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DTSTART;TZID=America/New_York:20221128T090000
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SUMMARY:Representation Theory\, Calabi–Yau Manifolds\, and Mirror Symmetry
DESCRIPTION:Videos are available on the CMSA Youtube Playlist. \nOn November 28 – Dec 1\, 2022\, the CMSA hosted a Workshop on Representation Theory\, Calabi-Yau Manifolds\, and Mirror Symmetry. \nOrganizers: An Huang (Brandeis University) | Siu-Cheong Lau (Boston University) | Tsung-Ju Lee (CMSA\, Harvard) | Andrew Linshaw (University of Denver) \nScientific Advisor: Shing-Tung Yau (Harvard\, Tsinghua) \nLocation: Room G10\, CMSA\, 20 Garden Street\, Cambridge MA 02138 \n  \nThe conference was held in hybrid format\, both in-person and online. \nThe workshop was partially supported by Simons and NSF Grant DMS-2227199. \n  \nSpeakers:  \n\nTomoyuki Arakawa (Kyoto)\nThomas Creutzig (Edmonton)\nJonathan Mboyo Esole (Northeastern)\nFei Han (National University of Singapore)\nShinobu Hosono (Gakushuin University)\nFlor Orosz Hunziker (Colorado)\nCuipo Jiang (Shanghai)\nShashank Kanade (Denver)\nMatt Kerr (Washington University in St. Louis)\nCarl Lian (Humboldt-Universität zu Berlin)\nNai-Chung Conan Leung (CUHK)\nIvan Loseu (Yale)\nRobert McRae (Tsinghua University)\nAnne Moreau (Université Paris-Saclay\, Orsay)\nTony Pantev (University of Pennsylvania)\nMauricio Romo (Tsinghua University)\nBailin Song (USTC)\nCumrun Vafa (Harvard University)\nChin-Lung Wang (National Taiwan University)\nWeiqiang Wang (Virginia)\nYaping Yang (University of Melbourne)\nShing-Tung Yau (Tsinghua University)\nChenglong Yu (Tsinghua University)\nGufang Zhao (University of Melbourne)\n\n \n  \nSchedule (Eastern Time) \nSchedule (pdf) \n11/28 (Monday) \n\n\n\n08:30am – 08:55am\nRefreshments\n\n\n08:55am – 09:00am\nOpening remarks by Horng-Tzer Yau\n\n\n09:00am – 09:45am\nShing-Tung Yau*\nTitle: The Hull-Strominger system through conifold transitions \nAbstract: In this talk I discuss the geometry of C-Y manifolds outside of the Kähler regime and especially describe the Hull-Strominger system through the conifold transitions.\n\n\n10:00am – 10:45am\nChenglong Yu*\nTitle: Commensurabilities among Lattices in PU(1\,n) \nAbstract: In joint work with Zhiwei Zheng\, we study commensurabilities among certain subgroups in PU(1\,n). Those groups arise from the monodromy of hypergeometric functions. Their discreteness and arithmeticity are classified by Deligne and Mostow. Thurston also obtained similar results via flat conic metrics. However\, the classification of the lattices among them up to conjugation and finite index (commensurability) is not completed. When n=1\, it is the commensurabilities of hyperbolic triangles. The cases of n=2 are almost resolved by Deligne-Mostow and Sauter’s commensurability pairs\, and commensurability invariants by Kappes-Möller and McMullen. Our approach relies on the study of some higher dimensional Calabi-Yau type varieties instead of complex reflection groups. We obtain some relations and commensurability indices for higher n and also give new proofs for existing pairs in n=2.\n\n\n11:00am – 11:45am\nThomas Creutzig*\nTitle: Shifted equivariant W-algebras \nAbstract: The CDO of a compact Lie group is a family of VOAs whose top level is the space of functions on the Lie group. Similar structures appear at the intersections of boundary conditions in 4-dimensional gauge theories\, I will call these new families of VOAs shifted equivariant W-algebras. I will introduce these algebras\, construct them and explain how they can be used to quickly prove the GKO-coset realization of principal W-algebras.\n\n\n11:45am – 1:30 pm\nLunch\n\n\n01:30pm – 02:15pm\nCumrun Vafa\nTitle: Reflections on Mirror Symmetry \nAbstract: In this talk I review some of the motivations leading to the search and discovery of mirror symmetry as well as some of the applications it has had.\n\n\n02:30pm – 03:15pm\nJonathan Mboyo Esole\nTitle: Algebraic topology and matter representations in F-theory \nAbstract: Recently\, it was observed that representations appearing in geometric engineering in F-theory all satisfy a unique property: they correspond to characteristic representations of embedding of Dynkin index one between Lie algebras. However\, the reason why that is the case is still being understood. In this talk\, I will present new insights\, giving a geometric explanation for this fact using K-theory and the topology of Lie groups and their classifying spaces. In physics\, this will be interpreted as conditions on the charge of instantons and the classifications of Wess-Zumino-Witten terms.