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April  April  April  April  April  1  2 
3  4  CMSA EVENT: On integral Stokes matrices
Speaker: John Alexander Cruz Morales – Universidad Nacional de Colombia 10:30 AM11:30 AM May 4, 2020 We will revisit the computations of Stokes matrices for tt*structures done by Cecotti and Vafa in the 90’s in the context of Frobenius manifolds and the socalled monodromy identity. We will argue that those cases provide examples of noncommutative Hodge structures of exponential type in the sense of Katzarkov, Kontsevich and Pantev. via Zoom Video Conferencing: https://harvard.zoom.us/j/837429475  CMSA EVENT: Math Science Literature Lecture Series
Speaker: Joe Harris – Harvard University 1:00 PM2:30 PM May 4, 2020 Title: Rationality questions in algebraic geometry Abstract: Over the course of the history of algebraic geometry, rationality questions — motivated by both geometric and arithmetic problems — have often driven the subject forward. The rationality or irrationality of cubic hypersurfaces in particular have led to the development of abelian integrals (dimension one), birational geometry (dimension two) and Hodge theory (dimension 3). But there is still much we don’t understand about the condition of rationality — we don’t know the answer for cubic fourfolds, for example; and it’s not known whether rationality is an open condition or a closed condition in families. In this talk I’ll try to give an overview of the history of rationality and the current state of our knowledge. Written articles will accompany each lecture in this series and be available as part of the publication “History and Literature of Mathematical Science.” The schedule will be updated as talks are confirmed.  CMSA EVENT: Math Science Literature Lecture Series
Speaker: Simon Donaldson – Stony Brook University 3:00 PM4:30 PM May 4, 2020 Title: The ADHM construction of YangMills instantons Abstract: In 1978 (Physics Letters 65A) Atiyah, Hitchin, Drinfeld and Manin (ADHM) described a construction of the general solution of the YangMills instanton equations over the 4sphere using linear algebra. This was a major landmark in the modern interaction between geometry and physics, and the construction has been the scene for much research activity up to the present day. In this lecture we will review the background and the original ADHM proof, using Penrose’s twistor theory and results on algebraic vector bundles over projective 3space. As time permits, we will also discuss some further developments, for example the work of Nahm on monopoles and connections to Mukai duality for bundles over complex tori. Written articles will accompany each lecture in this series and be available as part of the publication “History and Literature of Mathematical Science.” The schedule will be updated as talks are confirmed.
 5  MATHEMATICAL PICTURE LANGUAGE SEMINAR: The information in a wave
Speaker: Roberto Longo – University of Rome Tor Vergata 10:00 AM11:00 AM May 5, 2020 Suppose that some information is transmitted by an undulatory signal. In Classical Field Theory, the stressenergy tensor provides the energymomentum density of the wave packet at any time. But, how to measure the information, or entropy, carried by the wavepacket in a certain region at given time? Surprisingly, one can answer the above (entirely classical) question by means of Operator Algebras and Quantum Field Theory. In fact, in second quantisation a wave packet gives rise to a sector of the KleinGordon Quantum Field Theory on the Rindler spacetimeW. The associated vacuum noncommutative entropy of the global von Neumann algebras of W is the entropy of the wave packet in the wedge region W of the Minkowski spacetime. One can then read this result in first quantisation via a notion of entropy of a vectorof a Hilbert space with respect to a real linear subspace. I give a path to the above results by an overview of some of basic results in Operator Algebras and Quantum Field Theory and of the relation with the Quantum Null Energy Inequality. via Zoom: https://harvard.zoom.us/j/779283357  CMSA EVENT: Math Science Literature Lecture Series
