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DTSTART;TZID=America/New_York:20220329T090000
DTEND;TZID=America/New_York:20220329T100000
DTSTAMP:20260508T084744
CREATED:20240213T110525Z
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UID:10002473-1648544400-1648548000@cmsa.fas.harvard.edu
SUMMARY:Combinatorics\, Physics and Probability Seminar
DESCRIPTION:During the 2021–22 academic year\, the CMSA will be hosting a seminar on Combinatorics\, Physics and Probability\, organized by Matteo Parisi and Michael Simkin. This seminar will take place on Tuesdays at 9:00 am – 10:00 am (Boston time). The meetings will take place virtually on Zoom. To learn how to attend\, please fill out this form\, or contact the organizers Matteo (mparisi@cmsa.fas.harvard.edu) and Michael (msimkin@cmsa.fas.harvard.edu). \nThe schedule below will be updated as talks are confirmed. \nSpring 2022\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n1/25/2022\n*note special time 9:00–10:00 AM ET\nJacob Bourjaily (Penn State University\, Eberly College of Science\nTitle: Adventures in Perturbation Theory \nAbstract: Recent years have seen tremendous advances in our understanding of perturbative quantum field theory—fueled largely by discoveries (and eventual explanations and exploitation) of shocking simplicity in the mathematical form of the predictions made for experiment. Among the most important frontiers in this progress is the understanding of loop amplitudes—their mathematical form\, underlying geometric structure\, and how best to manifest the physical properties of finite observables in general quantum field theories. This work is motivated in part by the desire to simplify the difficult work of doing Feynman integrals. I review some of the examples of this progress\, and describe some ongoing efforts to recast perturbation theory in terms that expose as much simplicity (and as much physics) as possible.\n\n\n2/3/2022\nRan Tessler\n(Weizmann Institute of Science)\nTitle: The Amplituhedron BCFW Triangulation \nAbstract:  The (tree) amplituhedron was introduced in 2013 by Arkani-Hamed and Trnka in their study of N=4 SYM scattering amplitudes. A central conjecture in the field was to prove that the m=4 amplituhedron is triangulated by the images of certain positroid cells\, called the BCFW cells. In this talk I will describe a resolution of this conjecture. The seminar is based on a recent joint work with Chaim Even-Zohar and Tsviqa Lakrec.\n\n\n2/8/2022\nAnna Seigal (Harvard)\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\n2/15/2022\nIgor Balla\, Hebrew University of Jerusalem\nTitle: Equiangular lines and regular graphs \nAbstract: In 1973\, Lemmens and Seidel asked to determine N_alpha(r)\, the maximum number of equiangular lines in R^r with common angle arccos(alpha). Recently\, this problem has been almost completely settled when r is exponentially large relative to 1/alpha\, with the approach both relying on Ramsey’s theorem\, as well as being limited by it. In this talk\, we will show how orthogonal projections of matrices with respect to the Frobenius inner product can be used to overcome this limitation\, thereby obtaining significantly improved upper bounds on N_alpha(r) when r is polynomial in 1/alpha. In particular\, our results imply that N_alpha(r) = Theta(r) for alpha >= Omega(1 / r^1/5). \nOur projection method generalizes to complex equiangular lines in C^r\, which may be of independent interest in quantum theory. Applying this method also allows us to obtain\nthe first universal bound on the maximum number of complex equiangular lines in C^r with common Hermitian angle arccos(alpha)\, an extension of the Alon-Boppana theorem to dense regular graphs\, which is tight for strongly regular graphs corresponding to r(r+1)/2 equiangular lines in R^r\, an improvement to Welch’s bound in coding theory.\n\n\n\n\nFall 2021\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n9/21/2021\nNima Arkani-Hamed\nIAS (Institute for Advanced Study)\, School of Natural Sciences\nTitle: Surfacehedra and the Binary Positive Geometry of Particle and “String” Amplitudes\n\n\n9/28/2021\nMelissa Sherman-Bennett\nUniversity of Michigan\, Department of Mathematics\nTitle: The hypersimplex and the m=2 amplituhedron \nAbstract: I’ll discuss a 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). Along the way\, we prove the sign-flip 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 hypersimplex decomposition).\n\n\n10/5/2021\nDaniel Cizma\, Hebrew University\nTitle: Geodesic Geometry on Graphs \nAbstract: In a graph G = (V\, E) we consider a system of paths S so that for every two vertices u\,v in V there is a unique uv path in S connecting them. The path system is said to be consistent if it is closed under taking subpaths\, i.e. if P is a path in S then any subpath of P is also in S. Every positive weight function w: E–>R^+ gives rise to a consistent path system in G by taking the paths in S to be geodesics w.r.t. w. In this case\, we say w induces S. We say a graph G is metrizable if every consistent path system in G is induced by some such w. \nWe’ll discuss the concept of graph metrizability\, and\, in particular\, we’ll see that while metrizability is a rare property\, there exists infinitely many 2-connected metrizable graphs. \nJoint work with Nati Linial.\n\n\n10/12/2021\nLisa Sauermann\, MIT\nTitle: On counting algebraically defined graphs \nAbstract: For many classes of graphs that arise naturally in discrete geometry (for example intersection graphs of segments or disks in the plane)\, the edges of these graphs can be defined algebraically using the signs of a finite list of fixed polynomials. We investigate the number of n-vertex graphs in such an algebraically defined class of graphs. Warren’s theorem (a variant of a theorem of Milnor and Thom) implies upper bounds for the number of n-vertex graphs in such graph classes\, but all the previously known lower bounds were obtained from ad hoc constructions for very specific classes. We prove a general theorem giving a lower bound for this number (under some reasonable assumptions on the fixed list of polynomials)\, and this lower bound essentially matches the upper bound from Warren’s theorem.\n\n\n10/19/2021\nPavel Galashin\nUCLA\, Department of Mathematics\nTitle: Ising model\, total positivity\, and criticality \nAbstract: The Ising model\, introduced in 1920\, is one of the most well-studied models in statistical mechanics. It is known to undergo a phase transition at critical temperature\, and has attracted considerable interest over the last two decades due to special properties of its scaling limit at criticality.\nThe totally nonnegative Grassmannian is a subset of the real Grassmannian introduced by Postnikov in 2006. It arises naturally in Lusztig’s theory of total positivity and canonical bases\, and is closely related to cluster algebras and scattering amplitudes.\nI will give some background on the above objects and then explain a precise relationship between the planar Ising model and the totally nonnegative Grassmannian\, obtained in our recent work with P. Pylyavskyy. Building on this connection\, I will give a new boundary correlation formula for the critical Ising model.