\n\n\n03:15pm – 03:45 pm\nBreak\n\n\n03:45pm – 04:30pm\nWeiqiang Wang\nTitle: A Drinfeld presentation of affine i-quantum groups \nAbstract: A quantum symmetric pair of affine type (U\, U^i) consists of a Drinfeld-Jimbo affine quantum group (a quantum deformation of a loop algebra) U and its coideal subalgebra U^i (called i-quantum group). A loop presentation for U was formulated by Drinfeld and proved by Beck. In this talk\, we explain how i-quantum groups can be viewed as a generalization of quantum groups\, and then we give a Drinfeld type presentation for the affine quasi-split i-quantum group U^i. This is based on joint work with Ming Lu (Sichuan) and Weinan Zhang (Virginia).\n\n\n04:45pm – 05:30pm\nTony Pantev\nTitle: Decomposition\, anomalies\, and quantum symmetries \nAbstract: Decomposition is a phenomenon in quantum physics which converts quantum field theories with non-effectively acting gauge symmetries into equivalent more tractable theories in which the fields live on a disconnected space. I will explain the mathematical content of decomposition which turns out to be a higher categorical version of Pontryagin duality. I will examine how this duality interacts with quantum anomalies and secondary quantum symmetries and will show how the anomalies can be canceled by homotopy coherent actions of diagrams of groups. I will discuss in detail the case of 2-groupoids which plays a central role in anomaly cancellation\, and will describe a new duality operation that yields decomposition in the presence of anomalies. The talk is based on joint works with Robbins\, Sharpe\, and Vandermeulen.\n\n\n\n  \n11/29 (Tuesday) \n  \n\n\n\n\nRefreshments\n\n\n09:00am – 09:45am\nRobert MacRae*\nTitle: Rationality for a large class of affine W-algebras \nAbstract: One of the most important results in vertex operator algebras is Huang’s theorem that the representation category of a “strongly rational” vertex operator algebra is a semisimple modular tensor category. Conversely\, it has been conjectured that every (unitary) modular tensor category is the representation category of a strongly rational (unitary) vertex operator algebra. In this talk\, I will describe my results on strong rationality for a large class of affine W-algebras at admissible levels. This yields a large family of modular tensor categories which generalize those associated to affine Lie algebras at positive integer levels\, as well as those associated to the Virasoro algebra.\n\n\n10:00am – 10:45am\nBailin Song*\nTitle: The global sections of chiral de Rham complexes on compact Calabi-Yau manifolds \nAbstract: Chiral de Rham complex is a sheaf of vertex algebras on a complex manifold. We will describe the space of global sections of the chiral de Rham complexes on compact Calabi-Yau manifolds.\n\n\n11:00am – 11:45am\nCarl Lian*\nTitle: Curve-counting with fixed domain \nAbstract: The fixed-domain curve-counting problem asks for the number of pointed curves of fixed (general) complex structure in a target variety X subject to incidence conditions at the marked points. The question comes in two flavors: one can ask for a virtual count coming from Gromov-Witten theory\, in which case the answer can be computed (in principle) from the quantum cohomology of X\, or one can ask for the “honest” geometric count\, which tends to be more subtle. The answers are conjectured to agree in the presence of sufficient positivity\, but do not always. I will give an overview of some recent results and open directions. Some of this work is joint with Alessio Cela\, Gavril Farkas\, and Rahul Pandharipande. \n\n\n\n11:45am – 01:30pm\nLunch\n\n\n01:30pm – 02:15pm\nChin-Lung Wang\nTitle: A blowup formula in quantum cohomology \nAbstract: We study analytic continuations of quantum cohomology $QH(Y)$ under a blowup $\phi: Y \to X$ of complex projective manifolds along the extremal ray variable $q^{\ell}$. Under $H(Y) = \phi^* H(X) \oplus K$ where $K = \ker \phi_*$\, we show that (i) the restriction of quantum product along the $\phi^*H(X)$ direction\, denoted by $QH(Y)_X$\, is meromorphic in $x := 1/q^\ell$\, (ii) $K$ deforms uniquely to a quantum ideal $\widetilde K$ in $QH(Y)_X$\, (iii) the quotient ring $QH(Y)_X/\widetilde K$ is regular over $x$\, and its restriction to $x = 0$ is isomorphic to $QH(X)$. This is a joint work (in progress) with Y.-P. Lee and H.-W. Lin.\n\n\n02:30pm – 03:15pm\nIvan Loseu\nTitle: Quantizations of nilpotent orbits and their Lagrangian subvarieties \nAbstract: I’ll report on some recent progress on classifying quantizations of the algebras of regular functions of nilpotent orbits (and their covers) in semisimple Lie algebras\, as well as the classification of quantizations of certain Lagrangian subvarieties. An ultimate goal here is to understand the classification of unitary representations of real semisimple Lie groups.