Speaker: Lydia Bieri – University of Michigan 11:00 AM12:30 PM May 5, 2020 Title: Black Hole Formation Abstract: Can black holes form through the focusing of gravitational waves? This was an outstanding question since the early days of general relativity. In his breakthrough result of 2008, Demetrios Chrstodoulou answered this question with “Yes!” In order to investigate this result, we will delve deeper into the dynamical mathematical structures of the Einstein equations. Black holes are related to the presence of trapped surfaces in the spacetime manifold. Christodoulou proved that in the regime of pure general relativity and for arbitrarily dispersed initial data, trapped surfaces form through the focusing of gravitational waves provided the incoming energy is large enough in a precisely defined way. The proof combines new ideas from geometric analysis and nonlinear partial differential equations as well as it introduces new methods to solve large data problems. These methods have many applications beyond general relativity. D. Christodoulou’s result was generalized in various directions by many authors. It launched mathematical activities going into multiple fields in mathematics and physics. In this talk, we will discuss the mathematical framework of the above question. Then we will outline the main ideas of Christodoulou’s result and its generalizations, show relations to other questions and give an overview of implications in other fields. Written articles will accompany each lecture in this series and be available as part of the publication “History and Literature of Mathematical Science.” The schedule will be updated as talks are confirmed.  CMSA EVENT: Math Science Literature Lecture Series
Speaker: Pavel Etingof – MIT 3:00 PM4:30 PM May 5, 2020 Title: Quantum Groups Abstract: The theory of quantum groups developed in mid 1980s from attempts to construct and understand solutions of the quantum YangBaxter equation, an important equation arising in quantum field theory and statistical mechanics. Since then, it has grown into a vast subject with profound connections to many areas of mathematics, such as representation theory, the Langlands program, lowdimensional topology, category theory, enumerative geometry, quantum computation, algebraic combinatorics, conformal field theory, integrable systems, integrable probability, and others. I will review some of the main ideas and examples of quantum groups and try to briefly describe some of the applications. Written articles will accompany each lecture in this series and be available as part of the publication “History and Literature of Mathematical Science.” The schedule will be updated as talks are confirmed.
 6  CMSA EVENT: CMSA Quantum Matter/Quantum Field Theory Seminar: Domain walls, anomalies, and deconfinement
Speaker: Erich Poppitz – University of Toronto 10:30 AM12:00 PM May 6, 2020 “Generalized” ’t Hooft anomalies impose new constraints on nonperturbative gauge dynamics. In confining theories with domain walls, they imply that quarks become liberated on the walls. The pertinent anomalyinflow arguments have a formal flavor and our goal here is to shed light on dynamical aspects of domainwall deconfinement. We use semiclassical means in a theoretically controlled setting. While these tools do not require supersymmetry, for brevity (and elegance) we focus this talk on 4d N=1 super YangMills theory. We review the setup and study the domain walls’ properties, along the way deriving the “N choose k” multiplicity of kwalls (connecting vacua k “steps” apart). We use the results to explain how quarks of all Nalities become deconfined on all kwalls. A similar picture applies to deconfinement on domain walls in QCD at theta=pi, adjoint QCD, and axion domain walls. We end with discussing a “wish list” of not wellunderstood aspects. (The bulk of this talk is based on 1909.10979, with Cox and Wong. However, it relies heavily on 1501.06773, with Anber and Sulejmanpasic, as well as 2001.03631, with Anber.) via Zoom Video Conferencing: https://harvard.zoom.us/j/977347126  CMSA EVENT: Math Science Literature Lecture Series
Speaker: Robert Griess – University of Michigan 1:00 PM2:30 PM May 6, 2020 Title: My life and times with the sporadic simple groups Abstract: Five sporadic simple groups were proposed in 19th century and 21 additional ones arose during the period 19651975. There were many discussions about the nature of finite simple groups and how sporadic groups are placed in mathematics. While in mathematics grad school at University of Chicago, I became fascinated with the unfolding story of sporadic simple groups. It involved theory, detective work and experiments. During this lecture, I will describe some of the people, important ideas and evolution of thinking about sporadic simple groups. Most should be accessible to a general mathematical audience. Article Written articles will accompany each lecture in this series and be available as part of the publication “History and Literature of Mathematical Science.” The schedule will be updated as talks are confirmed.  RANDOM MATRIX SEMINAR: Joint Dept. of Mathematics and CMSA Random Matrix and Probability Theory Seminar
