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2  3  CMSA EVENT: CMSA Mathematical Physics Seminar: On product identities and the Chow rings of holomorphic symplectic varieties
12:00 PM1:00 PM February 3, 2020 20 Garden Street, Cambridge, MA 02138 For a moduli space $M$ of stable sheaves over a K3 surface $X$, we propose a series of conjectural identities in the Chow rings $CH_\star (M \times X^\ell),\, \ell \geq 1,$ generalizing the classic Beauville–Voisin identity for a K3 surface. We emphasize consequences of the conjecture for the structure of the tautological subring $R_\star (M) \subset CH_\star (M).$ We prove the proposed identities when $M$ is the Hilbert scheme of points on a K3 surface. This is based on joint work with L. Flapan, A. Marian and R. Silversmith.
 4  HARVARDMIT ALGEBRAIC GEOMETRY SEMINAR
3:00 PM4:00 PM February 4, 2020 1 Oxford Street, Cambridge, MA 02138 USA I will construct LG mirrors for the JohnsonKollár series of anticanonical del Pezzo surfaces in weighted projective 3spaces. The main feature of these surfaces is that their anticanonical linear system is empty. Thus they fall outside of the range of the known mirror constructions. For each of these surfaces, the LG mirror is a pencil of hyperelliptic curves. I will exhibit the regularised Ifunction of the surface as a period of the pencil and I will sketch how to construct the pencil starting from a work of Beukers, Cohen, and Mellit on finite hypergeometric functions. This is joint work with Alessio Corti.  DIFFERENTIAL GEOMETRY SEMINAR
4:15 PM5:15 PM February 4, 2020 1 Oxford Street, Cambridge, MA 02138 USA **CANCELED** Most 4manifolds do not admit symplectic forms, but most admit 2forms that are “nearly” symplectic. Just like the SeibergWitten (SW) invariants, there are Gromov invariants that are compatible with the nearsymplectic form. Although (potentially exotic) 4spheres don’t admit them, there is still a way to bring in nearsymplectic techniques and I will describe my ongoing pseudoholomorphic attempt(s) at analyzing them.
 5  CMSA EVENT: CMSA Quantum Matter & Quantum Field Theory Seminar: A new theory for pseudogap metal in hole doped cuprates
10:30 AM12:00 PM February 5, 2020 20 Garden Street, Cambridge, MA 02138 We provide a new parton theory for hole doped cuprates. We will describe both a pseudogap metal with small Fermi surfaces and the conventional Fermi liquid with large Fermi surfaces within mean field level of the same framework. For the pseudogap metal, “Fermi arc” observed in ARPES can be naturally reproduced. We also provide a theory for a critical point across which the carrier density jumps from x to 1+x. We will also discuss the generalization of the theory to Kondo breaking down transition in heavy fermion systems and generic SU(N) Hubbard model.  NUMBER THEORY SEMINAR
3:00 PM4:00 PM February 5, 2020 1 Oxford Street, Cambridge, MA 02138 USA There is a large literature about points of bounded height on varieties, and about number fields of bounded discriminant. We explain how to unify these two questions by means of a new definition of height for rational points on (certain) stacks over global fields. I talked about some aspects of this work at Barry’s birthday conference, and will try in this talk to emphasize different points, including a conjecture about the asymptotic counting function for points of bounded height on a stack X which simultaneously generalizes the Manin conjectures (the case where X is a variety) and the Malle conjectures (the case where X is a classifying stack BG.)  CMSA EVENT: CMSA Colloquium Gentle Measurement of Quantum States and Differential Privacy
4:30 PM5:30 PM February 5, 2020 20 Garden Street, Cambridge, MA 02138 I’ll discuss a recent connection between two seemingly unrelated problems: how to measure a collection of quantum states without damaging them too much (“gentle measurement”), and how to provide statistical data without leaking too much about individuals (“differential privacy,” an area of classical CS). This connection leads, among other things, to a new protocol for “shadow tomography” of quantum states (that is, answering a large number of questions about a quantum state given few copies of it).  LOGIC COLLOQUIUM
