematical Conjecture
DESCRIPTION:On April 15\, 2022\, the CMSA will hold a one-day workshop\, Machine Learning and Mathematical Conjecture\, related to the New Technologies in Mathematics Seminar Series. \nLocation: Room G10\, 20 Garden Street\, Cambridge\, MA 02138. \nOrganizers: Michael R. Douglas (CMSA/Stony Brook/IAIFI) and Peter Chin (CMSA/BU). \nMachine learning has driven many exciting recent scientific advances. It has enabled progress on long-standing challenges such as protein folding\, and it has helped mathematicians and mathematical physicists create new conjectures and theorems in knot theory\, algebraic geometry\, and representation theory. \nAt this workshop\, we will bring together mathematicians\, theoretical physicists\, and machine learning researchers to review the state of the art in machine learning\, discuss how ML results can be used to inspire\, test and refine precise conjectures\, and identify mathematical questions which may be suitable for this approach. \nSpeakers: \n\nJames Halverson\, Northeastern University Dept. of Physics and IAIFI\nFabian Ruehle\, Northeastern University Dept. of Physics and Mathematics and IAIFI\nAndrew Sutherland\, MIT Department of Mathematics\n\n  \n \n  \n  \n \n 
URL:https://cmsa.fas.harvard.edu/event/workshop-on-machine-learning-and-mathematical-conjecture/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Workshop
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Machine-Learning.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220418T093000
DTEND;TZID=America/New_York:20220418T110000
DTSTAMP:20260507T080326
CREATED:20230706T180022Z
LAST-MODIFIED:20250328T200252Z
UID:10000094-1650274200-1650279600@cmsa.fas.harvard.edu
SUMMARY:CMSA/Tsinghua Math-Science Literature Lecture: Three Introductory Lectures on Game Theory for Mathematicians: Game Theory Basics and Classical Existence Theorems
DESCRIPTION:Eric Maskin (Harvard University) Three Introductory Lectures on Game Theory for Mathematicians \nApril 18\, 2022 | 9:30 – 11:00 am ET \nTitle: Game Theory Basics and Classical Existence Theorems \nAbstract: Games in extensive and normal form. Equilibrium existence theorems by Nash\, von Neumann\, and Zermelo \nTalk chairs: Scott Kominers\, Sergiy Verstyuk \nSLIDES | VIDEO \n 
URL:https://cmsa.fas.harvard.edu/event/maskin_gametheory2022_1/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Mathlit_MASKIN-1583x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220418T130000
DTEND;TZID=America/New_York:20220418T140000
DTSTAMP:20260507T080326
CREATED:20230730T181614Z
LAST-MODIFIED:20240301T072639Z
UID:10001149-1650286800-1650290400@cmsa.fas.harvard.edu
SUMMARY:4/18/2022 Swampland Seminar
DESCRIPTION:Open mic Swampland Discussion \nTopic: Cobordism
URL:https://cmsa.fas.harvard.edu/event/4-18-2022-swampland-seminar/
LOCATION:Virtual
CATEGORIES:Swampland Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220419T093000
DTEND;TZID=America/New_York:20220419T103000
DTSTAMP:20260507T080326
CREATED:20230825T080357Z
LAST-MODIFIED:20240304T061057Z
UID:10001295-1650360600-1650364200@cmsa.fas.harvard.edu
SUMMARY:Equivariant Verlinde algebra and quantum K-theory of the moduli space of vortices
DESCRIPTION:Abstract:  In studying complex Chern-Simons theory on a Seifert manifold\, Gukov-Pei proposed an equivariant Verlinde formula\, a one-parameter deformation of the celebrated Verlinde formula. It computes\, among many things\, the graded dimension of the space of holomorphic sections of (powers of) a natural determinant line bundle over the Hitchin moduli space. Gukov-Pei conjectured that the equivariant Verlinde numbers are equal to the equivariant quantum K-invariants of a non-compact (Kahler) quotient space studied by Hanany-Tong. \nIn this talk\, I will explain the setup of this conjecture and its proof via wall-crossing of moduli spaces of (parabolic) Bradlow-Higgs triples. It is based on work in progress with Wei Gu and Du Pei.