Speaker: Antti Knowles – University of Geneva 2:00 PM3:00 PM May 6, 2020 will speak on: FIELD THEORY AS A LIMIT OF INTERACTING QUANTUM BOSE GASES We prove that the grand canonical Gibbs state of an interacting quantum Bose gas converges to the Gibbs measure of a nonlinear Schrödinger equation in the meanfield limit, where the density of the gas becomes large and the interaction strength is proportional to the inverse density. Our results hold in dimensions d = 1,2,3. For d > 1 the Gibbs measure is supported on distributions of negative regularity and we have to renormalize the interaction. The proof is based on a functional integral representation of the grand canonical Gibbs state, in which convergence to the meanfield limit follows formally from an infinitedimensional stationary phase argument for illdefined nonGaussian measures. We make this argument rigorous by introducing a whitenoisetype auxiliary field, through which the functional integral is expressed in terms of propagators of heat equations driven by timedependent periodic random potentials. Joint work with Jürg Fröhlich, Benjamin Schlein, and Vedran Sohinger. via Zoom: https://harvard.zoom.us/j/147308224  NUMBER THEORY SEMINAR: Symmetric power functoriality for modular forms
Speaker: James Newton – King’s College London 3:00 PM4:00 PM May 6, 2020 Langlands functoriality predicts the transfer of automorphic representations along maps of Lgroups. In particular, the symmetric power representation Symm^{n1} of GL(2) should give rise to a lifting from automorphic representations of GL(2) to automorphic representations of GL(n). I will discuss joint work with Jack Thorne, in which we prove the existence of all symmetric power lifts for many cuspidal Hecke eigenforms (for example, those of squarefree level).  INFORMAL GEOMETRY AND DYNAMICS SEMINAR: Coarse density of subsets of moduli space
Speaker: Benjamin Dozier – Stony Brook University 4:00 PM5:30 PM May 6, 2020 I will discuss coarse geometric properties of algebraic subvarieties of the moduli space of Riemann surfaces. In joint work with Jenya Sapir, we prove that such a subvariety is coarsely dense, with respect to either the Teichmuller or Thurston metric, iff it has full dimension in the moduli space. This work was motivated by an attempt to understand the geometry of the image of the projection map from a stratum of abelian or quadratic differentials to the moduli space of Riemann surfaces. As a corollary of our theorem, we characterize when this image is coarsely dense. A key part of the proof of the theorem involves comparing analytic plumbing coordinates at the DeligneMumford boundary to hyperbolic/extremal lengths of curves on nearby smooth surfaces. via Zoom: https://harvard.zoom.us/j/972495373
 7  CMSA EVENT: CMSA Condensed Matter/Math Seminar: Line Operators of Gauge Theories on NonSpin Manifolds
Speaker: Sahand Seifnashri – Stony Brook University 10:30 AM12:00 PM May 7, 2020 I will talk about line operators of fourdimensional gauge theories on nonspin manifolds. Line operators correspond to worldlines of heavy classical particles. Specifying the spectrum of such particles/lines, leads to distinct physical theories with different discrete theta parameters. We propose a formula for the spin of line operators (boson or fermion), and classify gauge theories with simple Lie algebras on nonspin manifolds. We also discuss the oneform symmetries of these theories and their ‘t Hooft anomalies. This talk is based on https://arxiv.org/abs/1911.00589, jointly with J.P. Ang and Konstantinos Roumpedakis. via Zoom Video Conferencing: https://harvard.zoom.us/s/977347126  DIFFERENTIAL GEOMETRY SEMINAR: Gauge theory for string algebroids
