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October  1  2  MATHEMATICAL PICTURE LANGUAGE SEMINAR: Quantum algorithms for topological and geometric analysis of data
Speaker: Seth Lloyd – MIT 9:30 AM10:30 AM November 2, 2021
Quantum computers exhibit a variety of exponential enhancements over classical computers for performing linear algebraic operations. This talk reviews quantum algorithms for algebraic topology: I show how the central problem of simplicial homology can be mapped into a quantum computation, with an exponential speedup over classical algorithms. The method is particularly well adapted to topological analysis of large data sets, including financial time series analysis.
https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09  CMSA EVENT: CMSA Algebraic Geometry in String Theory Seminar: GaussManin connection in disguise: Quasi Jacobi forms of index zero
Speaker: Hossein Movasati – IMPA 10:30 AM11:30 AM November 2, 2021
We consider the moduli space of abelian varieties with two marked points and a frame of the relative de Rham cohomology with boundary at these points compatible with its mixed Hodge structure. Such a moduli space gives a natural algebrogeometric framework for higher genus quasi Jacobi forms of index zero and their differential equations which are given as vector fields. In the case of elliptic curves we compute explicitly the GaussManin connection and such vector fields. This is a joint work with J. Cao and R. Villaflor. (arXiv:2109.00587)
https://harvard.zoom.us/j/98781914555?pwd=bmVzZGdlRThyUDREMExab20ybmg1Zz09  HARVARDMIT ALGEBRAIC GEOMETRY SEMINAR: DTinvariants from nonarchimedean integrals
Speaker: Dimitri Wyss – EPFL 3:00 PM4:00 PM November 2, 2021
Let $M(\beta,\chi)$ be the moduli space of onedimensional semistable sheaves on a del Pezzo surface $S$, supported on an ample curve class $\beta$ and with Eulercharacteristic $\chi$. Working over a nonarchimedean local field $F$, we define a natural measure on the $F$points of $M(\beta,\chi)$. We prove that the integral of a certain gerbe on $M(\beta,\chi)$ with respect to this measure is independent of $\chi$ if $S$ is toric. A recent result of MaulikShen then implies that these integrals compute the DonaldsonThomas invariants of $M(\beta,\chi)$. A similar result holds for suitably twisted Higgs bundles. This is joint work with Francesca Carocci and Giulio Orecchia.
 3  CMSA EVENT: CMSA Colloquium: Hitchin map as spectrum of equivariant cohomology
Speaker: Tamás Hausel – IST Austria 9:30 AM10:30 AM November 3, 2021
We will explain how to model the Hitchin integrable system on a certain Lagrangian upward flow as the spectrum of equivariant cohomology of a Grassmannian.  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics Seminar: NonInvertible Duality Defects in 3+1 Dimensions
Speaker: Clay Cordova – University of Chicago 2:00 PM3:30 PM November 3, 2021
For any quantum system invariant under gauging a higherform global symmetry, we construct a noninvertible topological defect by gauging in only half of spacetime. This generalizes the KramersWannier duality line in 1+1 dimensions to higher spacetime dimensions. We focus on the case of a oneform symmetry in 3+1 dimensions, and determine the fusion rule. From modular invariance and a direct analysis of oneform symmetry protected topological phases, we show that the existence of certain kinds of duality defects is intrinsically incompatible with a trivially gapped phase. By further assuming timereversal symmetry, we find that the presence of certain duality defects implies that the lowenergy phase has to be gapless unless the oneform symmetry is spontaneously broken. We give an explicit realization of this duality defect in the free Maxwell theory where the duality defect is realized by a ChernSimons coupling between the gauge fields from the two sides. *note special time* —– Subscribe to Harvard CMSA seminar videos (more to be uploaded): https://www.youtube.com/channel/UCBmPOOK1sa8T1oX_9aVhAg/playlists https://www.youtube.com/channel/UCM06KiUOw1vRrmvD8U274Ww  CMSA EVENT: CMSA New Technologies in Mathematics Seminar:When Computer Algebra Meets Satisfiability: A New Approach to Combinatorial Mathematics
Speaker: Curtis Bright and Vijay Ganesh – School of Computer Science, University of Windsor / Dept. of Electrical and Computer Engineering, University of Waterloo 2:00 PM3:00 PM November 3, 2021
Solvers for the Boolean satisfiability (SAT) problem have been increasingly used to resolve problems in mathematics due to their excellent search algorithms. This talk will describe a new method for mathematical search that couples SAT solvers with computer algebra systems (CAS), thereby combining the expressiveness of CASs with the search power of SAT solvers. This paradigm has led to a number of results on longstanding mathematical questions such as the first computerverifiable resolution of Lam’s problem and the discovery of a new infinite class of Williamson matrices.