URL:https://cmsa.fas.harvard.edu/event/equivariant-verlinde-algebra-and-quantum-k-theory-of-the-moduli-space-of-vortices/
LOCATION:Virtual
CATEGORIES:Algebraic Geometry in String Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Algebraic-Geometry-in-String-Theory-04.19.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220419T093000
DTEND;TZID=America/New_York:20220419T103000
DTSTAMP:20260507T080326
CREATED:20240214T070331Z
LAST-MODIFIED:20240304T084706Z
UID:10002554-1650360600-1650364200@cmsa.fas.harvard.edu
SUMMARY:Some combinatorics of Wilson loop diagrams
DESCRIPTION:Abstract: Wilson loop diagrams can be used to study amplitudes in N=4 SYM.  I will set them up and talk about some of their combinatorial aspects\, such as how many Wilson loop diagrams give the same positroid and how to combinatorially read off the dimension and the denominators for the integrands. \n**This talk will be hybrid. Talk will be held at CMSA (20 Garden St) Room G10. \nAll non-Harvard affiliated visitors to the CMSA building will need to complete this covid form prior to arrival. \nLINK TO FORM
URL:https://cmsa.fas.harvard.edu/event/4-19-2022-combinatorics-physics-and-probability-seminar/
LOCATION:Hybrid
CATEGORIES:Combinatorics Physics and Probability
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Combinatorics-Physics-and-Probability-Seminar-04.19.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220420T093000
DTEND;TZID=America/New_York:20220420T110000
DTSTAMP:20260507T080326
CREATED:20230706T180319Z
LAST-MODIFIED:20250328T200302Z
UID:10000095-1650447000-1650452400@cmsa.fas.harvard.edu
SUMMARY:CMSA/Tsinghua Math-Science Literature Lecture: Three Introductory Lectures on Game Theory for Mathematicians: Mechanism Design
DESCRIPTION:Eric Maskin (Harvard University) Three Introductory Lectures on Game Theory for Mathematicians \nApril 20\, 2022 | 9:30 – 11:00 am ET \nTitle: Mechanism Design \nAbstract: Given a social goal\, under what circumstances can we design a game to achieve that goal? \nTalk chairs: Scott Kominers\, Sergiy Verstyuk \nSLIDES | VIDEO
URL:https://cmsa.fas.harvard.edu/event/maskin_gametheory2022_2/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Mathlit_MASKIN-1583x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220420T103000
DTEND;TZID=America/New_York:20220420T130000
DTSTAMP:20260507T080326
CREATED:20240214T101836Z
LAST-MODIFIED:20240229T114304Z
UID:10002664-1650450600-1650459600@cmsa.fas.harvard.edu
SUMMARY:Superconductivity in infinite-layer nickelates
DESCRIPTION:Abstract: Since its discovery\, unconventional superconductivity in cuprates has motivated the search for materials with analogous electronic or atomic structure. We have used soft chemistry approaches to synthesize superconducting infinite layer nickelates from their perovskite precursor phase. We will present the synthesis and transport properties of the nickelates\, observation of a doping-dependent superconducting dome\, and our current understanding of their electronic and magnetic structure.
URL:https://cmsa.fas.harvard.edu/event/4-20-2022-strongly-correlated-quantum-materials-and-high-temperature-superconductors/
CATEGORIES:Strongly Correlated Quantum Materials and High-Temperature Superconductors
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Strongly-Correlated-Quantum-Materials-and-High-Temperature-Superconductors-04.20.21-1583x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220421T090000
DTEND;TZID=America/New_York:20220421T100000
DTSTAMP:20260507T080326
CREATED:20240214T113250Z
LAST-MODIFIED:20240301T103156Z
UID:10002700-1650531600-1650535200@cmsa.fas.harvard.edu
SUMMARY:Secure Multi-Party Computation: from Theory to Practice
DESCRIPTION:Abstract:\nEncryption is the backbone of cybersecurity. While encryption can secure data both in transit and at rest\, in the new era of ubiquitous computing\, modern cryptography also aims to protect data during computation. Secure multi-party computation (MPC) is a powerful technology to tackle this problem\, which enables distrustful parties to jointly perform computation over their private data without revealing their data to each other. Although it is theoretically feasible and provably secure\, the adoption of MPC in real industry is still very much limited as of today\, the biggest obstacle of which boils down to its efficiency. \nMy research goal is to bridge the gap between the theoretical feasibility and practical efficiency of MPC. Towards this goal\, my research spans both theoretical and applied cryptography. In theory\, I develop new techniques for achieving general MPC with the optimal complexity\, bringing theory closer to practice. In practice\, I design tailored MPC to achieve the best concrete efficiency for specific real-world applications. In this talk\, I will discuss the challenges in both directions and how to overcome these challenges using cryptographic approaches. I will also show strong connections between theory and practice. \nBiography:\nPeihan Miao is an assistant professor of computer science at the University of Illinois Chicago (UIC). Before coming to UIC\, she received her Ph.D. from the University of California\, Berkeley in 2019 and had brief stints at Google\, Facebook\, Microsoft Research\, and Visa Research. Her research interests lie broadly in cryptography\, theory\, and security\, with a focus on secure multi-party computation — especially in incorporating her industry experiences into academic research.