4:30 PM5:30 PM February 5, 2020 A ray in a graph G = (V, E) is a sequence X (possibly infinite) of distinct vertices x0, x1, . . . such that, for every i, E(xi , xi+1). A classical theorem of graph theory (Halin [1965]) states that if a graph has, for each k 2 N, a set of k many disjoint (say no vertices in common) infinite rays then there is an infinite set of disjoint infinite rays. The proof seems like an elementary argument by induction that uses the finite version of Menger’s theorem at each step. One would thus expect the theorem to follow by very elementary (even computable) methods plus a compactness argument (or equivalently arithmetic comprhension, ACA0). We show that this is not the case. Indeed, the construction of the infinite set of disjoint rays is much more complicated. It occupies a level of complexity previously inhabited by a number of logical principals and only one fact from the mathematical literature. Such theorems are called theorems of hyperarithmetic analysis. Formally this means that they imply (in !models) that for every set A all transfinite iterations (through wellorderings computable from A) of the Turing jump beginning with A exist. On the other hand, they are true in the (!model) consisting of the subsets of N generated from any single set A by these jump iterations. There are many variations of this theorem in the graph theory literature that inhabit the subject of ubiquity in graph theory. We discuss a number of them that also supply examples of theorems of hyperarithmetic analysis as well as classical variations that are proof theoretically even stronger. This work is joint with James Barnes and Jun Le Goh. If time permits we will also discuss a new class of theorems suggested by a “lemma” in one of the papers in the area. We call them almost theorems of hyperarithmetic analyisis. These are theorems that are proof theoretically very weak over Recursive Comprehension (RCA0) but become theorems of hyperarithmetic analysis once one assumes ACA0.  OPEN NEIGHBORHOOD SEMINAR
4:30 PM5:30 PM February 5, 2020 1 Oxford Street, Cambridge, MA 02138 USA Imagine the universe is a periodic crystal. If gravity makes space negatively curved, the thin walls of the crystalline structure might trace out a pattern of circles in the sky, visible at night. In this talk we will describe how to generate pictures of these patterns and how to think like a hyperbolic astronomer. We also touch on the connection to knots and links and arithmetic groups. The lecture is accompanied by an exhibit of prints in the Science Center lobby. (This talk will be accessible to members of the department at all levels.)
 6  CMSA EVENT: CMSA Condensed Matter/Math Seminar: Twistronics in Graphene Superlattices: Correlation and Superconductivity
10:30 AM12:00 PM February 6, 2020 20 Garden Street, Cambridge, MA 02138 No additional detail for this event.  THURSDAY SEMINAR SEMINAR
3:00 PM5:00 PM February 6, 2020 1 Oxford Street, Cambridge, MA 02138 USA I will give an introduction to the topic of this semester’s seminar: the automorphisms of E_noperads. Our main goal is to understand the computation of Fresse, Turchin and Willwacher of the rational homotopy of Map^h(E_m,E_n^Q) in terms of graph homology. We then discuss some potential applications, and lines of inquiry opened up by this result. This connects the topic to differential topology and number theory.
 7  CMSA GENERAL RELATIVITY SEMINAR CMSA EVENT
10:30 AM11:30 AM February 7, 2020 In this talk, we will introduce the concept of improvabilty of the dominant energy scalar and discuss strong consequences of nonimprovability. We employ new, large families of deformations of the modified Einstein constraint operator and show that, generically, their adjoint linearizations are either injective, or else one can prove that kernel elements satisfy a “nullvector equation”. Combined with a conformal argument, we make significant progress toward Bartnik’s stationary conjecture. More specifically, we prove that a Bartnik minimizing initial data set can be developed into a spacetime that both satisfies the dominant energy condition and carries a global Killing field. We also show that this spacetime is vacuum near spatial infinity. This talk is based on the joint work with Dan Lee.  GAUGETOPOLOGYSYMPLECTIC SEMINAR
3:30 PM4:30 PM February 7, 2020 1 Oxford Street, Cambridge, MA 02138 USA I’ll discuss the Viterbo transfer functor from the (partially) wrapped Fukaya category of a Liouville domain to that of a subdomain. It is a localization when everything in sight is Weinstein, and I’ll explain how much of that survives if we drop the assumption that the cobordism is Weinstein. The result allows us to turn natural questions about exact Lagrangians into interesting questions in homotopical algebra. Future schedule is found here: https://scholar.harvard.edu/gerig/seminar
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9  10  CMSA EVENT: CMSA Mathematical Physics Seminar: On eigenvalues and eigenfunctions of the clamped plate
12:00 PM1:00 PM February 10, 2020 20 Garden Street, Cambridge, MA 02138 A celebrated theorem of C.L. Siegel from 1929 shows that the multiplicity of eigenvalues for the Laplace eigenfunctions on the unit disk is at most two. We study the fourth order clamped plate problem, showing that the multiplicity of eigenvalues is uniformly bounded. Our method is based on new recursion formulas and Siegel–Shidlovskii theory. If time permits, we discuss possible applications also to nodal geometry. The talk is based on a joint work with Yuri Lvovsky.