\n\n\n10/26/2021\nCandida Bowtell\, University of Oxford\nTitle: The n-queens problem \nAbstract: The n-queens problem asks how many ways there are to place n queens on an n x n chessboard so that no two queens can attack one another\, and the toroidal n-queens problem asks the same question where the board is considered on the surface of a torus. Let Q(n) denote the number of n-queens configurations on the classical board and T(n) the number of toroidal n-queens configurations. The toroidal problem was first studied in 1918 by Pólya who showed that T(n)>0 if and only if n is not divisible by 2 or 3. Much more recently Luria showed that T(n) is at most ((1+o(1))ne^{-3})^n and conjectured equality when n is not divisible by 2 or 3. We prove this conjecture\, prior to which no non-trivial lower bounds were known to hold for all (sufficiently large) n not divisible by 2 or 3. We also show that Q(n) is at least ((1+o(1))ne^{-3})^n for all natural numbers n which was independently proved by Luria and Simkin and\, combined with our toroidal result\, completely settles a conjecture of Rivin\, Vardi and Zimmerman regarding both Q(n) and T(n). \nIn this talk we’ll discuss our methods used to prove these results. A crucial element of this is translating the problem to one of counting matchings in a 4-partite 4-uniform hypergraph. Our strategy combines a random greedy algorithm to count `almost’ configurations with a complex absorbing strategy that uses ideas from the methods of randomised algebraic construction and iterative absorption. \nThis is joint work with Peter Keevash.\n\n\n11/9/2021\nSteven Karp\nUniversite du Quebec a Montreal\, LaCIM (Laboratoire de combinatoire et d’informatique mathématique)\nTitle: Gradient flows on totally nonnegative flag varieties\n\nAbstract: One can view a partial flag variety in C^n as an adjoint orbit inside the Lie algebra of n x n skew-Hermitian matrices. We use the orbit context to study the totally nonnegative part of a partial flag variety from an algebraic\, geometric\, and dynamical perspective. We classify gradient flows on adjoint orbits in various metrics which are compatible with total positivity. As applications\, we show how the classical Toda flow fits into this framework\, and prove that a new family of amplituhedra are homeomorphic to closed balls. This is joint work with Anthony Bloch.\n\n\n11/16/2021\n*note special time 12:30–1:30 ET*\nYinon Spinka (University of British Columbia)\nTitle: A tale of two balloons \nAbstract: From each point of a Poisson point process start growing a balloon at rate 1. When two balloons touch\, they pop and disappear. Will balloons reach the origin infinitely often or not? We answer this question for various underlying spaces. En route we find a new(ish) 0-1 law\, and generalize bounds on independent sets that are factors of IID on trees.\nJoint work with Omer Angel and Gourab Ray.\n\n\n11/23/2021\nLutz Warnke (UC San Diego)\nTitle: Prague dimension of random graphs \nAbstract: The Prague dimension of graphs was introduced by Nesetril\, Pultr and Rodl in the 1970s: as a combinatorial measure of complexity\, it is closely related to clique edges coverings and partitions. Proving a conjecture of Furedi and Kantor\, we show that the Prague dimension of the binomial random graph is typically of order n/(log n) for constant edge-probabilities. The main new proof ingredient is a Pippenger-Spencer type edge-coloring result for random hypergraphs with large uniformities\, i.e.\, edges of size O(log n).\n\n\n11/30/2021\nKarel Devriendt (University of Oxford)\nTitle: Resistance curvature – a new discrete curvature on graphs \nAbstract: The last few decades have seen a surge of interest in building towards a theory of discrete curvature that attempts to translate the key properties of curvature in differential geometry to the setting of discrete objects and spaces. In the case of graphs there have been several successful proposals\, for instance by Lin-Lu-Yau\, Forman and Ollivier\, that replicate important curvature theorems and have inspired applications in a variety of practical settings.\nIn this talk\, I will introduce a new notion of discrete curvature on graphs\, which we call the resistance curvature\, and discuss some of its basic properties. The resistance curvature is defined based on the concept of effective resistance which is a metric between the vertices of a graph and has many other properties such as a close relation to random spanning trees. The rich theory of these effective resistances allows to study the resistance curvature in great detail; I will for instance show that “Lin-Lu-Yau >= resistance >= Forman curvature” in a specific sense\, show strong evidence that the resistance curvature converges to zero in expectation for Euclidean random graphs\, and give a connectivity theorem for positively curved graphs. The resistance curvature also has a naturally associated discrete Ricci flow which is a gradient flow and has a closed-form solution in the case of vertex-transitive and path graphs.\nFinally\, if time permits I will draw a connection with the geometry of hyperacute simplices\, following the work of Miroslav Fiedler.\nThis work was done in collaboration with Renaud Lambiotte.\n\n\n12/7/2021\nMatthew Jenssen (University of Birmingham)\nTitle: The singularity probability of random symmetric matrices \nAbstract: Let M_n be drawn uniformly from all n by n symmetric matrices with entries in {-1\,1}. In this talk I’ll consider the following basic question: what is the probability that M_n is singular? I’ll discuss recent joint work with Marcelo Campos\, Marcus Michelen and Julian Sahasrabudhe where we show that this probability is exponentially small. I hope to make the talk accessible to a fairly general audience.\n\n\n12/14/2021\nStefan Glock (ETH Zurich)\nTitle: The longest induced path in a sparse random graph \nAbstract: A long-standing problem in random graph theory has been to determine asymptotically the length of a longest induced path in sparse random graphs. Independent work of Luczak and Suen from the 90s showed the existence of an induced path of roughly half the optimal size\, which seems to be a barrier for certain natural approaches. Recently\, in joint work with Draganic and Krivelevich\, we solved this problem. In the talk\, I will discuss the history of the problem and give an overview of the proof.\n\n\n12/21/2021\n\n\n\n\n01/25/2022\nJacob Bourjaily\nPenn State University\, Department of Physics
URL:https://cmsa.fas.harvard.edu/event/combinatorics-physics-and-probability-seminar/
LOCATION:MA
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220328T130000
DTEND;TZID=America/New_York:20220328T140000
DTSTAMP:20260508T084744
CREATED:20240214T082503Z
LAST-MODIFIED:20240301T113123Z
UID:10002586-1648472400-1648476000@cmsa.fas.harvard.edu
SUMMARY:Black Hole Spectroscopy
DESCRIPTION:Abstract: According to general relativity\, the remnant of a binary black hole merger should be a perturbed Kerr black hole. Perturbed Kerr black holes emit “ringdown” radiation which is well described by a superposition of quasinormal modes\, with frequencies and damping times that depend only on the mass and spin of the remnant. Therefore the observation of gravitational radiation emitted by black hole mergers might finally provide direct evidence of black holes with the same certainty as\, say\, the 21 cm line identifies interstellar hydrogen. I will review the current status of this “black hole spectroscopy” program. I will focus on two important open issues: (1) When is the waveform well described by linear black hole perturbation theory? (2) What is the current observational status of black hole spectroscopy?