URL:https://cmsa.fas.harvard.edu/event/4-21-2022-interdisciplinary-science-seminar/
CATEGORIES:Interdisciplinary Science Seminar
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-Interdisciplinary-Science-Seminar-04.21.22-1583x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220421T100000
DTEND;TZID=America/New_York:20220421T110000
DTSTAMP:20260507T080326
CREATED:20240214T095030Z
LAST-MODIFIED:20240301T114330Z
UID:10002648-1650535200-1650538800@cmsa.fas.harvard.edu
SUMMARY:Future stability of the $1+3$ Milne model for the Einstein-Klein-Gordon system
DESCRIPTION:Abstract: We study the small perturbations of the $1+3$-dimensional Milne model for the Einstein-Klein-Gordon (EKG) system. We prove the nonlinear future stability\, and show that the perturbed spacetimes are future causally geodesically complete.  For the proof\, we work within the constant mean curvature (CMC) gauge and focus on the $1+3$ splitting of the Bianchi-Klein-Gordon equations. Moreover\, we treat the Bianchi-Klein-Gordon equations as evolution equations and establish the energy scheme in the sense that we only commute the Bianchi-Klein-Gordon equations with spatially covariant derivatives while normal derivative is not allowed. We propose some refined estimates for lapse and the hierarchies of energy estimates to close the energy argument.
URL:https://cmsa.fas.harvard.edu/event/4-21-2022-general-relativity-seminar/
CATEGORIES:General Relativity Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220422T093000
DTEND;TZID=America/New_York:20220422T230000
DTSTAMP:20260507T080326
CREATED:20230706T180541Z
LAST-MODIFIED:20250328T200643Z
UID:10000096-1650619800-1650668400@cmsa.fas.harvard.edu
SUMMARY:CMSA/Tsinghua Math-Science Literature Lecture: Three Introductory Lectures on Game Theory for Mathematicians: Auction Theory
DESCRIPTION:Eric Maskin (Harvard University) Three Introductory Lectures on Game Theory for Mathematicians \nApril 22\, 2022 | 9:30 – 11:00 am ET \nTitle: Auction Theory \nAbstract: Equivalences among four standard auctions: the high-bid auction (the high bidder wins and pays her bid); the second-bid auction (the high bidder wins and pays the second-highest bid); the Dutch auction (the auctioneer lowers the price successively until some bidder is willing to pay); and the English auction (bidders raise their bids successively until no one wants to bid higher). \nTalk chairs: Scott Kominers\, Sergiy Verstyuk \nSLIDES | VIDEO Answers to Questions from Talks 2 and 3
URL:https://cmsa.fas.harvard.edu/event/maskin_gametheory2022_3/
LOCATION:Virtual
CATEGORIES:Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Mathlit_MASKIN-1583x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220422T153000
DTEND;TZID=America/New_York:20220422T170000
DTSTAMP:20260507T080326
CREATED:20240214T101342Z
LAST-MODIFIED:20240229T112525Z
UID:10002662-1650641400-1650646800@cmsa.fas.harvard.edu
SUMMARY:Higgs = SPT
DESCRIPTION:Speaker: Ruben Verresen \nTitle: Higgs = SPT \nAbstract: The Higgs phase of a gauge theory is important to both fundamental physics (e.g.\, electroweak theory) as well as condensed matter systems (superconductors and other emergent phenomena). However\, such a charge condensate seems subtle and is sometimes described as the spontaneous breaking of gauge symmetry (or a global subgroup). In this talk\, I will argue that the Higgs phase is best understood as a symmetry-protected topological (SPT) phase. The concept of SPT phases arose out of the condensed matter community\, to describe systems with short-range entanglement and edge modes which cannot be removed in the presence of certain symmetries. The perspective that the Higgs phase is an SPT phase recovers known properties of the Higgs phase and provides new insights. In particular\, we revisit the Fradkin-Shenker model and the distinction between the Higgs and confined phases of a gauge theory.