https://harvard.zoom.us/j/99651364593?pwd=Q1R0RTMrZ2NZQjg1U1ZOaUYzSE02QT09  CMSA EVENT: CMSA New Technologies in Mathematics Seminar: When Computer Algebra Meets Satisfiability: A New Approach to Combinatorial Mathematics
Speaker: Curtis Bright and Vijay Ganesh – School of Computer Science, University of Windsor / Dept. of Electrical and Computer Engineering, University of Waterloo 2:00 PM3:00 PM November 3, 2021
Solvers for the Boolean satisfiability (SAT) problem have been increasingly used to resolve problems in mathematics due to their excellent search algorithms. This talk will describe a new method for mathematical search that couples SAT solvers with computer algebra systems (CAS), thereby combining the expressiveness of CASs with the search power of SAT solvers. This paradigm has led to a number of results on longstanding mathematical questions such as the first computerverifiable resolution of Lam’s problem and the discovery of a new infinite class of Williamson matrices.
https://harvard.zoom.us/j/99651364593?pwd=Q1R0RTMrZ2NZQjg1U1ZOaUYzSE02QT09  NUMBER THEORY SEMINAR: Special cycles for unitary Shtukas and modularity
Speaker: Zhiwei Yun – MIT 3:00 PM4:00 PM November 3, 2021 1 Oxford Street, Cambridge, MA 02138 USA
We define a generating series of algebraic cycles on the moduli stack of unitary Shtukas and conjecture that it is a Chowgroup valued automorphic form. This is a function field analogue of the special cycles defined by Kudla and Rapoport, but with an extra degree of freedom namely the number of legs of the Shtukas. I will talk about several pieces of evidence for the conjecture. This is joint work with Tony Feng and Wei Zhang.  OPEN NEIGHBORHOOD SEMINAR: The postgenomic era, as viewed by a mathematician
Speaker: Ronen Mukamel – Harvard Medical School 4:30 PM5:30 PM November 3, 2021 1 Oxford Street, Cambridge, MA 02138 USA
Recent technological developments now allow for the accurate, high resolution measurement of millions of human genomes. I will describe some of the challenges and opportunities of this postgenomic era, and how these technologies stand poised to revolutionize our understanding of human biology and human health.
 4  CMSA EVENT: CMSA Interdisciplinary Science Seminar: Exploring Invertibility in Image Processing and Restoration
Speaker: Qifeng Chen – The Hong Kong University of Science and Technology 9:00 AM10:00 AM November 4, 2021
Today’s smartphones have enabled numerous stunning visual effects from denoising to beautification, and we can share highquality JPEG images easily on the internet, but it is still valuable for photographers and researchers to keep the original raw camera data for further postprocessing (e.g., retouching) and analysis. However, the huge size of raw data hinders its popularity in practice, so can we almost perfectly restore the raw data from a compressed RGB image and thus avoid storing any raw data? This question leads us to design an invertible image signal processing pipeline. Then we further explore invertibility in other image processing and restoration tasks, including image compression, reversible image conversion (e.g., imagetovideo conversion), and embedding novel views in a single JPEG image. We demonstrate that customized invertible neural networks are highly effective in these inherently noninvertible tasks.