URL:https://cmsa.fas.harvard.edu/event/3-28-2022-general-relativity-seminar/
LOCATION:MA
CATEGORIES:General Relativity Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220328T130000
DTEND;TZID=America/New_York:20220328T140000
DTSTAMP:20260508T084744
CREATED:20230730T180327Z
LAST-MODIFIED:20240301T070636Z
UID:10001146-1648472400-1648476000@cmsa.fas.harvard.edu
SUMMARY:On renormalisation group induced moduli stabilisation and brane-antibrane inflation
DESCRIPTION:Abstract: A proposal to use the renormalisation group to address moduli stabilisation in IIB string perturbation theory will be described. We revisit brane-antibrane inflation combining this proposal with non-linearly realised supersymmetry.
URL:https://cmsa.fas.harvard.edu/event/3-28-2022-swampland-seminar-series/
LOCATION:MA
CATEGORIES:Swampland Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220325T093000
DTEND;TZID=America/New_York:20220325T103000
DTSTAMP:20260508T084744
CREATED:20240214T084728Z
LAST-MODIFIED:20240301T110538Z
UID:10002597-1648200600-1648204200@cmsa.fas.harvard.edu
SUMMARY:Periods for singular CY families and Riemann–Hilbert correspondence
DESCRIPTION:Member Seminar \nSpeaker: Tsung-Ju Lee \nTitle: Periods for singular CY families and Riemann–Hilbert correspondence \nAbstract: A GKZ system\, introduced by Gelfand\, Kapranov\, and Zelevinsky\, is a system of partial differential equations generalizing the hypergeometric structure studied by Euler and Gauss. The solutions to GKZ systems have been found applications in various branches of mathematics including number theory\, algebraic geometry and mirror symmetry. In this talk\, I will explain the details and demonstrate how to find the Riemann–Hilbert partner of the GKZ system with a fractional parameter which arises from the B model of singular CY varieties. This is a joint work with Dingxin Zhang.
URL:https://cmsa.fas.harvard.edu/event/3-25-2022-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220324T151700
DTEND;TZID=America/New_York:20220324T171700
DTSTAMP:20260508T084744
CREATED:20240215T091039Z
LAST-MODIFIED:20240301T104333Z
UID:10002708-1648135020-1648142220@cmsa.fas.harvard.edu
SUMMARY:An operadic structure on supermoduli spaces
DESCRIPTION:Abstract: The operadic structure on the moduli spaces of algebraic curves  encodes in a combinatorial way how nodal curves in the boundary can be obtained by glueing smooth curves along marked points. In this talk\, I will present a generalization of the operadic structure to moduli spaces of SUSY curves (or super Riemann surfaces). This requires colored graphs and generalized operads in the sense of Borisov-Manin. Based joint work with Yu. I. Manin and Y. Wu. https://arxiv.org/abs/2202.10321
URL:https://cmsa.fas.harvard.edu/event/3-24-2022-interdisciplinary-science-seminar/
LOCATION:MA
CATEGORIES:Interdisciplinary Science Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Interdisciplinary-Science-Seminar-03.24.2022-1583x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220324T130000
DTEND;TZID=America/New_York:20220324T142000
DTSTAMP:20260508T084744
CREATED:20230824T173250Z
LAST-MODIFIED:20240122T085257Z
UID:10001309-1648126800-1648131600@cmsa.fas.harvard.edu
SUMMARY:Topological defects drive layer formation in gliding bacteria colonies
DESCRIPTION:Abstract: The developmental cycle of Myxococcus xanthus involves the coordination of many hundreds of thousands of cells aggregating to form mounds known as fruiting bodies. This aggregation process begins with the sequential formation of more and more cell layers. Using three-dimensional confocal imaging we study this layer formation process by observing the formation of holes and second layers within a base monolayer of M xanthus cells. We find that cells align with each other over the majority of the monolayer forming an active nematic liquid crystal with defect point where cell alignment is undefined. We find that new layers and holes form at positive and negative topological defects respectively. We model the cell layer using hydrodynamic modeling and find that this layer and hole formation process is driven by active nematic forces through cell motility and anisotropic substrate friction.
URL:https://cmsa.fas.harvard.edu/event/topological-defects-drive-layer-formation-in-gliding-bacteria-colonies/
LOCATION:Virtual
CATEGORIES:Active Matter Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Active-Matter-Seminar-03.24.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220324T093000
DTEND;TZID=America/New_York:20220324T110000
DTSTAMP:20260508T084744
CREATED:20240214T103248Z
LAST-MODIFIED:20240813T162724Z
UID:10002675-1648114200-1648119600@cmsa.fas.harvard.edu
SUMMARY:Edge physics at the deconfined transition between a quantum spin Hall insulator and a superconductor
DESCRIPTION:Youtube Video \n  \nAbstract: I will talk about the edge physics of the deconfined quantum phase transition (DQCP) between a spontaneous quantum spin Hall (QSH) insulator and a spin-singlet superconductor (SC). Although the bulk of this transition is in the same universality class as the paradigmatic deconfined Neel to valence-bond-solid transition\, the boundary physics has a richer structure due to proximity to a quantum spin Hall state. We use the parton trick to write down an effective field theory for the QSH-SC transition in the presence of a boundary and calculate various edge properties in a large-N limit. We show that the boundary Luttinger liquid in the QSH state survives at the phase transition\, but only as fractional degrees of freedom that carry charge but not spin. The physical fermion remains gapless on the edge at the critical point\, with a universal jump in the fermion scaling dimension as the system approaches the transition from the QSH side. The critical point could be viewed as a gapless analogue of the QSH state but with the full SU(2) spin rotation symmetry\, which cannot be realized if the bulk is gapped. This talk reports on the work done with Liujun Zou and Chong Wang (arxiv:2110.08280).