\n\n\n03:15pm – 03:45pm\nBreak\n\n\n03:45pm – 04:30pm\nMatt Kerr*\nTitle: $K_2$ and quantum curves \nAbstract: The basic objects for this talk are motives consisting of a curve together with a $K_2$ class\, and their mixed Hodge-theoretic invariants. \nMy main objective will be to explain a connection (recently proved in joint work with C. Doran and S. Sinha Babu) between (i) Hodge-theoretically distinguished points in the moduli of such motives and (ii) eigenvalues of operators on L^2(R) obtained by quantizing the equations of the curves. \nBy local mirror symmetry\, this gives evidence for a conjecture in topological string theory (due to M. Marino\, A. Grassi\, and others) relating enumerative invariants of toric CY 3-folds to spectra of quantum curves.\n\n\n04:45pm – 05:30pm\nFlor Orosz Hunziker\nTitle: Tensor structures associated to the N=1 super Virasoro algebra \nAbstract:  We have recently shown that there is a natural category of representations associated to the N=1 super Virasoro vertex operator algebras that have braided tensor structure. We will describe this category and discuss the problem of establishing its rigidity at particular central charges. This talk is based on joint work in progress with Thomas Creutzig\, Robert McRae and Jinwei Yang.\n\n\n\n  \n  \n  \n11/30 (Wednesday) \n\n\n\n08:30am – 09:00am\nRefreshments\n\n\n09:00am – 09:45am\nTomoyuki Arakawa\nTitle: 4D/2D duality and representation theory \nAbstract: This talk is about the 4D/2D duality discovered by Beem et al. rather recently in physics. It associates a vertex operator algebra (VOA) to any 4-dimensional superconformal field theory\, which is expected to be a complete invariant of thl theory. The VOAs appearing in this manner may be regarded as chiralization of various symplectic singularities and their representations are expected to be closely related with the Coulomb branch of the 4D theory. I will talk about this remarkable 4D/2D duality from a representation theoretic perspective.\n\n\n10:00am – 10:45am\nShashank Kanade\nTitle: Combinatorics of principal W-algebras of type A \nAbstract: The combinatorics of principal W_r(p\,p’) algebras of type A is controlled by cylindric partitions. However\, very little seems to be known in general about fermionic expressions for the corresponding characters. Welsh’s work explains the case of Virasoro minimal models W_2(p\,p’). Andrews\, Schilling and Warnaar invented and used an A_2 version of the usual (A_1) Bailey machinery to give fermionic characters (up to a factor of (q)_\infty) of some\, but not all\, W_3(3\,p’) modules. In a recent joint work with Russell\, we have given a complete set of conjectures encompassing all of the remaining modules for W_3(3\,p’)\, and proved our conjectures for small values of p’. In another direction\, characters of W_r(p\,p’) algebras also arise as appropriate limits of certain sl_r coloured Jones invariants of torus knots T(p\,p’)\, and we expect this to provide further insights on the underlying combinatorics.\n\n\n11:00am – 11:45am\nGufang Zhao\nTitle: Quasimaps to quivers with potentials \nAbstract: This talk concerns non-compact GIT quotient of a vector space\, in the presence of an abelian group action and an equivariant regular function (potential) on the quotient. We define virtual counts of quasimaps from prestable curves to the critical locus of the potential. The construction borrows ideas from the theory of gauged linear sigma models as well as recent development in shifted symplectic geometry and Donaldson-Thomas theory of Calabi-Yau 4-folds. Examples of virtual counts arising from quivers with potentials are discussed. This is based on work in progress\, in collaboration with Yalong Cao.\n\n\n11:45am – 01:30pm\nGroup Photo\, Lunch\n\n\n01:30pm – 02:15pm\nYaping Yang\nTitle: Cohomological Hall algebras and perverse coherent sheaves on toric Calabi-Yau 3-folds \nAbstract: Let X be a smooth local toric Calabi-Yau 3-fold. On the cohomology of the moduli spaces of certain sheaves on X\, there is an action of the cohomological Hall algebra (COHA) of Kontsevich and Soibelman via “raising operators”. I will discuss the “double” of the COHA that acts on the cohomology of the moduli space by adding the “lowering operators”. We associate a root system to X. The double COHA is expected to be the shifted Yangian of this root system. We also give a prediction for the shift in terms of an intersection pairing. We provide evidence of the aforementioned expectation in various examples. This is based on my joint work with M. Rapcak\, Y. Soibelman\, and G. Zhao\n\n\n02:30pm – 03:15pm\nFei Han\nTitle: Graded T-duality with H-flux for 2d sigma models \nAbstract: T-duality in string theory can be realised as a transformation acting on the worldsheet fields in the two-dimensional nonlinear sigma model. Bouwknegt-Evslin-Mathai established the T-duality in a background flux for the first time upon compactifying spacetime in one direction to a principal circle by constructing the T-dual maps transforming the twisted cohomology of the dual spacetimes. In this talk\, we will describe our recent work on how to promote the T-duality maps of Bouwknegt-Evslin-Mathai in two aspects. More precisely\, we will introduce (1) graded T-duality\, concerning the graded T-duality maps of all levels of twistings; (2) the 2-dimensional sigma model picture\, concerning the double loop space of spacetimes. This represents our joint work with Mathai.