Speaker: Mario GarciaFernandez – ICMAT 4:00 PM5:00 PM May 7, 2020 We introduce a moment map picture for holomorphic string algebroids, a special class of holomorphic Courant algebroids introduced in arXiv:1807.10329. An interesting feature of our construction is that the Hamiltonian gauge action is described by means of Morita equivalences, as suggested by higher gauge theory. The zero locus of the moment map is given by the solutions of the Calabi system, a coupled system of equations which provides a unifying framework for the classical Calabi problem and the HullStrominger system. Our main results are concerned with the geometry of the moduli space of solutions, and assume a technical condition which is fulfilled in examples. We prove that the moduli space carries a pseudoKähler metric with Kähler potential given by the dilaton functional, a topological formula for the metric, and an infinitesimal DonaldsonUhlenbeckYau type theorem. Finally, we relate our topological formula to a physical prediction for the gravitino mass in order to obtain a new conjectural obstruction for the HullStrominger system. This is joint work with Roberto Rubio and Carl Tipler. *If you would like to attend, please email spicard@math.harvard.edu
 8  CMSA GENERAL RELATIVITY SEMINAR CMSA EVENT: The Jang equation and the positive mass theorem in the asymptotically hyperbolic setting
Speaker: Anna Sakovich – Uppsala University 11:00 AM12:00 PM May 8, 2020 We will be concerned with asymptotically hyperbolic ‘hyperboloidal’ initial data for the Einstein equations. Such initial data is modeled on the upper unit hyperboloid in Minkowski spacetime and consists of a Riemannian manifold (M, g) whose geometry at infinity approaches that of hyperbolic space, and a symmetric 2tensor K representing the second fundamental form of the embedding into spacetime, such that K > g at infinity. There is a notion of mass in this setting and a positive mass conjecture can be proven by spinor techniques. Other important results concern the case K = g, where the conjecture states that an asymptotically hyperbolic manifold whose scalar curvature is greater than or equal to that of hyperbolic space must have positive mass unless it is a hyperbolic space. In this talk, we will discuss how the method of Jang equation reduction, originally devised by Schoen and Yau to prove the positive mass conjecture for asymptotically Euclidean initial data sets, can be adapted to the asymptotically hyperbolic setting yielding a nonspinor proof of the respective positive mass conjecture. We will primarily focus on the case dim M = 3. via Zoom: https://harvard.zoom.us/j/579137378
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10  11  12  MATHEMATICAL PICTURE LANGUAGE SEMINAR: Euclidean quantum field theory: axioms and automorphic forms
Speaker: Werner Nahm – Dublin Institute for Advanced Study 10:00 AM11:00 AM May 12, 2020 The partition functions of euclidean quantum field theory can be described as functions on the moduli space of compact manifolds with Riemanninan metric that have few generalized derivatives. The conventional derivative with respect to the metric yields the energymomentum tensor. All fields can be described in an analogous fashion, but one has to introduce derivatives that can change the topology, The idea is tested for the (2,5) minimal model in twodimensional conformal field theory, where the partition function yields a natural generalization of the RogersRamanujan functions to arbitrary genus. via Zoom: https://harvard.zoom.us/j/779283357  DIFFERENTIAL GEOMETRY SEMINAR: Angular momentum in general relativity
Speaker: MuTao Wang – Columbia University 3:00 PM4:00 PM May 12, 2020 In the theory of general relativity, defining a valid notion of angular momentum is proven to be an even more challenging task than the definition of energy/mass. In this talk, I shall discuss this fundamental notion from the quasilocal level to null infinity. *If you would like to attend, please email spicard@math.harvard.edu
 13  CMSA EVENT: CMSA Quantum Matter/Quantum Field Theory Seminar: Continuum Quantum Field Theory for Fractons, Part I
Speaker: Nathan Seiberg – Institute for Advanced Study 10:30 AM12:00 PM May 13, 2020 Starting with a lattice system with local interactions at short distances, its longdistance behavior is captured by a continuum Quantum Field Theory (QFT). This description is universal, i.e. it is independent of most of the details of the microscopic system. Surprisingly, certain recently discovered lattice systems, and in particular models of fractons, seem to violate this general dogma. Motivated by this apparent contradiction, we will present exotic continuum QFTs that describe these systems. via Zoom Video Conferencing: https://harvard.zoom.us/s/977347126  RANDOM MATRIX SEMINAR: Joint Dept. of Mathematics and CMSA Random Matrix & Probability Theory Seminar