URL:https://cmsa.fas.harvard.edu/event/3-24-2022-quantum-matter-in-mathematics-and-physics/
LOCATION:MA
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-03.24.2022-1583x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220324T093000
DTEND;TZID=America/New_York:20220324T103000
DTSTAMP:20260508T084744
CREATED:20240214T082228Z
LAST-MODIFIED:20240301T113314Z
UID:10002585-1648114200-1648117800@cmsa.fas.harvard.edu
SUMMARY:Rough solutions of the $3$-D compressible Euler equations
DESCRIPTION:Abstract: I will talk about my work on the compressible Euler equations. We prove the local-in-time existence the solution of the compressible Euler equations in $3$-D\, for the Cauchy data of the velocity\, density and vorticity $(v\,\varrho\, \omega) \in H^s\times H^s\times H^{s’}$\, $2<s'<s$.  The result extends the sharp result of Smith-Tataru and Wang\, established in the irrotational case\, i.e $\omega=0$\, which is known to be optimal for $s>2$. At the opposite extreme\, in the incompressible case\, i.e. with a constant density\,  the result is known to hold for $\omega\in H^s$\, $s>3/2$ and fails for $s\le 3/2$\, see the work of Bourgain-Li. It is thus natural to conjecture that the optimal result should be  $(v\,\varrho\, \omega) \in H^s\times H^s\times H^{s’}$\, $s>2\, \\, s’>\frac{3}{2}$. We view our work as an important step in proving the conjecture. The main difficulty in establishing sharp well-posedness results for general compressible Euler flow is due to the highly nontrivial interaction between the sound waves\, governed by quasilinear wave equations\, and vorticity which is transported by the flow. To overcome this difficulty\, we separate the dispersive part of a sound wave from the transported part and gain regularity significantly by exploiting the nonlinear structure of the system and the geometric structures of the acoustic spacetime.
URL:https://cmsa.fas.harvard.edu/event/3-24-2022-general-relativity-seminar/
LOCATION:MA
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-03.24.22-2.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220323T140000
DTEND;TZID=America/New_York:20220323T150000
DTSTAMP:20260508T084744
CREATED:20230808T183247Z
LAST-MODIFIED:20240515T202339Z
UID:10001208-1648044000-1648047600@cmsa.fas.harvard.edu
SUMMARY:Formal Mathematics Statement Curriculum Learning
DESCRIPTION:Speaker: Stanislas Polu\, OpenAI \nTitle: Formal Mathematics Statement Curriculum Learning \nAbstract: We explore the use of expert iteration in the context of language modeling applied to formal mathematics. We show that at same compute budget\, expert iteration\, by which we mean proof search interleaved with learning\, dramatically outperforms proof search only.  We also observe that when applied to a collection of formal statements of sufficiently varied difficulty\, expert iteration is capable of finding and solving a curriculum of increasingly difficult problems\,  without the need for associated ground-truth proofs. Finally\, by applying this expert iteration to a manually curated set of problem statements\, we achieve state-of-the-art on the miniF2F benchmark\,  automatically solving multiple challenging problems drawn from high school olympiads.
URL:https://cmsa.fas.harvard.edu/event/3-23-2022-new-technologies-in-mathematics-seminar/
LOCATION:MA
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-03.23.2022-1553x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220323T103000
DTEND;TZID=America/New_York:20220323T120000
DTSTAMP:20260508T084744
CREATED:20240214T103754Z
LAST-MODIFIED:20240301T064719Z
UID:10002677-1648031400-1648036800@cmsa.fas.harvard.edu
SUMMARY:Non-zero momentum requires long-range entanglement
DESCRIPTION:Youtube Video \n  \nAbstract: I will show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has non-zero lattice momentum\, i.e. if it is an eigenstate of the translation symmetry with eigenvalue not equal to 1. Equivalently\, any state that can be connected with a non-zero momentum state through a finite-depth local unitary transformation must also be long-range entangled. The statement can also be generalized to fermion systems. I will then present two applications of this result: (1) several different types of Lieb-Schultz-Mattis (LSM) theorems\, including a previously unknown version involving only a discrete Z_n symmetry\, can be derived in a simple manner; (2) a gapped topological order (in space dimension d>1) must weakly break translation symmetry if one of its ground states on torus has nontrivial momentum – this generalizes the familiar physics of Tao-Thouless in fractional quantum Hall systems.
URL:https://cmsa.fas.harvard.edu/event/3-23-2022-quantum-matter-in-mathematics-and-physics/
LOCATION:MA
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-03.23.2022-1583x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220323T093000
DTEND;TZID=America/New_York:20220323T103000
DTSTAMP:20260508T084744
CREATED:20240214T040105Z
LAST-MODIFIED:20240507T192932Z
UID:10002519-1648027800-1648031400@cmsa.fas.harvard.edu
SUMMARY:Fluctuation scaling or Taylor’s law of heavy-tailed data\, illustrated by U.S. COVID-19 cases and deaths
DESCRIPTION:Speaker: Joel E. Cohen (Rockefeller University and Columbia University) \nTitle: Fluctuation scaling or Taylor’s law of heavy-tailed data\, illustrated by U.S. COVID-19 cases and deaths \nAbstract: Over the last century\, ecologists\, statisticians\, physicists\, financial quants\, and other scientists discovered that\, in many examples\, the sample variance approximates a power of the sample mean of each of a set of samples of nonnegative quantities. This power-law relationship of variance to mean is known as a power variance function in statistics\, as Taylor’s law in ecology\, and as fluctuation scaling in physics and financial mathematics. This survey talk will emphasize ideas\, motivations\, recent theoretical results\, and applications rather than detailed proofs. Many models intended to explain Taylor’s law assume the probability distribution underlying each sample has finite mean and variance. Recently\, colleagues and I generalized Taylor’s law to samples from probability distributions with infinite mean or infinite variance and higher moments. For such heavy-tailed distributions\, we extended Taylor’s law to higher moments than the mean and variance and to upper and lower semivariances (measures of upside and downside portfolio risk). In unpublished work\, we suggest that U.S. COVID-19 cases and deaths illustrate Taylor’s law arising from a distribution with finite mean and infinite variance. This model has practical implications. Collaborators in this work are Mark Brown\, Richard A. Davis\, Victor de la Peña\, Gennady Samorodnitsky\, Chuan-Fa Tang\, and Sheung Chi Phillip Yam.