URL:https://cmsa.fas.harvard.edu/event/4-22-2022-quantum-matter-in-mathematics-and-physics/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-Seminar-04.22.22-1583x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220426T090000
DTEND;TZID=America/New_York:20220426T100000
DTSTAMP:20260507T080326
CREATED:20240214T071014Z
LAST-MODIFIED:20240304T055455Z
UID:10002555-1650963600-1650967200@cmsa.fas.harvard.edu
SUMMARY:Algebraic Statistics with a View towards Physics
DESCRIPTION:Abstract: We discuss the algebraic geometry of maximum likelihood estimation from the perspective of scattering amplitudes in particle physics. A guiding examples the moduli space of n-pointed rational curves. The scattering potential plays the role of the log-likelihood function\, and its critical points are solutions to rational function equations. Their number is an Euler characteristic. Soft limit degenerations are combined with certified numerical methods for concrete computations. \n**This talk will be hybrid. Talk will be held at CMSA (20 Garden St) Room G10. \nAll non-Harvard affiliated visitors to the CMSA building will need to complete this covid form prior to arrival. \nLINK TO FORM
URL:https://cmsa.fas.harvard.edu/event/4-26-2022-combinatorics-physics-and-probability-seminar/
CATEGORIES:Combinatorics Physics and Probability
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Combinatorics-Physics-and-Probability-Seminar-04.26.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220426T093000
DTEND;TZID=America/New_York:20220426T103000
DTSTAMP:20260507T080326
CREATED:20230825T080553Z
LAST-MODIFIED:20240304T061555Z
UID:10001296-1650965400-1650969000@cmsa.fas.harvard.edu
SUMMARY:Modularity of mirror families of log Calabi–Yau surfaces
DESCRIPTION:Abstract:   In “Mirror symmetry for log Calabi–Yau surfaces I\,” given a smooth log Calabi–Yau surface pair (Y\,D)\, Gross–Hacking–Keel constructed its mirror family as the spectrum of an explicit algebra whose structure coefficients are determined by the enumerative geometry of (Y\,D). As a follow-up of the work of Gross–Hacking–Keel\, when (Y\,D) is positive\, we prove the modularity of the mirror family as the universal family of log Calabi-Yau surface pairs deformation equivalent to (Y\,D) with at worst du Val singularities. As a corollary\, we show that the ring of regular functions of a smooth affine log Calabi–Yau surface has a canonical basis of theta functions. The key step towards the proof of the main theorem is the application of the tropical construction of singular cycles and explicit formulas of period integrals given in the work of Helge–Siebert. This is joint work with Jonathan Lai.