 11  SEMINARS
11:00 AM12:30 PM February 11, 2020 Motivic complexes of Voevodsky have no right to two properties (1) cohomological sparsity and (2) a relationship with differential forms. This is, however, true padically over characteristic p by a result of GeisserLevine, relying on previous results of BlochKatoGabber. I will explain this result, including the cast of characters involved like the logarithmic de RhamWitt sheaves, Bloch’s higher Chow groups and algebraic/Milnor Ktheory.  HARVARDMIT ALGEBRAIC GEOMETRY SEMINAR
3:00 PM4:00 PM February 11, 2020 1 Oxford Street, Cambridge, MA 02138 USA The talk will revolve around combinatorial aspects Prym varieties, a class of Abelian varieties that occurs in the presence of double covers. Pryms have deep connections with torsion points of Jacobians, bitangent lines of curves, and spin structures. As I will explain, problems concerning Pryms may be reduced, via tropical geometry, to combinatorial games on graphs. As a consequence, we obtain new results concerning the geometry of special algebraic curves, and bounds on dimensions of certain Brill–Noether loci.  MATHEMATICAL PICTURE LANGUAGE SEMINAR
3:30 PM4:30 PM February 11, 2020 17 Oxford Street, Cambridge, MA 02138 USA Sampling from a classical, thermal distribution is, in general, a computationally hard problem. In particular, standard Monte Carlo algorithms converge slowly close to a phase transition or in the presence of frustration. In this work, we explore whether a quantum computer can provide a speedup for problems of this type. The sampling problem can be reduced to the task of preparing a pure quantum state, the socalled Gibbs state [1]. Samples from the thermal distribution are obtained by performing projective measurements on this state. To prepare the Gibbs state, we exploit a mapping from a classical Monte Carlo algorithm to a quantum Hamiltonian whose ground state is the Gibbs state [2]. We demonstrate with concrete examples that a quantum speedup can be achieved by identifying optimal adiabatic trajectories in an extended parameter space of the quantum Hamiltonian. Our approach elucidates intimate connections between computational complexity and phase transitions. Finally, we propose a realistic implementation of the algorithm using Rydberg atoms suitable for nearterm quantum devices. [1] R. D. Somma and C. D. Batista, Phys. Rev. Lett. 99, 030603 (2007). [2] F. Verstraete, M. M. Wolf, D. PerezGarcia, and J. I. Cirac, Phys. Rev. Lett. 96, 220601 (2006).  DIFFERENTIAL GEOMETRY SEMINAR
4:15 PM5:15 PM February 11, 2020 1 Oxford Street, Cambridge, MA 02138 USA In this talk, we discuss how to derive the equivariant SYZ mirror of toric manifolds by counting holomorphic discs. In the case of (semi)Fano toric manifolds, those mirrors recover Givental’s equivariant mirrors, which compute the equivariant quantum cohomology. Also, we formulate and compute open GromovWitten invariants of singular SYZ fiber, which are closely related to the open GromovWitten invariants of AganagicVafa branes. This talk is based on joint work with Hansol Hong, SiuCheong Lau, and Xiao Zheng. –Organized by Professor ShingTung Yau
 12  CMSA EVENT: CMSA Quantum Matter/Quantum Field Theory Seminar: Monopoles in QED3 Dirac Spin Liquids
10:30 AM12:00 PM February 12, 2020 20 Garden Street, Cambridge, MA 02138 No additional detail for this event.  NUMBER THEORY SEMINAR