URL:https://cmsa.fas.harvard.edu/event/colloquium_32223/
LOCATION:MA
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-03.23.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220322T093000
DTEND;TZID=America/New_York:20220322T103000
DTSTAMP:20260508T084744
CREATED:20240214T065544Z
LAST-MODIFIED:20240304T085053Z
UID:10002552-1647941400-1647945000@cmsa.fas.harvard.edu
SUMMARY:Flip processes
DESCRIPTION:Abstract: We introduce a class of random graph processes\, which we call \emph{flip processes}. Each such process is given by a \emph{rule} which is just a function $\mathcal{R}:\mathcal{H}_k\rightarrow \mathcal{H}_k$ from all labelled $k$-vertex graphs into itself ($k$ is fixed). The process starts with a given $n$-vertex graph $G_0$. In each step\, the graph $G_i$ is obtained by sampling $k$ random vertices $v_1\,\ldots\,v_k$ of $G_{i-1}$ and replacing the induced graph $F:=G_{i-1}[v_1\,\ldots\,v_k]$ by  $\mathcal{R}(F)$. This class contains several previously studied processes including the Erd\H{o}s–R\’enyi random graph process and the triangle removal process. \nGiven a flip process with a rule $\mathcal{R}$\, we construct time-indexed trajectories $\Phi:\Gra\times [0\,\infty)\rightarrow\Gra$ in the space of graphons. We prove that for any $T > 0$ starting with a large finite graph $G_0$ which is close to a graphon $W_0$ in the cut norm\, with high probability the flip process will stay in a thin sausage around the trajectory $(\Phi(W_0\,t))_{t=0}^T$ (after rescaling the time by the square of the order of the graph). \nThese graphon trajectories are then studied from the perspective of dynamical systems. Among others\, we study continuity properties of these trajectories with respect to time and the initial graphon\, existence and stability of fixed points and speed of convergence (whenever the infinite time limit exists). We give an example of a flip process with a periodic trajectory. This is joint work with Frederik Garbe\, Matas \v Sileikis and Fiona Skerman (arXiv:2201.12272). \nWe also study several specific families flip processes. This is joint work with Pedro Ara\’ujo\, Eng Keat Hng and Matas \v{S}ileikis (in preparation).\nA brief introduction to the necessary bits of the theory of graph limits will be given in the talk.
URL:https://cmsa.fas.harvard.edu/event/3-22-2022-combinatorics-physics-and-probability-seminar/
LOCATION:MA
CATEGORIES:Combinatorics Physics and Probability
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Combinatorics-Physics-and-Probability-Seminar-3.15.2022-1-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220321T130000
DTEND;TZID=America/New_York:20220321T140000
DTSTAMP:20260508T084744
CREATED:20240214T081657Z
LAST-MODIFIED:20240813T160939Z
UID:10002584-1647867600-1647871200@cmsa.fas.harvard.edu
SUMMARY:Bulk-boundary correspondence for vacuum asymptotically Anti-de Sitter spacetimes
DESCRIPTION:Abstract: The AdS/CFT conjecture in physics posits the existence of a correspondence between gravitational theories in asymptotically Anti-de Sitter (aAdS) spacetimes and field theories on their conformal boundary. In this presentation\, we prove rigorous mathematical statements toward this conjecture. \nIn particular\, we show there is a one-to-one correspondence between aAdS solutions of the Einstein-vacuum equations and a suitable space of data on the conformal boundary (consisting of the boundary metric and the boundary stress-energy tensor). We also discuss consequences of this result\, as well as the main ingredient behind its proof: a unique continuation property for wave equations on aAdS spacetimes. \nThis is joint work with Gustav Holzegel (and makes use of joint works with Alex McGill and Athanasios Chatzikaleas).
URL:https://cmsa.fas.harvard.edu/event/3-21-2022-general-relativity-seminar/
LOCATION:MA
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-03.21.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220321T130000
DTEND;TZID=America/New_York:20220321T140000
DTSTAMP:20260508T084744
CREATED:20230730T180020Z
LAST-MODIFIED:20240301T073804Z
UID:10001145-1647867600-1647871200@cmsa.fas.harvard.edu
SUMMARY:3/21/2022 – Swampland Seminar
DESCRIPTION:Open Mic Discussion\nTopic: Entropy bounds (species bound\, Bekenstein bound\, CKN bound\, and the like)
URL:https://cmsa.fas.harvard.edu/event/3-21-2022-swampland-seminar/
LOCATION:MA
CATEGORIES:Swampland Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220318T093000
DTEND;TZID=America/New_York:20220318T103000
DTSTAMP:20260508T084744
CREATED:20240214T084936Z
LAST-MODIFIED:20240301T111106Z
UID:10002599-1647595800-1647599400@cmsa.fas.harvard.edu
SUMMARY:Moduli Space of Metric SUSY Graphs
DESCRIPTION:Member Seminar \nSpeaker: Yingying Wu \nTitle: Moduli Space of Metric SUSY Graphs \nAbstract: SUSY curves are algebraic curves with additional supersymmetric or supergeometric structures. In this talk\, I will present the construction of dual graphs of SUSY curves with Neveu–Schwarz and Ramond punctures. Then\, I will introduce the concept of the metrized SUSY graph and the moduli space of the metric SUSY graphs. I will outline its geometric and topological properties\, followed by a discussion on the connection with the classical case.