\n\n\n03:15pm – 3:45pm\nBreak\n\n\n03:45pm – 04:30pm\nMauricio Romo\nTitle: Networks and BPS Counting: A-branes view point \nAbstract: I will review the countings of BPS invariants via exponential/spectral networks and present an interpretation of this counting as a count of certain points in the moduli space of A-branes corresponding to degenerate Lagrangians.\n\n\n04:45pm – 05:30pm\nShinobu Hosono\nTitle: Mirror symmetry of abelian fibered Calabi-Yau manifolds with ρ = 2 \nAbstract: I will describe mirror symmetry of Calabi-Yau manifolds fibered by (1\,8)-polarized abelian surfaces\, which have Picard number two. Finding a mirror family over a toric variety explicitly\, I  observe that mirror symmetry of all related Calabi-Yau manifods arises from the corresponding boundary points\, which are not necessarily toric boundary points.  Calculating Gromov-Witten invariants up to genus 2\, I find that the generating functions are expressed elliptic (quasi-)modular forms\, which reminds us the modular anomaly equation found for elliptic surfaces. This talk is based on a published work with Hiromichi Takaki (arXiv:2103.08150).\n\n\n06:00pm\nBanquet @ Royal East Restaurant\, 782 Main St\, Cambridge\, MA 02139\n\n\n\n  \n12/1 (Thursday) \n\n\n\n08:30am – 09:00am\nRefreshments\n\n\n09:00am – 09:45am\nConan Nai Chung Leung*\nTitle: Quantization of Kahler manifolds \nAbstract: I will explain my recent work on relationships among geometric quantization\, deformation quantization\, Berezin-Toeplitz quantization and brane quantization.\n\n\n10:00am – 10:45am\nCuipo Jiang*\nTitle: Cohomological varieties associated to vertex operator algebras \nAbstract: We define and examine the cohomological variety of a vertex algebra\, a notion cohomologically dual to that of the associated variety\, which measures the smoothness of the associated scheme at the vertex point.  We study its basic properties. As examples\, we construct a closed subvariety of the cohomological variety for rational affine vertex operator algebras constructed from finite dimensional simple Lie algebras. We also determine the cohomological varieties of the simple Virasoro vertex operator algebras. These examples indicate that\, although the associated variety for a rational $C_2$-cofinite vertex operator algebra is always a simple point\, the cohomological variety can have as large a dimension as possible. This talk is based on joint work with Antoine Caradot and Zongzhu Lin.\n\n\n11:00am – 11:45am\nAnne Moreau*\nTitle: Action of the automorphism group on the Jacobian of Klein’s quartic curve \nAbstract: In a joint work with Dimitri Markouchevitch\, we prove that the quotient variety of the 3-dimensional Jacobian of the plane Klein quartic curve by its full automorphism group of order 336 is isomorphic to the 3-dimensional weighted projective space with weights 1\,2\,4\,7. \nThe latter isomorphism is a particular case of the general conjecture of Bernstein and Schwarzman suggesting that a quotient of the n-dimensional complex space by the action of an irreducible complex crystallographic group generated by reflections is a weighted projective space. \nIn this talk\, I will explain this conjecture and the proof of our result. An important ingredient is the computation of the Hilbert function of the algebra of invariant theta-functions on the Jacobian.\n\n\n11:45am – 11:50am\nClosing remarks\n\n\n11:50am\nFree discussions and departure\n\n\n\n* = Online speaker \nCMSA COVID-19 Policies \n 
URL:https://cmsa.fas.harvard.edu/event/representation-theory-calabi-yau-manifolds-and-mirror-symmetry/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Workshop
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Workshop_HMS_11.28.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221201T103000
DTEND;TZID=America/New_York:20221201T113000
DTSTAMP:20260410T201244
CREATED:20240301T084120Z
LAST-MODIFIED:20240301T084141Z
UID:10002888-1669890600-1669894200@cmsa.fas.harvard.edu
SUMMARY:Symmetry in quantum field theory and quantum gravity 1
DESCRIPTION:Speaker: Daniel Harlow (MIT) \nTitle: Symmetry in quantum field theory and quantum gravity 1 \nAbstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence.  These conjectures are 1) that there are no global symmetries in quantum gravity\, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist\, and 3) all internal gauge symmetries must be compact.  Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity\, which leads to interesting applications in various related fields.  These definitions will be the focus of the first talk\, while the second will apply them to AdS/CFT to prove conjectures 1-3).