Speaker: Svan Bachmann – University of British Columbia 2:00 PM3:00 PM May 13, 2020 will speak on: Quantized quantum transport and Abelian anyons I’ll discuss recent developments in the study of quantized quantum transport, focussing on the quantum Hall effect. Beyond presenting an index taking rational values, and which is the Hall conductance in the adapted setting, I will explain how the index is intimately paired with the existence of quasiparticle excitations having nontrivial braiding properties. via Zoom: https://harvard.zoom.us/j/147308224  RANDOM MATRIX SEMINAR: Joint Dept. of Mathematics and CMSA Random Matrix & Probability Theory Seminar
Speaker: Svan Bachmann – University of British Columbia 2:00 PM3:00 PM May 13, 2020 will speak on: Quantized quantum transport and Abelian anyons I’ll discuss recent developments in the study of quantized quantum transport, focussing on the quantum Hall effect. Beyond presenting an index taking rational values, and which is the Hall conductance in the adapted setting, I will explain how the index is intimately paired with the existence of quasiparticle excitations having nontrivial braiding properties. via Zoom: https://harvard.zoom.us/j/147308224  NUMBER THEORY SEMINAR: Prismatic Dieudonné theory
Speaker: ArthurCesar Le Bras – CNRS/Paris13 3:00 PM4:00 PM May 13, 2020 I would like to explain a classification result for pdivisible groups, which unifies many of the existing results in the literature. The main tool is the theory of prisms and prismatic cohomology recently developed by Bhatt and Scholze. This is joint work with Johannes Anschütz.  INFORMAL GEOMETRY AND DYNAMICS SEMINAR: In the moduli space of Abelian differentials, big invariant subvarieties come from topology
Speaker: Paul Apisa – Yale University 4:00 PM5:30 PM May 13, 2020 It is a beautiful fact that any holomorphic oneform on a genus g Riemann surface can be presented as a collection of polygons in the plane with sides identified by translation. Since GL(2, R) acts on the plane (and polygons in it), it follows that there is an action of GL(2, R) on the collection of holomorphic oneforms on Riemann surfaces. This GL(2, R) action can also be described as the group action generated by scalar multiplication and Teichmuller geodesic flow. By work of McMullen in genus two, and Eskin, Mirzakhani, and Mohammadi in general, given any holomorphic oneform, the closure of its GL(2, R) orbit is an algebraic variety. While McMullen classified these orbit closures in genus two, little is known in higher genus. In the first part of the talk, I will describe the MirzakhaniWright boundary of an invariant subvariety (using mostly pictures) and a new result about reconstructing an orbit closure from its boundary. In the second part of the talk, I will define the rank of an invariant subvariety – a measure of size related to dimension – and explain why invariant subvarieties of rank greater than g/2 are loci of branched covers of lower genus Riemann surfaces. This will address a question of Mirzakhani. No background on Teichmuller theory or dynamics will be assumed. This material is work in progress with Alex Wright. Zoom: https://harvard.zoom.us/j/972495373
 14  CMSA EVENT: CMSA Condensed Matter/Math Seminar: Continuum Quantum Field Theory for Fractons, Part II
Speaker: ShuHeng Shao – Institute for Advanced Study 10:30 AM12:00 PM May 14, 2020 Starting with a lattice system with local interactions at short distances, its longdistance behavior is captured by a continuum Quantum Field Theory (QFT). This description is universal, i.e. it is independent of most of the details of the microscopic system. Surprisingly, certain recently discovered lattice systems, and in particular models of fractons, seem to violate this general dogma. Motivated by this apparent contradiction, we will present exotic continuum QFTs that describe these systems.  CMSA EVENT: CMSA Condensed Matter/Math Seminar: Continuum Quantum Field Theory for Fractons, Part II
Speaker: ShuHeng Shao – Institute for Advanced Study 10:30 AM12:00 PM May 14, 2020 Starting with a lattice system with local interactions at short distances, its longdistance behavior is captured by a continuum Quantum Field Theory (QFT). This description is universal, i.e. it is independent of most of the details of the microscopic system. Surprisingly, certain recently discovered lattice systems, and in particular models of fractons, seem to violate this general dogma. Motivated by this apparent contradiction, we will present exotic continuum QFTs that describe these systems.