URL:https://cmsa.fas.harvard.edu/event/3-18-2022-member-seminar/
LOCATION:Virtual
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220317T151500
DTEND;TZID=America/New_York:20220317T161500
DTSTAMP:20260508T084744
CREATED:20240215T091301Z
LAST-MODIFIED:20240301T104445Z
UID:10002709-1647530100-1647533700@cmsa.fas.harvard.edu
SUMMARY:On optimization and generalization in deep learning
DESCRIPTION:Abstract: Deep neural networks have achieved significant empirical success in many fields\, including the fields of computer vision and natural language processing. Along with its empirical success\, deep learning has been theoretically shown to be attractive in terms of its expressive power. However\, the theory of expressive power does not ensure that we can efficiently find an optimal solution in terms of optimization and generalization\, during the optimization process. In this talk\, I will discuss some mathematical properties of optimization and generalization for deep neural networks.
URL:https://cmsa.fas.harvard.edu/event/3-17-2022-interdisciplinary-science-seminar/
LOCATION:MA
CATEGORIES:Interdisciplinary Science Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Interdisciplinary-Science-Seminar-03.17.2022-1583x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220317T093000
DTEND;TZID=America/New_York:20220317T110000
DTSTAMP:20260508T084744
CREATED:20240214T104122Z
LAST-MODIFIED:20240813T163816Z
UID:10002678-1647509400-1647514800@cmsa.fas.harvard.edu
SUMMARY: A Hike through the Swampland
DESCRIPTION:Abstract: The Swampland program aims at uncovering the universal implications of quantum gravity at low-energy physics. I will review the basic ideas of the Swampland program\, formal and phenomenological implications\, and provide a survey of the techniques commonly used in Swampland research including tools from quantum information\, holography\, supersymmetry\, and string theory.
URL:https://cmsa.fas.harvard.edu/event/3-17-2022-quantum-matter-in-mathematics-and-physics/
LOCATION:MA
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-03.17.2022-1-1544x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220316T103000
DTEND;TZID=America/New_York:20220316T120000
DTSTAMP:20260508T084744
CREATED:20240214T104642Z
LAST-MODIFIED:20240301T065907Z
UID:10002679-1647426600-1647432000@cmsa.fas.harvard.edu
SUMMARY:Summing Over Bordisms In 2d TQFT
DESCRIPTION:Abstract: Some recent work in the quantum gravity literature has considered what happens when the amplitudes of a TQFT are summed over the bordisms between fixed in-going and out-going boundaries. We will comment on these constructions. The total amplitude\, that takes into account all in-going and out-going boundaries can be presented in a curious factorized form. This talk reports on work done with Anindya Banerjee and is based on the paper on the e-print arXiv  2201.00903.
URL:https://cmsa.fas.harvard.edu/event/3-16-2022-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-03.16.2022-1544x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220315T100000
DTEND;TZID=America/New_York:20220315T230000
DTSTAMP:20260508T084744
CREATED:20240214T092307Z
LAST-MODIFIED:20240301T113301Z
UID:10002622-1647338400-1647385200@cmsa.fas.harvard.edu
SUMMARY:Birkhoff’s conjecture on integrable billiards and Kac’s problem “hearing the shape of a drum”
DESCRIPTION:Abstract: Billiards on an elliptical billiard table are completely integrable: phase space is foliated by invariant submanifolds for the billiard flow. Birkhoff conjectured that ellipses are the only plane domains with integrable billiards. Avila-deSimoi- Kaloshin proved the conjecture for ellipses of sufficiently small eccentricity. Kaloshin-Sorrentino proved local results for all eccentricities. On the quantum level\, the analogous conjecture is that ellipses are uniquely determined by their Dirichlet (or\, Neumann) eigenvalues. Using the results on the Birkhoff conjecture\, Hamid Hezari and I proved that for ellipses of small eccentricity are indeed uniquely determined by their eigenvalues. Except for disks\, which Kac proved to be uniquely determined\, these are the only domains for which it is known that one can hear their shape.
URL:https://cmsa.fas.harvard.edu/event/3-15-2022-joint-harvard-cuhk-ymsc-differential-geometry-seminar/
LOCATION:MA
CATEGORIES:Joint Harvard-CUHK-YMSC Differential Geometry
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220315T093000
DTEND;TZID=America/New_York:20220315T103000
DTSTAMP:20260508T084744
CREATED:20230825T075742Z
LAST-MODIFIED:20240304T082952Z
UID:10001292-1647336600-1647340200@cmsa.fas.harvard.edu
SUMMARY:2-categorical 3d mirror symmetry
DESCRIPTION:Abstract: It is by now well-known that mirror symmetry may be expressed as an equivalence between categories associated to dual Kahler manifolds. Following a proposal of Teleman\, we inaugurate a program to understand 3d mirror symmetry as an equivalence between 2-categories associated to dual holomorphic symplectic stacks. We consider here the abelian case\, where our theorem expresses the 2-category of spherical functors as a 2-category of coherent sheaves of categories. Applications include categorifications of hypertoric category O and of many related constructions in representation theory. This is joint work with Justin Hilburn and Aaron Mazel-Gee.
URL:https://cmsa.fas.harvard.edu/event/2-categorical-3d-mirror-symmetry/
LOCATION:Virtual
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220315T090000
DTEND;TZID=America/New_York:20220315T100000
DTSTAMP:20260508T084744
CREATED:20240214T065321Z
LAST-MODIFIED:20240304T085303Z
UID:10002551-1647334800-1647338400@cmsa.fas.harvard.edu
SUMMARY:Moduli space of tropical curves\, graph Laplacians and physics
DESCRIPTION:Abstract: I will first review the construction of the moduli space of tropical curves (or metric graphs)\, and its relation to graph complexes. The graph Laplacian may be interpreted as a tropical version of the classical Torelli map and its determinant is the Kirchhoff graph polynomial (also called 1st Symanzik)\, which is one of the two key components in Feynman integrals in high energy physics.The other component is the so-called 2nd Symanzik polynomial\, which is defined for graphs with external half edges and involves particle masses (edge colourings). I will explain how this too may be interpreted as the determinant of a generalised graph Laplacian\, and how it leads to a volumetric interpretation of a certain class of Feynman integrals.