URL:https://cmsa.fas.harvard.edu/event/12-1-2021-quantum-matter-in-mathematics-and-physics/
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-12.01.21-1544x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221202T110000
DTEND;TZID=America/New_York:20221202T120000
DTSTAMP:20260410T201244
CREATED:20230817T164654Z
LAST-MODIFIED:20240229T111029Z
UID:10001230-1669978800-1669982400@cmsa.fas.harvard.edu
SUMMARY:Compactness and Anticompactness Principles in Set Theory
DESCRIPTION:Member Seminar \nSpeaker: Alejandro Poveda \nTitle: Compactness and Anticompactness Principles in Set Theory \nAbstract: Several fundamental properties in Topology\, Algebra or Logic are expressed in terms of Compactness Principles.For instance\, a natural algebraic question is the following: Suppose that G is an Abelian group whose all small subgroups are free – Is the group G free? If the answer is affirmative one says that compactness holds; otherwise\, we say that compactness fails. Loosely speaking\, a compactness principle is anything that fits the following slogan: Suppose that M is a mathematical structure (a group\, a topological space\, etc) such that all of its small substructures N have certain property $\varphi$; then the ambient structure M has property $\varphi$\, as well. Oftentimes when these questions are posed for infinite sets the problem becomes purely set-theoretical and axiom-sensitive. In this talk I will survey the most paradigmatic instances of compactness and present some related results of mine. If time permits\, I will hint the proof of a recent result (joint with Rinot and Sinapova) showing that stationary reflection and the failure of the Singular Cardinal Hypothesis can co-exist. These are instances of two antagonist set-theoretic principles: the first is a compactness principle while the second is an anti-compactness one. This result solves a question by M. Magidor from 1982.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-12222/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221205T090000
DTEND;TZID=America/New_York:20221205T103000
DTSTAMP:20260410T201244
CREATED:20240215T100106Z
LAST-MODIFIED:20240819T150452Z
UID:10002734-1670230800-1670236200@cmsa.fas.harvard.edu
SUMMARY:Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers
DESCRIPTION:Quantum Matter Seminar \nSpeaker: Junkai Dong (Harvard University) \nTitle: Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers \nAbstract: Motivated by the higher Chern bands of twisted graphene multilayers\, we consider flat bands with arbitrary Chern number C with ideal quantum geometry. While C>1 bands differ from Landau levels\, we show that these bands host exact fractional Chern insulator (FCI) ground states for short range interactions. We show how to decompose ideal higher Chern bands into separate ideal bands with Chern number 1 that are intertwined through translation and rotation symmetry. The decomposed bands admit an SU(C) action that combines real space and momentum space translations. Remarkably\, they also allow for analytic construction of exact many-body ground states\, such as generalized quantum Hall ferromagnets and FCIs\, including flavor-singlet Halperin states and Laughlin ferromagnets in the limit of short-range interactions. In this limit\, the SU(C) action is promoted to a symmetry on the ground state subspace. While flavor singlet states are translation symmetric\, the flavor ferromagnets correspond to translation broken states and admit charged skyrmion excitations corresponding to a spatially varying density wave pattern. We confirm our analytic predictions with numerical simulations of ideal bands of twisted chiral multilayers of graphene\, and discuss consequences for experimentally accessible systems such as monolayer graphene twisted relative to a Bernal bilayer. \n 
URL:https://cmsa.fas.harvard.edu/event/qm_12522/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-Seminar-12.5.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221205T110000
DTEND;TZID=America/New_York:20221205T120000
DTSTAMP:20260410T201244
CREATED:20230730T184816Z
LAST-MODIFIED:20240110T050720Z
UID:10001156-1670238000-1670241600@cmsa.fas.harvard.edu
SUMMARY:IIB Explored - Dualities\, Bordisms\, and the Swampland
DESCRIPTION:Swampland Seminar \nLocation: Jefferson Physical Laboratory\, Seminar room J356 \nSpeaker: Markus Dierigl (LMU Munich) \nTitle: IIB Explored – Dualities\, Bordisms\, and the Swampland \nAbstract: In this talk I will discuss the application of the Cobordism Conjecture to type IIB supergravity with non-trivial duality bundle. Calculating the relevant bordism groups we find that they are highly non-trivial and would predict the presence of various global symmetries in the underlying theory. Since quantum gravity theories do not allow for global symmetries\, we discuss which defects need to be included to break them completely. Interestingly\, we find many backgrounds that are well-known in the F-theory literature\, such as [p\,q]-7-branes\, non-Higgsable clusters\, as well as S-folds and their generalizations to higher codimensions. Further including worldsheet reflections\, predicts the existence of a new non-supersymmetric 7-brane with interesting properties and applications\, which I will discuss in more detail.