 15  CMSA GENERAL RELATIVITY SEMINAR CMSA EVENT: Polynomial tails and conservation laws of waves on black holes
Speaker: Dejan Gajic – University of Cambridge 11:00 AM12:00 PM May 15, 2020 In 1972, Price suggested that inverse polynomial tails should be present in the latetime behaviour of scalar fields on Schwarzschild black holes. In the decades since, many features of these tails have been explored both numerically and heuristically in more general settings. The presence of polynomial tails in the context of the Einstein equations has important implications for the nature of singularities inside dynamical black holes and the latetime behaviour of gravitational waves observed at infinity. In this talk I will discuss recent work in collaboration with Y. Angelopoulos and S. Aretakis that establishes rigorously the existence of Price’s polynomial latetime tails in the context of scalar fields on black holes. I will moreover describe how latetime tails are connected to the existence of conservation laws for scalar fields in asymptotically flat spacetimes. via Zoom: https://harvard.zoom.us/j/579137378  CMSA EVENT: CMSA Mathematical Physics Seminar – Eigenstate thermalization and disorder averaging in gravity
Speaker: James Sully – University of British Columbia 1:00 PM2:00 PM May 15, 2020 It has long been believed that progress in understanding the black hole information paradox would require coming to terms with microscopic details of quantum gravity, beyond the reach of semiclassical effective field theory. In that light, one of the most surprising discoveries of the last year has been that signature features of the unitary evaporation of black holes can already be seen within effective field theory, albeit with the inclusion of ‘euclidean wormholes’. However, these novel contributions are best understood when the gravitational theory is not a single microscopic theory, but an average over many different theories. To save unitarity must we then simultaneously throw it away? I will explain how the same story can be recovered within a single microscopic theory by thinking carefully about the right effective theory for finitelifetime observers. Zoom: https://harvard.zoom.us/j/837429475
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17  18  19  MATHEMATICAL PICTURE LANGUAGE SEMINAR: Buildings, C*algebras and new higher dimensional analogues of the Thompson groups
Speaker: Alina Vdovina – University of Newcastle 10:00 AM11:00 AM May 19, 2020 We present explicit constructions of infinite families of CW complexes of arbitrary dimension with buildings as the universal covers. These complexes give rise to new families of C*algebras, classifiable by their Ktheory. The underlying building structure allows explicit computation of the Ktheory. We will also present new higher dimensional generalizations of the Thompson groups, which are usually difficult to distinguish, but the Ktheory of C*algebras gives new invariants to recognize nonisomorphic groups. We will also discuss new directions of generalizations to higher dimensions of the work of Vaughan Jones and his collaborators on connections of the Thomson’s group and Conformal Field Theory. via Zoom: https://harvard.zoom.us/j/779283357
 20  CMSA EVENT: CMSA Quantum Matter/Quantum Field Theory Seminar: Boundary States for Fermions: SPT Phases, RG Flows, and a Whole Bunch of Related Things
Speaker: David Tong – University of Cambridge 10:30 AM12:00 PM May 20, 2020 I’ll describe boundary conditions for fermions in d=1+1 dimensions, using the framework of boundary conformal field theory. I’ll explain how boundary states are classified by a mod 2 index, related to their SPT phase, describe how one can follow RG flows from one boundary state to another, and give a novel perspective on the Z_8 classification of d=2+1 SPT phases. via Zoom Video Conferencing: https://harvard.zoom.us/j/977347126  RANDOM MATRIX SEMINAR: Fluctuation Results for General Ising Models — Block Spin Ising Models and Random Interactions
Speaker: Kristina Schubert – TU Dortmund 2:00 PM3:00 PM May 20, 2020 Starting from the classical CurieWeiss model in statistical mechanics, we will consider more general Ising models. On the one hand, we introduce a block structure, i.e. a model of spins in which the vertices are divided into a finite number of blocks and where pair interactions are given according to their blocks. The magnetization is then the vector of magnetizations within each block, and we are interested in its behaviour and in particular in its fluctuations. On the other hand, we consider Ising models on ErdősRényi random graphs. Here, I will also present results on the fluctuations of the magnetization. Zoom: https://harvard.zoom.us/j/147308224
 21  CMSA EVENT: CMSA Condensed Matter/Math Seminar: Gaugeinvariant pathintegral measure for the overlap Weyl fermions in 16 of SO(10)