URL:https://cmsa.fas.harvard.edu/event/3-15-2022-combinatorics-physics-and-probability-seminar/
LOCATION:MA
CATEGORIES:Combinatorics Physics and Probability
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Combinatorics-Physics-and-Probability-Seminar-3.15.2022-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220310T200000
DTEND;TZID=America/New_York:20220310T213000
DTSTAMP:20260508T084744
CREATED:20240214T104900Z
LAST-MODIFIED:20240813T163724Z
UID:10002680-1646942400-1646947800@cmsa.fas.harvard.edu
SUMMARY:Resonant side-jump thermal Hall effect of phonons coupled to dynamical defects
DESCRIPTION:Abstract: We present computations of the thermal Hall coefficient of phonons scattering off defects with multiple energy levels. Using a microscopic formulation based on the Kubo formula\, we find that the leading contribution perturbative in the phonon-defect coupling is of the ‘side-jump’ type\, which is proportional to the phonon lifetime. This contribution is at resonance when the phonon energy equals a defect level spacing. Our results are obtained for different defect models\, and include models of an impurity quantum spin in the presence of quasi-static magnetic order with an isotropic Zeeman coupling to the applied field. \nThis work is based on arxiv: 2201.11681
URL:https://cmsa.fas.harvard.edu/event/3-10-2022-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-03.10.2022-1544x2048-1-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220310T151300
DTEND;TZID=America/New_York:20220310T161300
DTSTAMP:20260508T084744
CREATED:20240215T091511Z
LAST-MODIFIED:20240301T104543Z
UID:10002710-1646925180-1646928780@cmsa.fas.harvard.edu
SUMMARY:Virtual Teams in Gig Economy — An End-to-End Data Science Approach
DESCRIPTION:Abstract: The gig economy provides workers with the benefits of autonomy and flexibility\, but it does so at the expense of work identity and co-worker bonds. Among the many reasons why gig workers leave their platforms\, an unexplored aspect is the organization identity. In a series of studies\, we develop a team formation and inter-team contest at a ride-sharing platform. We employ an end-to-end data science approach\, combining methodologies from randomized field experiments\, recommender systems\, and counterfactual machine learning. Together\, our results show that platform designers can leverage team identity and team contests to increase revenue and worker engagement in a gig economy. \nBio: Wei Ai is an Assistant Professor in the College of Information Studies (iSchool) and the Institute for Advanced Computer Studies (UMIACS) at the University of Maryland. His research interest lies in data science for social good\, where the advances of machine learning and data analysis algorithms translate into measurable impacts on society. He combines machine learning\, causal inference\, and field experiments in his research\, and has rich experience in collaborating with industrial partners. He earned his Ph.D. from the School of Information at the University of Michigan. His research has been published in top journals and conferences\, including PNAS\, ACM TOIS\, WWW\, and ICWSM.
URL:https://cmsa.fas.harvard.edu/event/3-10-2022-interdisciplinary-science-seminar/
LOCATION:MA
CATEGORIES:Interdisciplinary Science Seminar
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-Interdisciplinary-Science-Seminar-03.10.2022-1583x2048-1-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220310T130000
DTEND;TZID=America/New_York:20220310T140000
DTSTAMP:20260508T084744
CREATED:20240214T080539Z
LAST-MODIFIED:20240813T160832Z
UID:10002579-1646917200-1646920800@cmsa.fas.harvard.edu
SUMMARY:The Einstein-flow on manifolds of negative curvature
DESCRIPTION:Abstract: We consider the Cauchy problem for the Einstein equations for cosmological spacetimes\, i.e. spacetimes with compact spatial hypersurfaces. Various classes of those dynamical spacetimes have been constructed and analyzed using CMC foliations or equivalently the CMC-Einstein flow. We will briefly review the Andersson-Moncrief stability result of negative Einstein metrics under the vacuum Einstein flow and then present various recent generalizations to the nonvacuum case. We will emphasize what difficulties arise in those generalizations\, how they can be handled depending on the matter model at hand\, and what implications we can draw from these results for cosmology. We then turn to a scenario where the CMC Einstein flow leads to a large data result in 2+1-dimensions.
URL:https://cmsa.fas.harvard.edu/event/3-10-2022-general-relativity-seminar/
LOCATION:MA
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-03.10.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220309T140000
DTEND;TZID=America/New_York:20220309T140000
DTSTAMP:20260508T084744
CREATED:20230808T182829Z
LAST-MODIFIED:20240813T160025Z
UID:10001207-1646834400-1646834400@cmsa.fas.harvard.edu
SUMMARY:Machine Learning 30 STEM Courses in 12 Departments
DESCRIPTION:Speaker: Iddo Drori\, MIT EE&CS and Columbia School of Engineering \nTitle: Machine Learning 30 STEM Courses in 12 Departments \nAbstract: We automatically solve\, explain\, and generate university-level course problems from thirty STEM courses (at MIT\, Harvard\, and Columbia) for the first time.\nWe curate a new dataset of course questions and answers across a dozen departments: Aeronautics and Astronautics\, Chemical Engineering\, Chemistry\, Computer Science\, Economics\, Electrical Engineering\, Materials Science\, Mathematics\, Mechanical Engineering\, Nuclear Science\, Physics\, and Statistics.\nWe generate new questions and use them in a Columbia University course\, and perform A/B tests demonstrating that these machine generated questions are indistinguishable from human-written questions and that machine generated explanations are as useful as human-written explanations\, again for the first time.\nOur approach consists of five steps:\n(i) Given course questions\, turn them into programming tasks;\n(ii) Automatically generate programs from the programming tasks using a Transformer model\, OpenAI Codex\, pre-trained on text and fine-tuned on code;\n(iii) Execute the programs to obtain and evaluate the answers;\n(iv) Automatically explain the correct solutions using Codex;\n(v) Automatically generate new questions that are qualitatively indistinguishable from human-written questions.\nThis work is a significant step forward in applying machine learning for education\, automating a considerable part of the work involved in teaching.\nOur approach allows personalization of questions based on difficulty level and student backgrounds\, and scales up to a broad range of courses across the schools of engineering and science. \nThis is joint work with students and colleagues at MIT\, Harvard University\, Columbia University\, Worcester Polytechnic Institute\, and the University of Waterloo.