Zoom ID: 950 2372 5230 (Password: cmsa)  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics Seminar: Fusion Category Symmetries in Quantum Field Theory
Speaker: Yifan Wang – NYU 10:30 AM12:00 PM November 4, 2021
Topological defects provide a modern perspective on symmetries in quantum field theory. They generalize the familiar invertible symmetries described by groups to noninvertible symmetries described by fusion categories. Such generalized symmetries are ubiquitous in quantum field theory and provide new constraints on renormalization group flows and the IR phase diagram. In this talk I’ll review some recent progress in identifying and understanding fusion category symmetries in 1+1d conformal field theories. Time permitting, I’ll also comment on higher dimensional generalizations. —– Subscribe to Harvard CMSA seminar videos (more to be uploaded): https://www.youtube.com/channel/UCBmPOOK1sa8T1oX_9aVhAg/playlists https://www.youtube.com/channel/UCM06KiUOw1vRrmvD8U274Ww —– Subscribe to Harvard CMSA seminar videos (more to be uploaded): https://www.youtube.com/channel/UCBmPOOK1sa8T1oX_9aVhAg/playlists https://www.youtube.com/channel/UCM06KiUOw1vRrmvD8U274Ww
—– Subscribe to Harvard CMSA seminar videos (more to be uploaded): https://www.youtube.com/channel/UCBmPOOK1sa8T1oX_9aVhAg/playlists https://www.youtube.com/channel/UCM06KiUOw1vRrmvD8U274Ww  ALGEBRAIC DYNAMICS SEMINAR: A transcendental birational dynamical degree
Speaker: Holly Krieger – University of Cambridge and Radcliffe Institute 4:00 PM6:00 PM November 4, 2021
I will speak about recent joint work with Bell, Diller, and Jonsson in which we refute a conjecture of BellonViallet by constructing (mostly) explicit examples of birational maps of projective 3space with transcendental dynamical degree, also known as algebraic entropy. The set of possible dynamical degrees for birational maps of projective space is known to be a countable set, with nearly all examples given by eigenvalues of integer matrices (and thus algebraic), yet we demonstrate the existence of infinitely many transcendental values in this set. The proof builds on previous work of BellDillerJonsson, combining the study of monomial maps of toric varieties with classical techniques from Diophantine approximation.
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7  8  9  MATHEMATICAL PICTURE LANGUAGE SEMINAR: Resonances for open quantum maps
Speaker: Semyon Dyatlov – MIT 9:30 AM10:30 AM November 9, 2021
Quantum maps are a popular model in physics: symplectic relations on tori are quantized to produce families of $N\times N$ matrices and the high energy limit corresponds to the large $N$ limit. They share a lot of features with more complicated quantum systems but are easier to study numerically. We consider open quantum baker’s maps, whose underlying classical systems have a hole allowing energy escape. The eigenvalues of the resulting matrices lie inside the unit disk and are a model for scattering resonances of more general chaotic quantum systems. We establish a spectral gap (that is, the spectral radius of the matrix is separated from 1 as $N\to\infty$) for all the systems considered. The proof relies on the notion of fractal uncertainty principle and uses the fine structure of the trapped sets, which in our case are given by Cantor sets, together with simple tools from harmonic analysis, algebra, combinatorics, and number theory. We also obtain a fractal Weyl upper bound for the number of eigenvalues in annuli. These results are illustrated by numerical experiments which also suggest some conjectures.
https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09  CMSA EVENT: CMSA Combinatorics, Physics and Probability Seminar: Gradient flows on totally nonnegative flag varieties
Speaker: Steven Karp – Universite du Quebec a Montreal, Laboratoire de combinatoire et d’informatique mathématique 9:30 AM10:30 AM November 9, 2021
One can view a partial flag variety in C^n as an adjoint orbit inside the Lie algebra of n x n skewHermitian 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.
https://harvard.zoom.us/j/94191911494?pwd=RnN3ZnIwcFYwd0QyT0MwZWVISmR5Zz09 Password: 1251442  CMSA EVENT: CMSA Algebraic Geometry in String Theory Seminar: Cosection localization for virtual fundamental classes of dmanifolds and DonaldsonThomas invariants of CalabiYau fourfolds
Speaker: Michail Savvas – University of Texas at Austin 10:30 AM11:30 AM November 9, 2021
Localization by cosection, first introduced by KiemLi in 2010, is one of the fundamental techniques used to study invariants in complex enumerative geometry. DonaldsonThomas (DT) invariants counting sheaves on CalabiYau fourfolds were first defined by BorisovJoyce in 2015 by combining derived algebraic and differential geometry. In this talk, we develop the theory of cosection localization for derived manifolds in the context of derived differential geometry of Joyce. As a consequence, we also obtain cosection localization results for (2)shifted symplectic derived schemes. This provides a cosection localization formalism for the BorisovJoyce DT invariant. As an immediate application, the stable pair invariants of hyperkähler fourfolds, constructed by MaulikCaoToda, vanish, as expected.