3:00 PM4:00 PM February 12, 2020 1 Oxford Street, Cambridge, MA 02138 USA Every Newton polygon satisfying the Kottwitz conditions occurs on Shimura varieties of PELtype in positive characteristic (Viehmann/Wedhorn). In most cases, it is not known whether these Newton polygon strata contain points representing the Jacobians of smooth curves. In some cases, this is not even known for the muordinary stratum. We provide a positive answer for the muordinary and almost muordinary strata in infinitely many cases. For base cases, we consider the arithmetic of some of Moonen’s families of cyclic covers of the projective line. As an application, we produce infinitely many new examples of unusual Newton polygons which occur for Jacobians of smooth curves. This is joint work with Li, Mantovan, and Tang.  CMSA EVENT: CMSA Colloquium: A Compact, Logical Approach to LargeMarket Analysis
4:30 PM5:30 PM February 12, 2020 20 Garden Street, Cambridge, MA 02138 In game theory, we often use infinite models to represent “limit” settings, such as markets with a large number of agents or games with a long time horizon. Yet many gametheoretic models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. Here, we show how to extend key results from (finite) models of matching, games on graphs, and trading networks to infinite models by way of Logical Compactness, a core result from Propositional Logic. Using Compactness, we prove the existence of manoptimal stable matchings in infinite economies, as well as strategyproofness of the manoptimal stable matching mechanism. We then use Compactness to eliminate the need for a finite start time in a dynamic matching model. Finally, we use Compactness to prove the existence of both Nash equilibria in infinite games on graphs and Walrasian equilibria in infinite trading networks.
 13  CMSA EVENT: CMSA Condensed Matter/Math Seminar: Spontaneous symmetry breaking in SYK models
10:30 AM12:00 PM February 13, 2020 20 Garden Street, Cambridge, MA 02138 No additional detail for this event.  COLLOQUIUMS
3:00 PM5:00 PM February 13, 2020 1 Oxford Street, Cambridge, MA 02138 USA No additional detail for this event.  COLLOQUIUMS
4:00 PM5:30 PM February 13, 2020 1 Oxford Street, Cambridge, MA 02138 will speak on: “Symplectic, or mirrorical, look at the FarguesFontaine curve” Homological mirror symmetry describes Lagrangian Floer theory on a torus in terms of vector bundles on the Tate elliptic curve. A version of Lekili and Perutz’s works “over Z[[t]]”, where t is the Novikov parameter. I will review this story and describe a modified form of it, which is joint work with Lekili, where the Floer theory is altered by a locally constant sheaf of rings on the torus. When the fiber of this sheaf of rings is perfectoid of characteristic p, and the holonomy around one of the circles in the torus is the pth power map, it is possible to specialize to t = 1, and the resulting theory there is described in terms of vector bundles on the equalcharacteristicversion of the FarguesFontaine curve. Tea at 4:00 pm – Math Common Room, 4th Floor Talk at 4:30 pm – Hall A
 14  CMSA GENERAL RELATIVITY SEMINAR CMSA EVENT
10:30 AM11:30 AM February 14, 2020 Jang’s equation is a degenerate elliptic differential equation which plays an important role in the positive mass theorem. In this talk, we describe a high order WENO (Weighted Essentially NonOscillatory) scheme for the Jang’s equation. Some special solutions will be shown, such as those possessing spherical symmetry and axial symmetry.