Speaker: Yoshio Kikukawa – Institute of Physics, the University of Tokyo 10:30 AM12:00 PM May 21, 2020 We consider a lattice formulation of the SO(10) chiral gauge theory with lefthanded Weyl fermions in the sixteen dimensional spinor representation 16 in the framework of the overlap fermion/the GinspargWilson relation. We propose a manifestly gaugeinvariant pathintegral measure for the lefthanded Weyl field on the lattice using all the components of the Dirac field, but the righthanded part of which is just saturated completely by inserting a suitable product of the SO(10)invariant ‘t Hooft vertices in terms of the righthanded field. The definition of the measure applies to all possible topological sectors. The measure possesses all required transformation properties under lattice symmetries and the induced effective action is CP invariant. The global U(1) symmetry of the lefthanded field is anomalous due to the nontrivial transformation of the measure, while that of the righthanded field is explicitly broken by the ’t Hooft vertices. There remains the issue of smoothness/locality in the gaugefield dependence of the Weyl fermion measure. We also discuss the relations of our formulation to other approaches/proposals to decouple the speciesdoubling/mirror degrees of freedom. Those include EichtenPreskill model, GinspargWilson Mirrorfermion model, Domain wall fermion model with the boundary EichtenPreskill term, and 4D Topological Insulator/Superconductor with gapped boundary phase. We clarify the similarity and the difference in technical detail and show that our proposal is a welldefined and unified testing ground for that basic question. via Zoom: https://harvard.zoom.us/j/977347126
 22  CMSA EVENT: Math Science Literature Lecture Series
Speaker: Ciprian Manolescu – Stanford University 12:30 PM2:00 PM May 22, 2020 Title: Fourdimensional topology Abstract: I will outline the history of fourdimensional topology. Some major events were the work of Donaldson and Freedman from 1982, and the introduction of the SeibergWitten equations in 1994. I will discuss these, and then move on to what has been done in the last 20 years, when the focus shifted to fourmanifolds with boundary and cobordisms. Floer homology has led to numerous applications, and recently there have also been a few novel results (and proofs of old results) using Khovanov homology. The talk will be accessible to a general mathematical audience. Written articles will accompany each lecture in this series and be available as part of the publication “History and Literature of Mathematical Science.” The schedule will be updated as talks are confirmed.  CMSA EVENT: Math Science Literature Lecture Series
Speaker: Bong Lian – Brandeis University 2:00 PM3:30 PM May 22, 2020 Title: From string theory and Moonshine to vertex algebras Abstract: This is a brief survey of the early historical development of vertex algebras, beginning in the seventies from Physics and Representation Theory. We shall also discuss some of the ideas that led to various early formulations of the theory’s foundation, and their relationships, as well as some of the subsequent and recent developments. The lecture is aimed for a general audience. Written articles will accompany each lecture in this series and be available as part of the publication “History and Literature of Mathematical Science.” The schedule will be updated as talks are confirmed.
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24  25  26  MATHEMATICAL PICTURE LANGUAGE SEMINAR: From Archimedes to Quantum Supremacy
Speaker: Scott Aaronson – University of Texas at Austin 10:00 AM11:00 AM May 26, 2020 I’ll tell a mathematical story that runs from Archimedes’ hatbox theorem of ~200BC (which he used to calculate the surface area of the sphere), to the properties of “PorterThomas” probability distributions, all the way to my and others’ work establishing the theoretical foundations of Google’s quantum supremacy experiment from this past fall. While this admittedly has little to do with mathematical picture languages, there will be pictures of spheres. via Zoom: https://harvard.zoom.us/j/779283357
 27  28  CMSA EVENT: CMSA Condensed Matter/Math Seminar: Supermetal from a highorder Van Hove singularity
Speaker: Hiroki Isobe – MIT 10:30 AM12:00 PM May 28, 2020 A Van Hove singularity (VHS) of the density of states (DOS) is universal in a periodic system. In two dimensions, a saddle point of energy dispersion yields a logarithmic divergence in the DOS. Here, we introduce a new kind of VHS, motivated by the recent development of moiré materials. We define a highorder VHS, which gives a powerlaw DOS divergence [1]. It requires only a single tuning parameter, such as a twist angle of a moiré material, pressure, and strain. We further perform a renormalization group analysis near a highorder VHS to study the effect of electron interactions [2]. We reveal a nontrivial metallic state, where various divergent susceptibilities coexist, but no longrange order appears. We call such a metallic state as a supermetal. Our controlled analysis shows that a supermetal at the interacting fixed point is a nonFermi liquid. [1] N. F. Q. Yuan, H. Isobe, and L. Fu, Nat. Commun. 10, 5769 (2019). [2] H. Isobe and L. Fu, Phys. Rev. Research 1, 033206 (2019). via Zoom: https://harvard.zoom.us/j/977347126
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