https://harvard.zoom.us/j/98781914555?pwd=bmVzZGdlRThyUDREMExab20ybmg1Zz09  HARVARDMIT ALGEBRAIC GEOMETRY SEMINAR: The Torelli map restricted to the hyperelliptic locus
Speaker: Aaron Landesman – Harvard University 3:00 PM4:00 PM November 9, 2021 1 Oxford Street, Cambridge, MA 02138 USA
The classical Torelli theorem states that the Torelli map, sending a curve to its Jacobian, is an injection on points. However, the Torelli map is not injective on tangent spaces at points corresponding to hyperelliptic curves. This leads to the natural question: If one restricts the Torelli map to the locus of hyperelliptic curves, is it then an immersion? We will give a complete answer to this question, starting out by describing the classical history.
 10  DIFFERENTIAL GEOMETRY SEMINAR: Joint HarvardCUHKYMSC Differential Geometry Seminar
Speaker: Richard Thomas – Department of Mathematics, Imperial College London 3:00 AM4:00 AM November 10, 2021 will speak on: Higher rank DT theory from rank 1
Fix a CalabiYau 3fold X. Its DT invariants count stable bundles and sheaves on X. The generalised DT invariants of JoyceSong count semistable bundles and sheaves on X. I will describe work with Soheyla Feyzbakhsh showing these generalised DT invariants in any rank r can be written in terms of rank 1 invariants. By the MNOP conjecture the latter are determined by the GW invariants of X. Along the way we also show they are determined by rank 0 invariants counting sheaves supported on surfaces in X. These invariants are predicted by Sduality to be governed by (vectorvalued, mock) modular forms. ******************************************************************** For details visit: http://www.ims.cuhk.edu.hk/cgibin/SeminarAdmin/bin/Web http://www.ims.cuhk.edu.hk/activities/seminar/jointdgseminar/ **Please note time is HONG KONG TIME** (3 am EST)  CMSA EVENT: CMSA Colloquium: Hypergraph decompositions and their applications
Speaker: Peter Keevash – University of Oxford 9:30 AM10:30 AM November 10, 2021
Many combinatorial objects can be thought of as a hypergraph decomposition, i.e. a partition of (the edge set of) one hypergraph into (the edge sets of) copies of some other hypergraphs. For example, a Steiner Triple System is equivalent to a decomposition of a complete graph into triangles. In general, Steiner Systems are equivalent to decompositions of complete uniform hypergraphs into other complete uniform hypergraphs (of some specified sizes). The Existence Conjecture for Combinatorial Designs, which I proved in 2014, states that, bar finitely many exceptions, such decompositions exist whenever the necessary `divisibility conditions’ hold. I also obtained a generalisation to the quasirandom setting, which implies an approximate formula for the number of designs; in particular, this resolved Wilson’s Conjecture on the number of Steiner Triple Systems. A more general result that I proved in 2018 on decomposing latticevalued vectors indexed by labelled complexes provides many further existence and counting results for a wide range of combinatorial objects, such as resolvable designs (the generalised form of Kirkman’s Schoolgirl Problem), whist tournaments or generalised Sudoku squares. In this talk, I plan to review this background and then describe some more recent and ongoing applications of these results and developments of the ideas behind them.  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics Seminar: Euclidean Majorana fermions in all dimensions, Bott periodicity and CPT
Speaker: Michael Stone – UIUC 10:00 AM11:30 AM November 10, 2021
*Note special time*
It is widely asserted that there is no such thing as a Majorana fermion in four Euclidean dimensions. This is a pity because we might like to study Majorana fermions using heatkernel regularized path integrals or by latticetheory computations, and these tools are only available in Euclidean signature. I will show that to the contrary there are natural definitions of Euclidean MajoranaFermion path integrals in all dimensions, and that key issue is not whether the gamma matrices are real or not, but whether the timereversal and/or charge conjugation matrices are symmetric or antisymmetric. —– Subscribe to Harvard CMSA seminar videos (more to be uploaded): https://www.youtube.com/channel/UCBmPOOK1sa8T1oX_9aVhAg/playlists https://www.youtube.com/channel/UCM06KiUOw1vRrmvD8U274Ww  NUMBER THEORY SEMINAR: The Galois action on symplectic Ktheory
Speaker: Tony Feng – MIT 3:00 PM4:00 PM November 10, 2021 1 Oxford Street, Cambridge, MA 02138 USA
A phenomenon underlying many remarkable results in number theory is the natural Galois action on the cohomology of symplectic groups of integers. In joint work with Soren Galatius and Akshay Venkatesh, we define a symplectic variant of algebraic Ktheory, which carries a natural Galois action for similar reasons. We compute this Galois action and characterize it in terms of a universality property, in the spirit of the Langlands philosophy.