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16  17  18  MATHEMATICAL PICTURE LANGUAGE SEMINAR
3:00 PM4:00 PM February 18, 2020 The outoftimeordered correlation (OTOC) and entanglement are two physically motivated and widely used probes of the “scrambling” of quantum information, a phenomenon that has drawn great interest recently in quantum gravity and manybody physics. We argue that the corresponding notions of scrambling can be fundamentally different, by proving an asymptotic separation between the time scales of the saturation of OTOC and that of entanglement entropy in a random quantum circuit model defined on graphs with a tight bottleneck, such as tree graphs connected at the roots. Our result counters the intuition that a random quantum circuit mixes in time proportional to the diameter of the underlying graph of interactions. It also provides a more rigorous justification for an argument of arXiv:1807.04363, that black holes may be slow information scramblers. Such observations may be of fundamental importance in the understanding of the black hole information problem. The bounds we obtained for OTOC are interesting in their own right in that they generalize previous studies of OTOC on lattices to the geometries on graphs in a rigorous and general fashion.  DIFFERENTIAL GEOMETRY SEMINAR
4:15 PM5:15 PM February 18, 2020 1 Oxford Street, Cambridge, MA 02138 USA In 2008, Christodoulou achieved a major breakthrough in the context of mathematical general relativity in being able to form trapped surfaces dynamically from initial data for the Einstein vacuum system. The results and methods which he lays out in his 600+ page manuscript has led to a flurry of activity in the last decade. I will give a rough overview of the basic ideas, describe how far theorems have come, and describe some recent progress – joint with Nikos Athanasiou – in this direction. –Organized by Professor ShingTung Yau
 19  CMSA EVENT: CMSA Quantum Matter/Quantum Field Theory Seminar:Modeling the pseudogap state in cuprates: quantum disordered pair density wave
10:30 AM12:00 PM February 19, 2020 20 Garden Street, Cambridge, MA 02138 I will briefly review the pseudogap phenomenology in high Tc cuprate superconductors, especially recent experiments related to charge density waves and pair density waves, and propose a simple theory of the pseudogap. By quantum disordering a pair density wave, we found a state composed of insulating antinodal pairs and a nodal electron pocket. We compare the theoretical predictions with ARPES results, optical conductivity, quantum oscillation and other experiments.  NUMBER THEORY SEMINAR
3:00 PM4:00 PM February 19, 2020 1 Oxford Street, Cambridge, MA 02138 USA We consider the family of normal octic fields with Galois group $D_4$, ordered by their discriminant. In forthcoming joint work with Arul Shankar, we verify the strong form of Malle’s conjecture for this family of number fields, obtaining the order of growth as well as the constant of proportionality. In this talk, we will discuss and review the combination of techniques from analytic number theory and geometryofnumbers methods used to prove this and related results.  SEMINARS
4:00 PM6:00 PM February 19, 2020 Can you use the homotopy type of the space of knots in a simplyconnected 4manifold to distinguish smooth structures? The answer is no, using embedding calculus. I will also give some examples which show that embedding calculus does distinguish smooth structures in high dimensions. This is joint with Ben Knudsen.  OPEN NEIGHBORHOOD SEMINAR
4:30 PM5:30 PM February 19, 2020 1 Oxford Street, Cambridge, MA 02138 USA Max Dehn made many remarkable contributions to mathematics, and his name pops up in lots of places, most often in topology, where we have “Dehn surgery”, the “Dehn twist”, and “Dehn’s lemma”. Famously, Dehn supplied an incorrect proof of the lemma that bears his name. The mistake wasn’t noticed for nearly a decade, and took nearly another four decades to fix. In this talk, I won’t mention the lemma, but I will say a few words about Dehn himself, a few more about his early work on “scissors congruences”, and then yet more on the Dehn twist, closing with a recent result about Dehn twists in four dimensions. (This talk will be accessible to members of the department at all levels.)  CMSA EVENT: CMSA Colloquium: Quantum Money from Lattices
5:15 PM6:15 PM February 19, 2020 20 Garden Street, Cambridge, MA 02138 Quantum money is a cryptographic protocol for quantum computers. A quantum money protocol consists of a quantum state which can be created (by the mint) and verified (by anybody with a quantum computer who knows what the “serial number” of the money is), but which cannot be duplicated, even by somebody with a copy of the quantum state who knows the verification protocol. Several previous proposals have been made for quantum money protocols. We will discuss the history of quantum money and give a protocol which cannot be broken unless lattice cryptosystems are insecure.