URL:https://cmsa.fas.harvard.edu/event/modularity-of-mirror-families-of-log-calabi-yau-surfaces/
LOCATION:Virtual
CATEGORIES:Algebraic Geometry in String Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Algebraic-Geometry-in-String-Theory-04.26.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220427T090000
DTEND;TZID=America/New_York:20220429T170000
DTSTAMP:20260507T080326
CREATED:20230706T180811Z
LAST-MODIFIED:20250305T172643Z
UID:10000098-1651050000-1651251600@cmsa.fas.harvard.edu
SUMMARY:Workshop on Nonlinear Algebra and Combinatorics from Physics
DESCRIPTION:On April 27–29\, 2022\, the CMSA hosted a workshop on Nonlinear Algebra and Combinatorics. \nOrganizers: Bernd Sturmfels (MPI Leipzig) and Lauren Williams (Harvard). \nIn recent years\, ideas from integrable systems and scattering amplitudes have led to advances in nonlinear algebra and combinatorics. In this short workshop\, aimed at younger participants in the field\, we will explore some of the interactions between the above topics. \nSpeakers: \n\nFederico Ardila (San Francisco State)\nNima Arkani-Hamed (IAS)\nMadeline Brandt (Brown)\nNick Early (Max Planck Institute)\nChris Eur (Harvard)\nClaudia Fevola (Max Planck Institute)\nChristian Gaetz (Harvard)\nYuji Kodama (Ohio State University)\nYelena Mandelshtam (Berkeley)\nSebastian Mizera (IAS)\nMatteo Parisi (Harvard CMSA)\nEmma Previato (Boston University)\nAnna Seigal (Harvard)\nMelissa Sherman-Bennett (University of Michigan)\nSimon Telen (Max Planck Institute)\nCharles Wang (Harvard)\n\n\nSchedule\nWednesday\, April 27\, 2022 \n\n\n\n\n9:30 am–10:30 am\nFederico Ardila\nTitle: Nonlinear spaces from linear spaces \nAbstract: Matroid theory provides a combinatorial model for linearity\, but it plays useful roles beyond linearity. In the classical setup\, a linear subspace V of an n-dimensional vector space gives rise to a matroid M(V) on {1\,…\,n}. However\, the matroid M(V) also knows about some nonlinear geometric spaces related to V. Conversely\, those nonlinear spaces teach us things we didn’t know about matroids. My talk will discuss some examples.\n\n\n10:30 am–11:00 am\nCOFFEE BREAK\n\n\n\n11:00 am–11:45 am\nChris Eur\nTitle: Tautological classes of matroids \nAbstract: Algebraic geometry has furnished fruitful tools for studying matroids\, which are combinatorial abstractions of hyperplane arrangements. We first survey some recent developments\, pointing out how these developments remained partially disjoint. We then introduce certain vector bundles (K-classes) on permutohedral varieties\, which we call “tautological bundles (classes)” of matroids\, as a new framework that unifies\, recovers\, and extends these recent developments. Our framework leads to new questions that further probe the boundary between combinatorics and geometry. Joint work with Andrew Berget\, Hunter Spink\, and Dennis Tseng.\n\n\n11:45 am–2:00 pm\nLUNCH BREAK\n\n\n\n2:00 pm–2:45 pm\nNick Early\nTitle: Biadjoint Scalars and Associahedra from Residues of Generalized Amplitudes \nAbstract: The associahedron is known to encapsulate physical properties such as the notion of tree-level factorization for one of the simplest Quantum Field Theories\, the biadjoint scalar\, which has only cubic interactions.  I will discuss novel instances of the associahedron and the biadjoint scalar in a class of generalized amplitudes\, discovered by Cachazo\, Early\, Guevara and Mizera\, by taking certain limits thereof. This connection leads to a simple proof of a new realization of the associahedron involving a Minkowski sum of certain positroid polytopes in the second hypersimplex.\n\n\n2:45 pm–3:30 pm\nAnna Seigal\nTitle: Invariant theory for maximum likelihood estimation \nAbstract: I will talk about work to uncover connections between invariant theory and maximum likelihood estimation. I will describe how norm minimization over a torus orbit is equivalent to maximum likelihood estimation in log-linear models. We will see the role played by polytopes and discuss connections to scaling algorithms. Based on joint work with Carlos Améndola\, Kathlén Kohn\, and Philipp Reichenbach.\n\n\n3:30 pm–4:00 pm\nCOFFEE BREAK\n\n\n\n4:00 pm–4:45 pm\nMatteo Parisi\nTitle: Amplituhedra\, Scattering Amplitudes\, and Triangulations \nAbstract: In this talk I will discuss about Amplituhedra – generalizations of polytopes inside the Grassmannian – introduced by physicists to encode interactions of elementary particles in certain Quantum Field Theories. In particular\, I will explain how the problem of finding triangulations of Amplituhedra is connected to computing scattering amplitudes of N=4 super Yang-Mills theory.