URL:https://cmsa.fas.harvard.edu/event/swampland_12522/
LOCATION:Jefferson 356
CATEGORIES:Swampland Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Topological-Seminar-11.09.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221206T090000
DTEND;TZID=America/New_York:20221206T103000
DTSTAMP:20260410T201244
CREATED:20240215T094810Z
LAST-MODIFIED:20240819T150002Z
UID:10002729-1670317200-1670322600@cmsa.fas.harvard.edu
SUMMARY:Neutrino Masses from Generalized Symmetry Breaking
DESCRIPTION:Quantum Matter Seminar \nSpeaker: Sungwoo Hong (U Chicago & KAIST) \nTitle: Neutrino Masses from Generalized Symmetry Breaking \nAbstract: We explore generalized global symmetries in theories of physics beyond the Standard Model. Theories of Z′ bosons generically contain ‘non-invertible’ chiral symmetries\, whose presence indicates a natural paradigm to break this symmetry by an exponentially small amount in an ultraviolet completion. For example\, in models of gauged lepton family difference such as the phenomenologically well-motivated U(1)Lμ−Lτ\, there is a non-invertible lepton number symmetry which protects neutrino masses. We embed these theories in gauged non-Abelian horizontal lepton symmetries\, e.g. U(1)Lμ−Lτ⊂SU(3)H\, where the generalized symmetries are broken nonperturbatively by the existence of lepton family magnetic monopoles. In such theories\, either Majorana or Dirac neutrino masses may be generated through quantum gauge theory effects from the charged lepton Yukawas e.g. yν∼yτexp(−Sinst). These theories require no bevy of new fields nor ad hoc additional global symmetries\, but are instead simple\, natural\, and predictive: the discovery of a lepton family Z′ at low energies will reveal the scale at which Lμ−Lτ emerges from a larger gauge symmetry. \n 
URL:https://cmsa.fas.harvard.edu/event/qm_12622/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-Seminar-12.06.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221207T100000
DTEND;TZID=America/New_York:20221207T110000
DTSTAMP:20260410T201244
CREATED:20230705T075744Z
LAST-MODIFIED:20240216T091837Z
UID:10001134-1670407200-1670410800@cmsa.fas.harvard.edu
SUMMARY:Controlling Quantum Matter with Quantum Cavity Fields
DESCRIPTION:Topological Quantum Matter Seminar \nSpeaker: Vasil Rokaj (Harvard) \nTitle: Controlling Quantum Matter with Quantum Cavity Fields \nAbstract: Cavity modification of material properties and phenomena is a novel research field motivated by the advances in strong light-matter interactions [1]. For condensed matter systems it has been demonstrated experimentally that the transport properties of 2D materials can be modified via coupling to vacuum fields [2\,3]. While in polaritonic chemistry it has been shown that ground state chemical properties can be controlled with cavity fields [4]. In the first part of my talk\, I will present how the quantized cavity field can alter the conduction properties of a condensed matter system by focusing on the paradigmatic Sommerfeld model of the free electron gas [5]. The exact analytic solution of the Sommerfeld model in the cavity will be presented as well as its fundamental properties. Then\, in the second part of the talk\, I will focus on a many-particle system of cold ions in a harmonic trap coupled to the cavity field. I will show how this system couples collectively to the cavity and that hybrid states between light and matter\, known as polaritons\, emerge. The formation of polaritons leads to the modification of the properties of the cold ions and enhances the localization of the many-body wave function [6]. Connections to experiments will be discussed as well. \n[1] F. Garcia-Vidal\, C. Ciuti\, T. W. Ebbesen\, Science\, 373\, 178 (2021) \n[2] G. L. Paravicini-Bagliani et al.\, Nat. Phys. 15\, 186-190 (2019) \n[3] F. Appugliese et al.\, Science 375 (6584)\, 1030-1034 (2022) \n[4] T. W. Ebbesen\, Acc. Chem. Res. 49\, 11\, 2403–2412 (2016) \n[5] V. Rokaj\, M. Ruggenthaler\, F. G. Eich\, A. Rubio\, Phys. Rev. Research 4\, 013012 (2022) \n[6] V. Rokaj\, S.I. Mistakidis\, H.R. Sadeghpour\, arXiv:2207.03436 (2022)
URL:https://cmsa.fas.harvard.edu/event/tqms_12722/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Topological Quantum Matter Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Topological-Seminar-12.07.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221207T140000
DTEND;TZID=America/New_York:20221207T150000
DTSTAMP:20260410T201244
CREATED:20230808T185642Z
LAST-MODIFIED:20240116T060930Z
UID:10001215-1670421600-1670425200@cmsa.fas.harvard.edu
SUMMARY:How do Transformers reason? First principles via automata\, semigroups\, and circuits
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Cyril Zhang\, Microsoft Research \nTitle: How do Transformers reason? First principles via automata\, semigroups\, and circuits \nAbstract: The current “Transformer era” of deep learning is marked by the emergence of combinatorial and algorithmic reasoning capabilities in large sequence models\, leading to dramatic advances in natural language understanding\, program synthesis\, and theorem proving. What is the nature of these models’ internal representations (i.e. how do they represent the states and computational steps of the algorithms they execute)? How can we understand and mitigate their weaknesses\, given that they resist interpretation? In this work\, we present some insights (and many further mysteries) through the lens of automata and their algebraic structure. \nSpecifically\, we investigate the apparent mismatch between recurrent models of computation (automata & Turing machines) and Transformers (which are typically shallow and non-recurrent). Using tools from circuit complexity and semigroup theory\, we characterize shortcut solutions\, whereby a shallow Transformer with only o(T) layers can exactly replicate T computational steps of an automaton. We show that Transformers can efficiently represent these shortcuts in theory; furthermore\, in synthetic experiments\, standard training successfully finds these shortcuts. We demonstrate that shortcuts can lead to statistical brittleness\, and discuss mitigations. \nJoint work with Bingbin Liu\, Jordan Ash\, Surbhi Goel\, and Akshay Krishnamurthy.