URL:https://cmsa.fas.harvard.edu/event/3-9-2022-new-technologies-in-mathematics-seminar/
LOCATION:MA
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-03.09.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220309T103000
DTEND;TZID=America/New_York:20220309T120000
DTSTAMP:20260508T084744
CREATED:20240214T105142Z
LAST-MODIFIED:20240301T070302Z
UID:10002682-1646821800-1646827200@cmsa.fas.harvard.edu
SUMMARY:Anomalies\, topological insulators and Kaehler-Dirac fermions
DESCRIPTION:Abstract: Motivated by a puzzle arising from recent work on staggered lattice fermions we introduce Kaehler-Dirac fermions and describe their connection both to Dirac fermions and staggered fermions. We show that they suffer from a gravitational anomaly that breaks a chiral U(1) symmetry specific to Kaehler-Dirac fermions down to Z_4 in any even dimension. In odd dimensions we show that the effective theory that results from integrating out massive Kaehler-Dirac fermions is a topological gravity theory. Such theories generalize Witten’s construction of (2+1) gravity as a Chern Simons theory. In the presence of a domain wall massless modes appear on the wall which can be consistently coupled to gravity due to anomaly inflow from the bulk gravitational theory. Much of this story parallels the usual discussion of topological insulators. The key difference is that the twisted chiral symmetry and anomaly structure of Kaehler-Dirac theories survives intact under discretization and governs the behavior of the lattice models. $Z_4$ invariant four fermion interactions can be used to gap out states in such theories without breaking symmetries and in flat space yields the known constraints on the number of Majorana fermions needed symmetric mass generation namely eight and sixteen Majorana spinors in two and four dimensions.
URL:https://cmsa.fas.harvard.edu/event/3-9-2022-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-03.09.2022-1544x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220309T093000
DTEND;TZID=America/New_York:20220309T103000
DTSTAMP:20260508T084744
CREATED:20240214T040341Z
LAST-MODIFIED:20240304T074318Z
UID:10002520-1646818200-1646821800@cmsa.fas.harvard.edu
SUMMARY:Side-effects of Learning from Low Dimensional Data Embedded in an Euclidean Space
DESCRIPTION:Abstract: The  low  dimensional  manifold  hypothesis  posits  that  the  data  found  in many applications\, such as those involving natural images\, lie (approximately) on low dimensional manifolds embedded in a high dimensional Euclidean space. In this setting\, a typical neural network defines a function that takes a finite number of vectors in the embedding space as input.  However\, one often needs to  consider  evaluating  the  optimized  network  at  points  outside  the  training distribution.  We analyze the cases where the training data are distributed in a linear subspace of Rd.  We derive estimates on the variation of the learning function\, defined by a neural network\, in the direction transversal to the subspace.  We study the potential regularization effects associated with the network’s depth and noise in the codimension of the data manifold.
URL:https://cmsa.fas.harvard.edu/event/side-effects-of-learning-from-low-dimensional-data-embedded-in-an-euclidean-space/
LOCATION:MA
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/02CMSA-Colloquium-03.09.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220308T090000
DTEND;TZID=America/New_York:20220308T100000
DTSTAMP:20260508T084744
CREATED:20240214T064241Z
LAST-MODIFIED:20240304T090552Z
UID:10002550-1646730000-1646733600@cmsa.fas.harvard.edu
SUMMARY:Greedy maximal independent sets via local limits
DESCRIPTION:Abstract: The random greedy algorithm for finding a maximal independent set in a graph has been studied extensively in various settings in combinatorics\, probability\, computer science\, and chemistry. The algorithm builds a maximal independent set by inspecting the graph’s vertices one at a time according to a random order\, adding the current vertex to the independent set if it is not connected to any previously added vertex by an edge. \nIn this talk\, I will present a simple yet general framework for calculating the asymptotics of the proportion of the yielded independent set for sequences of (possibly random) graphs\, involving a valuable notion of local convergence. I will demonstrate the applicability of this framework by giving short and straightforward proofs for results on previously studied families of graphs\, such as paths and various random graphs\, and by providing new results for other models such as random trees. \nIf time allows\, I will discuss a more delicate (and combinatorial) result\, according to which\, in expectation\, the cardinality of a random greedy independent set in the path is no larger than that in any other tree of the same order. \nThe talk is based on joint work with Michael Krivelevich\, Tamás Mészáros and Clara Shikhelman.
URL:https://cmsa.fas.harvard.edu/event/3-8-2022-combinatorics-physics-and-probability-seminar/
LOCATION:MA
CATEGORIES:Combinatorics Physics and Probability
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Combinatorics-Physics-and-Probability-Seminar-3.08.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220307T100000
DTEND;TZID=America/New_York:20220307T113000
DTSTAMP:20260508T084744
CREATED:20230730T175629Z
LAST-MODIFIED:20240301T073931Z
UID:10001144-1646647200-1646652600@cmsa.fas.harvard.edu
SUMMARY:4d strings at strong coupling
DESCRIPTION:Speakers: Fernando Marchesano (UAM-CSIC\, Madrid)  and Max Wiesner (Harvard CMSA)\n\n\n\nTitle: 4d strings at strong coupling\n\n\nAs usual\, the format will be 45 min talk + 30 min discussion\, to encourage participation from the audience.\nLooking forward to seeing you there!
URL:https://cmsa.fas.harvard.edu/event/3-7-2022-swampland-seminar/
LOCATION:Virtual
CATEGORIES:Swampland Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220304T093000
DTEND;TZID=America/New_York:20220304T103000
DTSTAMP:20260508T084744
CREATED:20240214T085309Z
LAST-MODIFIED:20240301T111217Z
UID:10002600-1646386200-1646389800@cmsa.fas.harvard.edu
SUMMARY:Positive Mass\, Density\, and Scalar Curvature on Noncompact Manifolds
DESCRIPTION:Member Seminar \nSpeaker: Martin Lesourd \nTitle: Positive Mass\, Density\, and Scalar Curvature on Noncompact Manifolds \nAbstract: I’ll describe some recent work spanning a couple of different papers on the topics mentioned in the title: Positive Mass\, Density\, and Scalar Curvature on Noncompact Manifolds. Two of these are with R. Unger\, Prof. S-T. Yau\, and two others are with R. Unger\, and Prof. D. A. Lee.
URL:https://cmsa.fas.harvard.edu/event/3-4-2022-member-seminar/
LOCATION:Hybrid – G10
CATEGORIES:Member Seminar
END:VEVENT
END:VCALENDAR