 20  CMSA EVENT: CMSA Condensed Matter/Math Seminar: Lattice models that realize $Z_n$ 1symmetryprotected topological states for even $n$
10:30 AM12:00 PM February 20, 2020 20 Garden Street, Cambridge, MA 02138 Higher symmetries can emerge at low energies in a topologically ordered state with no symmetry, when some topological excitations have very high energy scales while other topological excitations have low energies. The low energy properties of topological orders in this limit, with the emergent higher symmetries, may be described by higher symmetry protected topological order. This motivates us, as a simplest example, to study a lattice model of $Z_n$1symmetry protected topological (1SPT) states in 3+1D for even $n$. We write down an exactly solvable lattice model and study its boundary transformation. On the boundary, we show the existence of anyons with nontrivial selfstatistics. For the $n=2$ case, where the bulk classification is given by an integer $m$ mod 4, we show that the boundary can be gapped with double semion topological order for $m=1$ and toric code for $m=2$. The bulk ground state wavefunction amplitude is given in terms of the linking numbers of loops in the dual lattice. Our construction can be generalized to arbitrary 1SPT protected by finite unitary symmetry.  THURSDAY SEMINAR SEMINAR
3:00 PM5:00 PM February 20, 2020 1 Oxford Street, Cambridge, MA 02138 USA No additional detail for this event.
 21  CMSA GENERAL RELATIVITY SEMINAR CMSA EVENT
10:30 AM11:30 AM February 21, 2020 The Event Horizon Telescope image of the supermassive black hole in the galaxy M87 is dominated by a bright, unresolved ring. General relativity predicts that embedded within this image lies a thin “photon ring,” which is itself composed of an infinite sequence of selfsimilar subrings. Each subring is a lensed image of the main emission, indexed by the number of photon orbits executed around the black hole. I will review recent theoretical advances in our understanding of lensing by Kerr black holes, based on arXiv:1907.04329, 1910.12873, and 1910.12881. In particular, I will describe the critical parameters γ, δ, and τ that respectively control the demagnification, rotation, and time delay of successive lensed images of a source. These observable parameters encode universal effects of general relativity, which are independent of the details of the emitting matter and also produce strong, universal signatures on long interferometric baselines. These signatures offer the possibility of precise measurements of black hole mass and spin, as well as tests of general relativity, using only a sparse interferometric array such as a future extension of the EHT to space
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23  24  CMSA EVENT: CMSA Mathematical Physics Seminar: Coisotropic branes on symplectic tori and homological mirror symmetry
12:00 PM1:00 PM February 24, 2020 20 Garden Street, Cambridge, MA 02138 Homological mirror symmetry (HMS) asserts that the Fukaya category of a symplectic manifold is derived equivalent to the category of coherent sheaves on the mirror complex manifold. Without suitable enlargement (split closure) of the Fukaya category, certain objects of it are missing to prevent HMS from being true. Kapustin and Orlov conjecture that coisotropic branes should be included into the Fukaya category from a physics view point. In this talk, I will construct for linear symplectic tori a version of the Fukaya category including coisotropic branes and show that the usual Fukaya category embeds fully faithfully into it. I will also explain the motivation of the construction through the perspective of Homological mirror symmetry.  CMSA EVENT: CMSA Special Seminar: How will we do Mathematics in 2030?
3:00 PM4:00 PM February 24, 2020 20 Garden Street, Cambridge, MA 02138 We make the case that over the coming decade, computer assisted reasoning will become far more widely used in the mathematical sciences. This includes interactive and automatic theorem verification, symbolic algebra, and emerging technologies such as formal knowledge repositories, semantic search and intelligent textbooks. After a short review of the state of the art, we survey directions where we expect progress, such as mathematical search and formal abstracts, developments in computational mathematics, integration of computation into textbooks, and organizing and verifying large calculations and proofs. For each we try to identify the barriers and potential solutions.