\nTriangulations of polygons are encoded in the associahedron\, studied by Stasheff in the sixties; in the case of polytopes\, triangulations are captured by secondary polytopes\, constructed by Gelfand et al. in the nineties. Whereas a “secondary” geometry describing triangulations of Amplituhedra is still not known\, and we pave the way for such studies. I will discuss how the combinatorics of triangulations interplays with T-duality from String Theory\, in connection with the Momentum Amplituhedron. A generalization of T-duality led us to discover a striking duality between Amplituhedra of “m=2” type and a seemingly unrelated object – the Hypersimplex. The latter is a polytope which appears in many contexts\, from matroid theory to tropical geometry.\nBased on joint works with Lauren Williams\, Melissa Sherman-Bennett\, Tomasz Lukowski.\n\n\n4:45 pm–5:30 pm\nMelissa Sherman-Bennett\nTitle: The hypersimplex and the m=2 amplituhedron \nAbstract: In this talk\, I’ll continue where Matteo left off. I’ll give some more details about the curious correspondence between the m=2 amplituhedron\, a 2k-dimensional subset of Gr(k\, k+2)\, and the hypersimplex\, an (n-1)-dimensional polytope in R^n. The amplituhedron and hypersimplex are both images of the totally nonnegative Grassmannian under some map (the amplituhedron map and the moment map\, respectively)\, but are different dimensions and live in very different ambient spaces. I’ll talk about joint work with Matteo Parisi and Lauren Williams in which we give a bijection between decompositions of the amplituhedron and decompositions of the hypersimplex (originally conjectured by Lukowski–Parisi–Williams). The hypersimplex decompositions are closely related to matroidal subdivisions. Along the way\, we prove a nice description of the m=2 amplituhedron conjectured by Arkani-Hamed–Thomas–Trnka and give a new decomposition of the m=2 amplituhedron into Eulerian-number-many chambers\, inspired by an analogous triangulation of the hypersimplex into Eulerian-number-many simplices.\n\n\n\n\n  \nThursday\, April 28\, 2022 \n\n\n\n\n9:30 am–10:30 am\nClaudia Fevola\nTitle: Nonlinear Algebra meets Feynman integrals \nAbstract: Feynman integrals play a central role in particle physics in the theory of scattering amplitudes. They form a finite-dimensional vector space and the elements of a basis are named “master integrals” in the physics literature. The number of master integrals has been interpreted in different ways: it equals the dimension of a twisted de Rham cohomology group\, the Euler characteristic of a very affine variety\, and the holonomic rank of a D-module. In this talk\, we are interested in a more general family of integrals that contains Feynman integrals as a special case. We explore this setting using tools coming from nonlinear algebra. This is an ongoing project with Daniele Agostini\, Anna-Laura Sattelberger\, and Simon Telen.\n\n\n10:30 am–11:00 am\nCOFFEE BREAK\n\n\n\n11:00 am–11:45 am\nSimon Telen\nTitle: Landau discriminants \nAbstract: The Landau discriminant is a projective variety containing kinematic parameters for which a Feynman integral can have singularities. We present a definition and geometric properties. We discuss how to compute Landau discriminants using symbolic and numerical methods. Our methods can be used\, for instance\, to compute the Landau discriminant of the pentabox diagram\, which is a degree 12 hypersurface in 6-space. This is joint work with Sebastian Mizera.\n\n\n11:45 am–2:00 pm\nLUNCH BREAK\n\n\n\n2:00 pm–2:45 pm\nChristian Gaetz\nTitle: 1-skeleton posets of Bruhat interval polytopes \nAbstract: Bruhat interval polytopes are a well-studied class of generalized permutohedra which arise as moment map images of various toric varieties and totally positive spaces in the flag variety. I will describe work in progress in which I study the 1-skeleta of these polytopes\, viewed as posets interpolating between weak order and Bruhat order. In many cases these posets are lattices and the polytopes\, despite not being simple\, have interesting h-vectors. In a special case\, work of Williams shows that Bruhat interval polytopes are isomorphic to bridge polytopes\, so that chains in the 1-skeleton poset correspond to BCFW-bridge decompositions of plabic graphs.\n\n\n2:45 pm–3:30 pm\nMadeleine Brandt\nTitle: Top Weight Cohomology of $A_g$ \nAbstract: I will discuss a recent project in computing the top weight cohomology of the moduli space $A_g$ of principally polarized abelian varieties of dimension $g$ for small values of $g$. This piece of the cohomology is controlled by the combinatorics of the boundary strata of a compactification of $A_g$. Thus\, it can be computed combinatorially. This is joint work with Juliette Bruce\, Melody Chan\, Margarida Melo\, Gwyneth Moreland\, and Corey Wolfe.\n\n\n3:30 pm–4:00 pm\nCOFFEE BREAK\n\n\n\n4:00 pm–5:00 pm\nEmma Previato\nTitle: Sigma function on curves with non-symmetric semigroup \nAbstract: We start with an overview of the correspondence between spectral curves and commutative rings of differential operators\, integrable hierarchies of non-linear PDEs and Jacobian vector fields. The coefficients of the operators can be written explicitly in terms of the Kleinian sigma function: Weierstrass’ sigma function was generalized to genus greater than one by Klein\, and is a ubiquitous tool in integrability. The most accessible case is the sigma function of telescopic curves. In joint work with J. Komeda and S. Matsutani\, we construct a curve with non-symmetric Weierstrass semigroup (equivalently\, Young tableau)\, consequently non-telescopic\, and its sigma function. We conclude with possible applications to commutative rings of differential operators.