 11  CMSA EVENT: CMSA Interdisciplinary Science Seminar: The Kervaire conjecture and the minimal complexity of surfaces
Speaker: Lvzhou Chen – University of Texas, Austin 9:00 AM10:00 AM November 11, 2021 We use topological methods to solve special cases of a fundamental problem in group theory, the Kervaire conjecture. The conjecture asserts that, for any nontrivial group G and any element w in the free product G*Z, the quotient (G*Z)/<<w>> is still nontrivial. We interpret this as a problem of estimating the minimal complexity (in terms of Euler characteristic) of surfaces in HNN extensions. This gives a conceptually simple proof of Klyachko’s theorem that confirms the Kervaire conjecture for any G torsionfree. I will also explain new results obtained using this approach. Zoom ID: 950 2372 5230 (Password: cmsa)  CMSA EVENT: CMSA Active Matter Seminar: Nonreciprocal matter: living chiral crystals
Speaker: Nikta Fakri – MIT 1:00 PM2:00 PM November 11, 2021
Active crystals are highly ordered structures that emerge from the nonequilibrium selforganization of motile objects, and have been widely studied in synthetic and bacterial active matter. In this talk, I will describe how swimming sea star embryos spontaneously assemble into chiral crystals that span thousands of spinning organisms and persist for tens of hours. Combining experiment, hydrodynamic theory, and simulations, we demonstrate that the formation, dynamics, and dissolution of these living crystals are controlled by the natural development of the embryos. Remarkably, due to nonreciprocal force and torque exchange between the embryos, the living chiral crystals exhibit selfsustained oscillations with dynamic signatures recently predicted to emerge in materials with odd elasticity.
https://harvard.zoom.us/j/96657833341 Password: cmsa  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics Seminar
Speaker: Jeongwan Haah – Microsoft 2:00 PM3:30 PM November 11, 2021
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14  15  16  MATHEMATICAL PICTURE LANGUAGE SEMINAR: Holographic Algorithms
Speaker: Leslie Valiant – Harvard University 9:30 AM10:30 AM November 16, 2021
When are two mathematical functions the same? One might think that this can be generally answered immediately from their definitions. However, functions may have numerous dissimilar alternative definitions. Fortunately, sameness can be often demonstrated systematically by certain linear mappings internal to the function definitions. These mappings, called holographic transformations, offer a powerful tool for showing that a function class is equivalent to one known to be efficiently computable, or, alternatively, that it is equivalent to one known to be in a completeness class suspected to be computationally intractable. We shall survey these ideas and their applications in computational complexity.
https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09  CMSA EVENT: CMSA Algebraic Geometry in String Theory Seminar: GromovWitten theory of complete intersections
Speaker: Pierrick Bousseau – ETH Zurich 9:30 AM10:30 AM November 16, 2021
I will describe an inductive algorithm computing GromovWitten invariants in all genera with arbitrary insertions of all smooth complete intersections in projective space. The main idea is to show that invariants with insertions of primitive cohomology classes are controlled by their monodromy and by invariants defined without primitive insertions but with imposed nodes in the domain curve. To compute these nodal GromovWitten invariants, we introduce the new notion of nodal relative GromovWitten invariants. This is joint work with Hülya Argüz, Rahul Pandharipande, and Dimitri Zvonkine (arxiv:2109.13323). https://harvard.zoom.us/j/98781914555?pwd=bmVzZGdlRThyUDREMExab20ybmg1Zz09 **note change in time**  CMSA EVENT: CMSA Combinatorics, Probability and Physics Seminar: A tale of two balloons
Speaker: Yinon Spinka – University British Columbia 12:30 PM1:30 PM November 16, 2021
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) 01 law, and generalize bounds on independent sets that are factors of IID on trees. Joint work with Omer Angel and Gourab Ray. https://harvard.zoom.us/j/99715031954?pwd=eVRvbERvUWtOWU9Vc3M2bjN3VndBQT09 Password: 1251442 *note unusual time*  HARVARDMIT ALGEBRAIC GEOMETRY SEMINAR: Limits of Hodge structures via Dmodules
Speaker: Qianyu Chen – Stony Brook University 3:00 PM4:00 PM November 16, 2021 1 Oxford Street, Cambridge, MA 02138 USA