 25  CMSA EVENT: CMSA Fluid Dynamics Seminar: Flexible spectral simulations of lowMachnumber astrophysical fluids
3:00 PM4:00 PM February 25, 2020 20 Garden Street, Cambridge, MA 02138 Fluid dynamical processes are key to understanding the formation and evolution of stars and planets. While the astrophysical community has made exceptional progress in simulating highly compressible flows, models of lowMachnumber stellar and planetary flows typically use simplified equations based on numerical techniques for incompressible fluids. In this talk, we will discuss improved numerical models of three lowMachnumber astrophysical phenomena: tidal instabilities in binary neutron stars, waves and convection in massive stars, and iceocean interactions in icy moons. We will cover the basic physics of these systems and how ongoing additions to the opensource Dedalus Project are enabling their efficient simulation in spherical domains with spectral accuracy, implicit timestepping, phasefield methods, and complex equations of state.  HARVARDMIT ALGEBRAIC GEOMETRY SEMINAR
3:00 PM4:00 PM February 25, 2020 1 Oxford Street, Cambridge, MA 02138 USA It is well known that, for pointed nodal curves, considering flat and proper families of pairs (X,D) leads to a proper moduli space. Still, while the notion of stable pairs is a higher dimensional analogue of pointed nodal curves, the right definition of a family of stable pairs is far from obvious. In this work, building on an idea of Kollár and the work of Abramovich and Hassett, we give an alternative definition of a family of stable pairs, in the case where the divisor D is reduced. This definition is more amenable to the tools of deformation theory. As an application we produce functorial gluing morphisms on the moduli spaces of surfaces, generalizing the clutching and gluing morphisms that describe the boundary strata of the moduli of curves. This is joint work with D. Bejleri.  MATHEMATICAL PICTURE LANGUAGE SEMINAR
3:30 PM4:30 PM February 25, 2020 17 Oxford Street, Cambridge, MA 02138 USA In this work, we propose a systematical framework to construct Bell inequalities from stabilizers which are maximally violated by general stabilizer states. We show that the constructed Bell inequalities can selftest any stabilizer state which is essentially deviceindependent, if and only if these stabilizers can uniquely determine the state in a devicedependent manner. This bridges the gap between deviceindependent and devicedependent verification methods. Our framework can not only inspire more fruitful multipartite Bell inequalities from conventional verification methods, but also pave the way for their practical applications. Joint work with Qi Zhao, arXiv:2002.01843  DIFFERENTIAL GEOMETRY SEMINAR
4:15 PM5:15 PM February 25, 2020 1 Oxford Street, Cambridge, MA 02138 USA Let $M$ be a complete Ricciflat manifold with Euclidean volume growth. A theorem of ColdingMinicozzi states that if a tangent cone at infinity of $M$ is smooth, then it is the unique tangent cone. The key component in their proof is an infinite dimensional LojasiewiczSimon inequality, which implies rapid decay of the $L^2$norm of the tracefree Hessian of the Green function. In this talk we discuss how this inequality can be exploited to identify two arbitrarily far apart scales in $M$ in a natural manner through a diffeomorphism. We also prove a pointwise Hessian estimate for the Green function when there is an additional condition on sectional curvature, which is an analogue of various matrix Harnack inequalities obtained by Hamilton and LiCao in different timedependent settings. — Organized by Prof. ShingTung Yau
 26  RANDOM MATRIX SEMINAR
2:00 PM3:00 PM February 26, 2020 20 Garden Street, Cambridge, MA 02138 I will describe how certain recursive distributional equations can be solved by importing rigorous results on the convergence of approximation schemes for degenerate PDEs, from numerical analysis. This project is joint work with Luc Devroye, Hannah Cairns, Celine Kerriou, and Rivka Maclaine Mitchell.  NUMBER THEORY SEMINAR
3:00 PM4:00 PM February 26, 2020 1 Oxford Street, Cambridge, MA 02138 USA One of the fundamental challenges in number theory is to understand the intricate way in which the additive and multiplicative structures in the integers intertwine. We will explore a dynamical approach to this topic. After introducing a new dynamical framework for treating questions in multiplicative number theory, we will present an ergodic theorem which contains various classical numbertheoretic results, such as the Prime Number Theorem, as special cases. This naturally leads to a formulation of an extended form of Sarnak’s conjecture, which deals with the disjointness of actions of (N,+) and (N,*). This talk is based on joint work with Vitaly Bergelson.  CMSA EVENT: CMSA Colloquium: The Cubical Route to Understanding Groups
4:30 PM5:30 PM February 26, 2020 20 Garden Street, Cambridge, MA 02138 Cube complexes have come to play an increasingly central role within geometric group theory, as their connection to rightangled Artin groups provides a powerful combinatorial bridge between geometry and algebra. This talk will introduce nonpositively curved cube complexes, and then describe the developments that culminated in the resolution of the virtual Haken conjecture for 3manifolds and simultaneously dramatically extended our understanding of many infinite groups.