URL:https://cmsa.fas.harvard.edu/event/nt-12722/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/12.07.2022.png
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221207T153000
DTEND;TZID=America/New_York:20221207T163000
DTSTAMP:20260410T201245
CREATED:20230807T165823Z
LAST-MODIFIED:20240110T091938Z
UID:10001187-1670427000-1670430600@cmsa.fas.harvard.edu
SUMMARY:Fourier quasicrystals and stable polynomials
DESCRIPTION:Probability Seminar \nNote location change: Science Center Room 300H \nSpeaker: Lior Alon (MIT) \nTitle: Fourier quasicrystals and stable polynomials \nAbstract: The Poisson summation formula says that the countable sum of exp(int)\, over all integers n\, vanishes as long as t is not an integer multiple of 2 pi. Can we find a non-periodic discrete set A\, such that the sum of exp(iat)\, over a in A\, vanishes for all t outside of a discrete set? The surprising answer is yes. Yves Meyer called the atomic measure supported on such a set a crystalline measure. Crystalline measures provide another surprising connection between physics (quasicrystals) and number theory (the zeros of the Zeta and L functions under GRH). A recent work of Pavel Kurasov and Peter Sarnak provided a construction of crystalline measures with ‘good’ convergence (Fourier quasicrystals) using stable polynomials\, a family of multivariate polynomials that were previously used in proving the Lee-Yang circle theorem and the Kadison-Singer conjecture. After providing the needed background\, I will discuss a recent work in progress with Cynthia Vinzant on the classification of these Kurasov-Sarnak measures and their supporting sets. We prove that these sets have well-defined gap distributions. We show that each Kurasov-Sarnak measure decomposes according to the irreducible decomposition of its associated polynomial\, and the measures associated with each irreducible factor is either supported on an arithmetic progression\, or its support has a bounded intersection with any arithmetic progression. Finally\, we construct random Kurasov-Sarnak measures with gap distribution as close as we want to the eigenvalues spacing of a random unitary matrix. \nBased on joint work with Pravesh Kothari.
URL:https://cmsa.fas.harvard.edu/event/probability-12722/
LOCATION:Harvard Science Center\, 1 Oxford Street\, Cambridge\, MA\, 02138
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-12.07.22.png
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221208T093000
DTEND;TZID=America/New_York:20221208T103000
DTSTAMP:20260410T201245
CREATED:20230817T182138Z
LAST-MODIFIED:20240228T111217Z
UID:10001250-1670491800-1670495400@cmsa.fas.harvard.edu
SUMMARY:A new proof for the nonlinear stability of slowly-rotating Kerr-de Sitter
DESCRIPTION:General Relativity Seminar \n\nSpeaker: Allen Fang (Princeton) \nTitle: A new proof for the nonlinear stability of slowly-rotating Kerr-de Sitter \nAbstract: The nonlinear stability of the slowly-rotating Kerr-de Sitter family was first proven by Hintz and Vasy in 2016 using microlocal techniques. In my talk\, I will present a novel proof of the nonlinear stability of slowly-rotating Kerr-de Sitter spacetimes that avoids frequency-space techniques outside of a neighborhood of the trapped set. The proof uses vector field techniques to uncover a spectral gap corresponding to exponential decay at the level of the linearized equation. The exponential decay of solutions to the linearized problem is then used in a bootstrap proof to conclude nonlinear stability.