It is wellknown that each cohomology group of a compact K\”ahler manifold carries a Hodge structure. If we consider a degeneration of compact K\”ahler manifolds over a disk then it is natural to ask how the Hodge structures of smooth fibers degenerate. When the degeneration only allows a reduced singular fiber with simple normal crossings (i.e. semistable), Steenbrink constructed the limit of Hodge structure algebraically. A consequence of the existence of the limit of Hodge structure is the local invariant cycle theorem: the cohomology classes invariant under monodromy action come from the cohomology classes of the total space. In this talk, I will try to explain a method using Dmodules to construct the limit of Hodge structure even when the degeneration is not semistable. Webpage: https://sites.google.com/view/harvardmitag
 17  CMSA EVENT: CMSA Colloquium: Curve counting on surfaces and topological strings
Speaker: Andrea Brini – University of Sheffield 9:30 AM10:30 AM November 17, 2021
Enumerative geometry is a venerable subfield of Mathematics, with roots dating back to Greek Antiquity and a present inextricably linked with developments in other domains. Since the early 90s, in particular, the interaction with String Theory has sent shockwaves through the subject, giving both unexpected new perspectives and a remarkably powerful, physicsmotivated toolkit to tackle several traditionally hard questions in the field. I will survey some recent developments in this vein for the case of enumerative invariants associated to a pair (X,D), with X a complex algebraic surface and D a singular anticanonical divisor in it. I will describe a surprising web of correspondences linking together several a priori distant classes of enumerative invariants associated to (X,D), including the log Gromov–Witten invariants of the pair, the Gromov–Witten invariants of an associated higher dimensional Calabi–Yau variety, the open Gromov–Witten invariants of certain special Lagrangians in toric Calabi–Yau threefolds, the Donaldson–Thomas theory of a class of symmetric quivers, and certain open and closed Gopakumar–Vafatype invariants. I will also discuss how these correspondences can be effectively used to provide a complete closedform solution to the calculation of all these invariants. https://harvard.zoom.us/j/95767170359 (Password: cmsa)  NUMBER THEORY SEMINAR: Arithmetic volumes of unitary Shimura varieties
Speaker: Benjamin Howard – Boston College 3:00 PM4:00 PM November 17, 2021 1 Oxford Street, Cambridge, MA 02138 USA
The integral model of a GU(n1,1) Shimura variety carries a natural metrized line bundle of modular forms. Viewing this metrized line bundle as a class in the codimension one arithmetic Chow group, one can define its arithmetic volume as an iterated selfintersection. We will show that this volume can be expressed in terms of logarithmic derivatives of Dirichlet Lfunctions at integer points, and explain the connection with the arithmetic SiegelWeil conjecture of KudlaRapoport. This is joint work with Jan Bruinier.  NUMBER THEORY SEMINAR: Arithmetic volumes of unitary Shimura varieties
Speaker: Benjamin Howard – Boston College 3:00 PM4:00 PM November 17, 2021 1 Oxford Street, Cambridge, MA 02138 USA
The integral model of a GU(n1,1) Shimura variety carries a natural metrized line bundle of modular forms. Viewing this metrized line bundle as a class in the codimension one arithmetic Chow group, one can define its arithmetic volume as an iterated selfintersection. We will show that this volume can be expressed in terms of logarithmic derivatives of Dirichlet Lfunctions at integer points, and explain the connection with the arithmetic SiegelWeil conjecture of KudlaRapoport. This is joint work with Jan Bruinier.  SEMINARS: Joint HarvardCUHKYMSC Differential Geometry Seminar
Speaker: Nick Sheridan – School of Mathematics, University of Edinburgh 4:00 PM5:00 PM November 17, 2021 will speak on: Quantum cohomology as a deformation of symplectic cohomology
Let X be a compact symplectic manifold, and D a normal crossings symplectic divisor in X. We give a criterion under which the quantum cohomology of X is the cohomology of a natural deformation of the symplectic cochain complex of X \ D. The criterion can be thought of in terms of the Kodaira dimension of X (which should be nonpositive), and the log Kodaira dimension of X \ D (which should be nonnegative). We will discuss applications to mirror symmetry. This is joint work with Strom Borman and Umut Varolgunes.