\n\n\n6:00 pm\n\nDinner Banquet\, Gran Gusto Trattoria\n\n\n\n\n  \nFriday\, April 29\, 2022 \n\n\n\n\n9:00 am–10:00 am\nYuji Kodama\nTitle: KP solitons and algebraic curves \nAbstract: It is well-known that soliton solutions of the KdV hierarchy are obtained by singular limits of hyper-elliptic curves. However\, there is no general results for soliton solutions of the KP hierarchy\, KP solitons. In this talk\, I will show that some of the KP solitons are related to the singular space curves associated with certain class of numerical semigroups.\n\n\n10:00 am–10:30 am\nCOFFEE BREAK\n\n\n\n10:30 am–11:15 am\nYelena Mandelshtam\nTitle: Curves\, degenerations\, and Hirota varieties \nAbstract: The Kadomtsev-Petviashvili (KP) equation is a differential equation whose study yields interesting connections between integrable systems and algebraic geometry. In this talk I will discuss solutions to the KP equation whose underlying algebraic curves undergo tropical degenerations. In these cases\, Riemann’s theta function becomes a finite exponential sum that is supported on a Delaunay polytope. I will introduce the Hirota variety which parametrizes all KP solutions arising from such a sum. I will then discuss a special case\, studying the Hirota variety of a rational nodal curve. Of particular interest is an irreducible subvariety that is the image of a parameterization map. Proving that this is a component of the Hirota variety entails solving a weak Schottky problem for rational nodal curves. This talk is based on joint work with Daniele Agostini\, Claudia Fevola\, and Bernd Sturmfels.\n\n\n11:15 am–12:00 pm\nCharles Wang\nTitle: Differential Algebra of Commuting Operators \nAbstract: In this talk\, we will give an overview of the problem of finding the centralizer of a fixed differential operator in a ring of differential operators\, along with connections to integrable hierarchies and soliton solutions to e.g. the KdV or KP equations. Given these interesting connections\, it is important to be able to compute centralizers of differential operators\, and we discuss how to use techniques from differential algebra to approach this question\, as well as how having these computational tools can help in understanding the structure of soliton solutions to these equations.\n\n\n12:00 pm–2:00 pm\nLUNCH BREAK\n\n\n\n2:00 pm–3:00 pm\nSebastian Mizera\nTitle: Feynman Polytopes \nAbstract: I will give an introduction to a class of polytopes that recently emerged in the study of scattering amplitudes in quantum field theory.\n\n\n3:00 pm–3:30 pm\nCOFFEE BREAK\n\n\n\n3:30 pm–4:30 pm\nNima Arkani-Hamed\nTitle: Spacetime\, Quantum Mechanics and Combinatorial Geometries at Infinity
URL:https://cmsa.fas.harvard.edu/event/workshop-on-nonlinear-algebra-and-combinatorics-from-physics/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Workshop
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Nonlinear-Workshop_4.27-29.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220427T093000
DTEND;TZID=America/New_York:20220427T103000
DTSTAMP:20260507T080326
CREATED:20240214T034934Z
LAST-MODIFIED:20240304T073208Z
UID:10002515-1651051800-1651055400@cmsa.fas.harvard.edu
SUMMARY:Long common subsequences between bit-strings and the zero-rate threshold of deletion-correcting codes
DESCRIPTION:Speaker: Venkatesan Guruswami\, UC Berkeley \nTitle: Long common subsequences between bit-strings and the zero-rate threshold of deletion-correcting codes \nAbstract: Suppose we transmit n bits on a noisy channel that deletes some fraction of the bits arbitrarily. What’s the supremum p* of deletion fractions that can be corrected with a binary code of non-vanishing rate? Evidently p* is at most 1/2 as the adversary can delete all occurrences of the minority bit. It was unknown whether this simple upper bound could be improved\, or one could in fact correct deletion fractions approaching 1/2.\nWe show that there exist absolute constants A and delta > 0 such that any subset of n-bit strings of size exp((log n)^A) must contain two strings with a common subsequence of length (1/2+delta)n. This immediately implies that the zero-rate threshold p* of worst-case bit deletions is bounded away from 1/2. \nOur techniques include string regularity arguments and a structural lemma that classifies bit-strings by their oscillation patterns. Leveraging these tools\, we find in any large code two strings with similar oscillation patterns\, which is exploited to find a long common subsequence. \nThis is joint work with Xiaoyu He and Ray Li.