URL:https://cmsa.fas.harvard.edu/event/gr_12822/
LOCATION:Virtual
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-12.08.22-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221208T130000
DTEND;TZID=America/New_York:20221208T140000
DTSTAMP:20260410T201245
CREATED:20230824T180707Z
LAST-MODIFIED:20240215T094558Z
UID:10001316-1670504400-1670508000@cmsa.fas.harvard.edu
SUMMARY:Self-organization of motile cells by quorum-sensing or chemotactic interactions
DESCRIPTION:Active Matter Seminar\n\nSpeaker: Julien Tailleur (MIT) \nTitle: Self-organization of motile cells by quorum-sensing or chemotactic interactions \nAbstract: Equilibrium statistical mechanics tells us how to control the self-assembly of passive materials by tuning the competition between energy and entropy to achieve desired states of organization. Out of equilibrium\, no such principles apply and self-organization principles are scarce. Active matter describes systems in which individual units dissipate energy to exert forces on their environment. Dissipation and injection of energy are then disconnected at the microscopic scale\, hence driving the system strongly out of thermal equilibrium. This leads to a phenomenology markedly different from that of equilibrium systems\, such as the emergence of dense phases in the absence of cohesive attractive forces\, but it also leaves us without guiding principles to understand the self-organization of active matter. In this talk\, I will review the progress which has been made over the past ten years to control the organization of self-propelled agents using motility control\, either externally or through interactions. I will show that generic principles apply and illustrate the theoretical developments presented in the talk using recent experiments on the motility-induced self-organization of bacterial mixtures.
URL:https://cmsa.fas.harvard.edu/event/am-12822/
CATEGORIES:Active Matter Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Active-Matter-Seminar-12.08.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221212T090000
DTEND;TZID=America/New_York:20221212T103000
DTSTAMP:20260410T201245
CREATED:20240215T095743Z
LAST-MODIFIED:20240819T150302Z
UID:10002733-1670835600-1670841000@cmsa.fas.harvard.edu
SUMMARY:Non-Invertible Symmetries from Holography and Branes
DESCRIPTION:Quantum Matter Seminar \nSpeaker: Federico Bonetti (Oxford) \nTitle: Non-Invertible Symmetries from Holography and Branes \nAbstract:  The notion of global symmetry in quantum field theory (QFT) has witnessed dramatic generalizations in the past few years. One of the most exciting developments has been the identification of 4d QFTs possessing non-invertible symmetries\, i.e. global symmetries whose generators exhibit fusion rules that are not group-like. In this talk\, I will discuss realizations of non-invertible symmetries in string theory and holography. As a concrete case study\, I will consider the Klebanov-Strassler setup for holographic confinement in Type IIB string theory. The global symmetries of the holographic 4d QFT (both invertible and non-invertible) can be accessed by studying the topological couplings of the low-energy effective action of the dual 5d supergravity theory. Moreover\, non-invertible symmetry defects can be realized in terms of D-branes. The D-brane picture captures non-trivial aspects of the fusion of non-invertible symmetry defects\, and of their action on extended operators of the 4d QFT.
URL:https://cmsa.fas.harvard.edu/event/qm_121222/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-12.12.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221220T090000
DTEND;TZID=America/New_York:20221220T103000
DTSTAMP:20260410T201245
CREATED:20240215T105412Z
LAST-MODIFIED:20240819T150130Z
UID:10002746-1671526800-1671532200@cmsa.fas.harvard.edu
SUMMARY:Phase Fluctuations in Two-Dimensional Superconductors and Pseudogap Phenomenon
DESCRIPTION:Quantum Matter Seminar \nSpeaker: Yang Qi (Fudan) \nTitle: Phase Fluctuations in Two-Dimensional Superconductors and Pseudogap Phenomenon \nAbstract: We study the phase fluctuations in the normal state of a general two-dimensional (2d) superconducting system with s-wave pairing. The effect of phase fluctuations of the pairing fields can be dealt with perturbatively using disorder averaging\, after we treat the local superconducting order parameter as a static disordered background. It is then confirmed that the phase fluctuations above the 2d Berenzinskii-Kosterlitz-Thouless (BKT) transition give birth to the pseudogap phenomenon\, leading to a significant broadening of the single-particle spectral functions. Quantitatively\, the broadening of the spectral weights at the BCS gap is characterized by the ratio of the superconducting coherence length and the spatial correlation length of the superconducting pairing order parameter. Our results are tested on the attractive-U fermion Hubbard model on the square lattice\, using unbiased determinant quantum Monte Carlo method and stochastic analytic continuation. We also apply our method to 2d superconductors with d-wave pairing and observe that the phase fluctuations may lead to Fermi-arc phenomenon above the BKT transition.
URL:https://cmsa.fas.harvard.edu/event/qm_122022/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-Seminar-12.20.22.png
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END:VCALENDAR