Zoom Link: https://cuhk.zoom.us/j/94377988344 Meeting ID: 943 7798 8344 Passcode: 20211117  OPEN NEIGHBORHOOD SEMINAR: Tales of random projections: where probability meets geometry
Speaker: Kavita Ramanan – Brown University 4:30 PM5:30 PM November 17, 2021 1 Oxford Street, Cambridge, MA 02138 USA In several areas of mathematics, including probability theory, asymptotic functional analysis, statistics and data science, one is interested in highdimensional objects, such as measures, data or convex bodies. One common theme is to try to understand what lowerdimensional projections can say about the corresponding highdimensional objects. I will describe several results that address this question, starting with classical results and moving on to more recent breakthroughs, my own research and some open questions. The talk will be selfcontained and accessible to undergraduate students. Website: https://people.math.harvard.edu/~ana/ons/
 18  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics Seminar: Exact Eigenstates in NonIntegrable Systems: A violation of the ETH
Speaker: B. Andrei Bernevig – Princeton University 2:30 PM4:00 PM November 18, 2021 We find that several nonintegrable systems exhibit some exact eigenstates that span the energy spectrum from lowest to the highest state. In the AKLT Hamiltonian and in several others “special” nonintegrable models, we are able to obtain the analytic expression of states exactly and to compute their entanglement spectrum and entropy to show that they violate the eigenstate thermalization hypothesis. This represented the first example of ETH violation in a nonintegrable system; these types of states have gained notoriety since then as quantum Scars in the context of Rydberg atoms experiments. We furthermore show that the structure of these states, in most models where they are found is that of an almost spectrum generating algebra which we call Restricted Spectrum Generating Algebra. This includes the (extended) Hubbard model, as well as some thintorus limits of Fractional Quantum Hall states. Yet in other examples, such as the recently found chiral nonlinear luttinger liquid, their structure is more complicated and not understood. —– Subscribe to Harvard CMSA seminar videos (more to be uploaded): https://www.youtube.com/channel/UCBmPOOK1sa8T1oX_9aVhAg/playlists https://www.youtube.com/channel/UCM06KiUOw1vRrmvD8U274Ww
—– Subscribe to Harvard CMSA seminar videos (more to be uploaded): https://www.youtube.com/channel/UCBmPOOK1sa8T1oX_9aVhAg/playlists https://www.youtube.com/channel/UCM06KiUOw1vRrmvD8U274Ww  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics Seminar: Exact Eigenstates in NonIntegrable Systems: A violation of the ETH
Speaker: B. Andrei Bernevig – Princeton University 2:30 PM4:00 PM November 18, 2021 We find that several nonintegrable systems exhibit some exact eigenstates that span the energy spectrum from lowest to the highest state. In the AKLT Hamiltonian and in several others “special” nonintegrable models, we are able to obtain the analytic expression of states exactly and to compute their entanglement spectrum and entropy to show that they violate the eigenstate thermalization hypothesis. This represented the first example of ETH violation in a nonintegrable system; these types of states have gained notoriety since then as quantum Scars in the context of Rydberg atoms experiments. We furthermore show that the structure of these states, in most models where they are found is that of an almost spectrum generating algebra which we call Restricted Spectrum Generating Algebra. This includes the (extended) Hubbard model, as well as some thintorus limits of Fractional Quantum Hall states. Yet in other examples, such as the recently found chiral nonlinear luttinger liquid, their structure is more complicated and not understood. —– Subscribe to Harvard CMSA seminar videos (more to be uploaded): https://www.youtube.com/channel/UCBmPOOK1sa8T1oX_9aVhAg/playlists https://www.youtube.com/channel/UCM06KiUOw1vRrmvD8U274Ww
—– Subscribe to Harvard CMSA seminar videos (more to be uploaded): https://www.youtube.com/channel/UCBmPOOK1sa8T1oX_9aVhAg/playlists https://www.youtube.com/channel/UCM06KiUOw1vRrmvD8U274Ww
 19  SEMINARS: HarvardMITMSR Combinatorics Seminar
Speaker: Grant Barkley – Harvard University 3:30 PM4:30 PM November 19, 2021 1 Oxford Street, Cambridge, MA 02138 USA will speak on: Extended weak order in affine type
The extended weak order is a partial order associated to a Coxeter system (W,S). It is the containment order on “biclosed” sets of positive roots in the (real) root system associated to W. When W is finite, this order coincides with the (right) weak order on W, but when W is infinite, the weak order on W is a proper order ideal in the extended weak order. It is wellknown that the weak order on W is a lattice if and only if W is finite. In contrast, it is a longstanding conjecture of Matthew Dyer that the extended weak order is a lattice for any W, which is open in the case that W is infinite. I will present joint work with David Speyer where we prove this conjecture for the affine Coxeter groups.