URL:https://cmsa.fas.harvard.edu/event/long-common-subsequences-between-bit-strings-and-the-zero-rate-threshold-of-deletion-correcting-codes/
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-04.27.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220428T103000
DTEND;TZID=America/New_York:20220428T120000
DTSTAMP:20260507T080326
CREATED:20240214T101152Z
LAST-MODIFIED:20240229T112257Z
UID:10002661-1651141800-1651147200@cmsa.fas.harvard.edu
SUMMARY:Aspects of 4d supersymmetric dynamics and geometry
DESCRIPTION:Abstract: We will overview the program of geometrically engineering four dimensional supersymmetric QFTs as compactifications of six dimensional SCFTs. In particular we will discuss how strong coupling phenomena in four dimensions\, such as duality and emergence of symmetry\, can be better understood in such geometric constructions.
URL:https://cmsa.fas.harvard.edu/event/4-28-2022-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-Seminar-04.28.22-1583x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220428T130000
DTEND;TZID=America/New_York:20220428T143000
DTSTAMP:20260507T080326
CREATED:20230824T174429Z
LAST-MODIFIED:20240304T081149Z
UID:10001813-1651150800-1651156200@cmsa.fas.harvard.edu
SUMMARY:Building active nematic and active polar liquids out of biological machines
DESCRIPTION:Speaker: Guillaume Duclos (Brandeis)\n\n\nTitle: Building active nematic and active polar liquids out of biological machines\nAbstract: Active matter describes out-of-equilibrium materials composed of motile building blocks that convert free energy into mechanical work. The continuous input of energy at the particle scale liberates these systems from the constraints of thermodynamic equilibrium\, leading to emergent collective behaviors not found in passive materials. In this talk\, I will describe our recent efforts to build simple active systems composed of purified proteins and identify generic emergent behaviors in active systems. I will first discuss two distinct activity-driven instabilities in suspensions of microtubules and molecular motors. Second\, I will describe a new model system for polar fluid whose collective dynamics are driven by the non-equilibrium turnover of actin filaments. Our results illustrate how biomimetic materials can serve as a platform for studying non-equilibrium statistical mechanics\, as well as shine light on the physical mechanisms that regulate self-organization in living matter. \n  \nVideo (Youtube)
URL:https://cmsa.fas.harvard.edu/event/building-active-nematic-and-active-polar-liquids-out-of-biological-machines/
LOCATION:Virtual
CATEGORIES:Active Matter Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Active-Matter-Seminar-04.28.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220428T153300
DTEND;TZID=America/New_York:20220428T173300
DTSTAMP:20260507T080326
CREATED:20240214T112923Z
LAST-MODIFIED:20240301T103000Z
UID:10002698-1651159980-1651167180@cmsa.fas.harvard.edu
SUMMARY:Intersection number and systole on hyperbolic surfaces
DESCRIPTION:Abstract: Let X be a compact hyperbolic surface. We can see that there is a constant C(X) such that the intersection number of the closed geodesics is  \leq C(X) times the product of their lengths. Consider the optimum constant C(X). In this talk\, we describe its asymptotic behavior in terms of systole\,  length of the shortest closed geodesic on X.
URL:https://cmsa.fas.harvard.edu/event/4-28-2022-interdisciplinary-science-seminar/
CATEGORIES:Interdisciplinary Science Seminar
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-Interdisciplinary-Science-Seminar-04.28.22-1583x2048-1.jpg
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END:VCALENDAR