 27  CMSA EVENT: CMSA Quantum Matter/Quantum Field Theory Seminar: JordanWigner dualities for translationinvariant Hamiltonians in any dimension
10:30 AM12:00 PM February 27, 2020 20 Garden Street, Cambridge, MA 02138 Inspired by recent constructions of JordanWigner transformations in higher dimensions by Kapustin et. al., I will present a framework for an exact bosonization, which locally maps a translationinvariant model of spinless fermions to a gauge theory of Pauli spins. I will show that the duality exists for an arbitrary number of (possibly manybody) “hopping” operators in any dimension and provide an explicit construction. The duality can be concisely stated in terms of an algebraic formalism of translationinvariant Hamiltonians proposed by Haah. I will then present two interesting applications. First, bosonizing Majorana stabilizer codes, such as the Majorana color code or the checkerboard model, into Pauli stabilizer codes. Second, bosonizing fermionic systems where fermion parity is conserved on submanifolds such as higherform, line, planar or fractal symmetry. In 3+1D, the latter two can give rise to fracton models where emergent particles are immobile, but yet can be “fermionic”. This may give rise to new nonrelativistic ‘t Hooft anomalies.  THURSDAY SEMINAR SEMINAR
3:00 PM5:00 PM February 27, 2020 1 Oxford Street, Cambridge, MA 02138 USA I plan to sketch Kontsevich’s proof of formality of the little ndisk operad, and time permitting, intrinsic formality.  HARVARDMITBUBRANDEISNORTHEASTERN COLLOQUIUM
4:30 PM5:30 PM February 27, 2020 1 Oxford Street, Cambridge, MA 02138 The groups of homeomorphisms or diffeomorphisms of a manifold have many striking parallels with finite dimensional Lie groups. In this talk, I’ll describe some of these, and explain new work, joint with Lei Chen, that gives an orbit classification theorem and a structure theorem for actions of homeomorphism and diffeomorphism groups on other spaces, analogous to some classical results for actions of locally compact Lie groups. As applications, we answer many concrete questions towards classifying all actions of Diff(M) on other manifolds (many of which are nontrivial, for instance Diff(M) acts naturally on the unit tangent bundle of M…) and resolve several threads in a research program initiated by Ghys. I’ll aim to give both a broad overview and several toy applications in the talk. Tea at 4:00 pm – Math Common Room Talk at 4:30 pm – Hall A
 28  CMSA GENERAL RELATIVITY SEMINAR CMSA EVENT
10:30 AM11:30 AM February 28, 2020 In this talk, we will discuss a quasilocal Penrose inequality with charges for timesymmetric initial data of the EinsteinMaxwell equation. Namely, we derive a lower bound for BrownYork type quasilocal mass in terms of the horizon area and the electric charge. The inequality we obtained is sharp in the sense that equality holds for surfaces in the ReissnerNordström manifold. This talk is based on joint work with Stephen McCormick.  GAUGETOPOLOGYSYMPLECTIC SEMINAR
3:30 PM4:30 PM February 28, 2020 1 Oxford Street, Cambridge, MA 02138 USA We give the first examples of codimension1 knotting in the 4sphere, i.e. there is a 3ball B_1 with boundary the standard linear 2sphere, which is not isotopic rel boundary to the standard linear 3ball B_0. Actually, there is an infinite family of distinct isotopy classes of such balls. This implies that there exist inequivalent fiberings of the unknot in 4sphere, in contrast to the situation in dimension3. Also, that there exists diffeomorphisms of S^1 x B^3 homotopic rel boundary to the identity, but not isotopic rel boundary to the identity. Joint work with Ryan Budney. Future schedule is found here: https://scholar.harvard.edu/gerig/seminar
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