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21  22  23  CMSA EVENT: CMSA Combinatorics, Probability and Physics Seminar: Prague dimension of random graphs
Speaker: Lutz Warnke – UC San Diego 9:30 AM10:30 AM November 23, 2021
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 edgeprobabilities. The main new proof ingredient is a PippengerSpencer type edgecoloring result for random hypergraphs with large uniformities, i.e., edges of size O(log n). Password: 1251442  CMSA EVENT: CMSA Algebraic Geometry in String Theory Seminar: Wall crossing for moduli of stable log varieties
Speaker: Dori Bejleri – Harvard University 9:30 AM10:30 AM November 23, 2021
Stable log varieties or stable pairs (X,D) are the higher dimensional generalization of pointed stable curves. They form proper moduli spaces which compactify the moduli space of normal crossings, or more generally klt, pairs. These stable pairs compactifications depend on a choice of parameters, namely the coefficients of the boundary divisor D. In this talk, after introducing the theory of stable log varieties, I will explain the wallcrossing behavior that governs how these compactifications change as one varies the coefficients. I will also discuss some examples and applications. This is joint work with Kenny Ascher, Giovanni Inchiostro, and Zsolt Patakfalvi. https://harvard.zoom.us/j/98781914555?pwd=bmVzZGdlRThyUDREMExab20ybmg1Zz09
 24  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics Seminar: Multipartitioning topological phases and quantum entanglement
Speaker: Shinsei Ryu – Princeton University 10:30 AM12:00 PM November 24, 2021
We discuss multipartitions of the gapped ground states of (2+1)dimensional topological liquids into three (or more) spatial regions that are adjacent to each other and meet at points. By considering the reduced density matrix obtained by tracing over a subset of the regions, we compute various correlation measures, such as entanglement negativity, reflected entropy, and associated spectra. We utilize the bulkboundary correspondence to achieve such multipartitions and construct the reduced density matrix near the entangling boundaries. We find the fingerprints of topological liquid in these quantities, such as (universal pieces in) the scaling of the entanglement negativity, and a nontrivial distribution of the spectrum of the partially transposed density matrix.
https://harvard.zoom.us/j/977347126 Password: cmsa  DIFFERENTIAL GEOMETRY SEMINAR: Joint HarvardCUHKYMSC Differential Geometry Seminar
Speaker: Nick Sheridan – School of Mathematics, University of Edinburgh 4:00 PM5:00 PM November 24, 2021 will speak on: Quantum cohomology as a deformation of symplectic cohomology
Let X be a compact symplectic manifold, and D a normal crossings symplectic divisor in X. We give a criterion under which the quantum cohomology of X is the cohomology of a natural deformation of the symplectic cochain complex of X D. The criterion can be thought of in terms of the Kodaira dimension of X (which should be nonpositive), and the log Kodaira dimension of X D (which should be nonnegative). We will discuss applications to mirror symmetry. This is joint work with Strom Borman and Umut Varolgunes.
Zoom Link: https://cuhk.zoom.us/j/94377988344 Meeting ID: 943 7798 8344 Passcode: 20211117 **Rescheduled from 11/17/21**
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28  29  30  CMSA EVENT: CMSA Combinatorics, Probability and Physics Seminar: Resistance curvature – a new discrete curvature on graphs
Speaker: Karel Devriendt – University of Oxford, Mathematical Institute 9:30 AM10:30 AM November 30, 2021
The last few decades has 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 LinLuYau, Forman and Ollivier, that replicate important curvature theorems and have inspired applications in a variety of practical settings. In 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 “LinLuYau >= 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 closedform solution in the case of vertextransitive and path graphs. Finally, if time permits I will draw a connection with the geometry of hyperacute simplices, following the work of Miroslav Fiedler. This work was done in collaboration with Renaud Lambiotte.
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