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Speaker: Michael SimkinTitle: Randomized algorithms in combinatoricsVenue: CMSA Room G10Member Seminar Speaker: Michael Simkin Title: Randomized algorithms in combinatorics Abstract: Randomized algorithms have been a computational workhorse for almost as long as there have been computers. Surprisingly, such algorithms can also be used to attack problems that are neither algorithmic nor probabilistic. Time permitting I will discuss the following combintorial examples: Enumerative combinatorics and the n-queens problem: In how many ways can one place n queens on an n x n chessboard so that no queen threatens any other? Constructions of combinatorial designs and the Erdos high-girth Steiner triple system problem: An order-n Steiner triple system (STS) is a collection of triples on n vertices such that every pair of vertices is contained in exactly one triple. In… |
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Speaker: Juven WangTitle: Categorical Symmetry of the Standard Model from Gravitational AnomalyVenue: CMSA Room G10Member Seminar Speaker: Juven Wang Title: Categorical Symmetry of the Standard Model from Gravitational Anomaly Abstract: In the Standard Model, the total “sterile right-handed” neutrino number n_{νR} is not equal to the family number Nf. The anomaly index (-Nf+n_{νR}) had been advocated to play an important role in our previous work on Cobordism and Deformation Class of the Standard Model [2112.14765, 2204.08393] and Ultra Unification [2012.15860] in order to predict new highly entangled sectors beyond the Standard Model. Moreover, the invertible baryon minus lepton number B−L symmetry current conservation can be violated quantum mechanically by gravitational backgrounds such as gravitational instantons. In specific, we show that a noninvertible categorical counterpart of the B−L symmetry still survives in gravitational backgrounds. In general, we… |
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Speaker: Barak WeissTitle: New bounds on lattice covering volumes, and nearly uniform coversVenue: CMSA Room G10Member Seminar Speaker: Barak Weiss Title: New bounds on lattice covering volumes, and nearly uniform covers Abstract: Let L be a lattice in R^n and let K be a convex body. The covering volume of L with respect to K is the minimal volume of a dilate rK, such that L+rK = R^n, normalized by the covolume of L. Pairs (L,K) with small covering volume correspond to efficient coverings of space by translates of K, where the translates lie in a lattice. Finding upper bounds on the covering volume as the dimension n grows is a well studied problem, with connections to practical questions arising in computer science and electrical engineering. In a recent paper with Or Ordentlich (EE,… |
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Speaker: Dan KapecTitle: Hints of Flat Space HolographyVenue: CMSA Room G10Member Seminar Speaker: Dan Kapec Title: Hints of Flat Space Holography Abstract: Despite our detailed understanding of holography in Anti-de Sitter space, flat space holography remains somewhat mysterious. “Celestial CFT” is a formalism which attempts to recast quantum gravity in (d+2)-dimensional asymptotically flat spacetimes in terms of a d-dimensional Euclidean conformal field theory residing at the conformal boundary. I will discuss certain universal aspects of this correspondence. As in Anti-de Sitter space, bulk gravitons produce a boundary stress tensor, and bulk gluons furnish boundary-conserved currents. I will also show that continuous spaces of vacua in the bulk map directly onto the conformal manifold of the boundary CFT. This correspondence provides a new perspective on the role of the BMS group… |
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Speaker: Farzan VafaTitle: Dynamics of active nematic defects on conesVenue: CMSA Room G10Member Seminar Speaker: Farzan Vafa Title: Dynamics of active nematic defects on cones Abstract: In the first part of the talk, we investigate the ground-state configurations of two-dimensional liquid crystals with p-fold rotational symmetry (p-atics) on cones. The cone apex develops an effective topological charge, which in analogy to electrostatics, leads to defect absorption and emission at the cone apex as the deficit angle of the cone is varied. We find three types of ground-state configurations as a function of cone angle, which is determined by charged defects screening the effective apex charge: (i) for sharp cones, all of the +1/p defects are absorbed by the apex; (ii) at intermediate cone angles, some of the +1/p defects are absorbed… |
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Speaker: Chuck DoranTitle: Motivic Geometry of Two-Loop Feynman IntegralsVenue: CMSA Room G10Member Seminar Speaker: Chuck Doran Title: Motivic Geometry of Two-Loop Feynman Integrals Abstract: We study the geometry and Hodge theory of the cubic hypersurfaces attached to two-loop Feynman integrals for generic physical parameters. We show that the Hodge structure attached to planar two-loop Feynman graphs decomposes into a mixed Tate piece and a variation of Hodge structure from families of hyperelliptic curves, elliptic curves, or rational curves depending on the space-time dimension. We give more precise results for two-loop graphs with a small number of edges. In particular, we recover a result of Spencer Bloch that in the well-known double box example there is an underlying family of elliptic curves, and we give a concrete description of these elliptic curves. We show… |
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Speaker: Michael DouglasTitle: AI and Theorem ProvingVenue: CMSA Room G10Member Seminar Speaker: Mike Douglas Title: AI and Theorem Proving Abstract: We survey interactive theorem proving and the Lean theorem prover, and the use of AI and large language models to improve this technology. We hope to start a discussion on projects we can do at the CMSA. |
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Speaker: Alejandro PovedaTitle: Compactness and Anticompactness Principles in Set TheoryVenue: CMSA Room G10Member Seminar Speaker: Alejandro Poveda Title: Compactness and Anticompactness Principles in Set Theory Abstract: Several fundamental properties in Topology, Algebra or Logic are expressed in terms of Compactness Principles.For instance, a natural algebraic question is the following: Suppose that G is an Abelian group whose all small subgroups are free – Is the group G free? If the answer is affirmative one says that compactness holds; otherwise, we say that compactness fails. Loosely speaking, a compactness principle is anything that fits the following slogan: Suppose that M is a mathematical structure (a group, a topological space, etc) such that all of its small substructures N have certain property $\varphi$; then the ambient structure M has property $\varphi$, as well…. |
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Speaker: Damian van de HeisteegTitle: Light states in the interior of CY moduli spacesVenue: CMSA Room G10Member Seminar Speaker: Damian van de Heisteeg Title: Light states in the interior of CY moduli spaces Abstract: In string theory one finds that states become massless as one approaches boundaries in Calabi-Yau moduli spaces. In this talk we look in the opposite direction, that is, we search for points where the mass gap for these light states is maximized — the so-called desert. In explicit examples we identify these desert points, and find that they correspond to special points in the moduli space of the CY, such as orbifold points and rank two attractors. |
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Speaker: Mauricio RomoTitle: Quantum trace and length conjecture for hyperbolic knotVenue: CMSA Room G10Member Seminar Speaker: Mauricio Romo Title: Quantum trace and length conjecture for hyperbolic knot Abstract: I will define the quantum trace map for an ideally triangulated hyperbolic knot complement on S^3. This map assigns an operator to each element L of the Kauffman Skein module of knot complement. Motivated by an interpretation of this operator in the context of SL(2,C) Chern-Simons theory, one can formulate a ‘length conjecture’ for the hyperbolic length of L. |
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Speaker: Shuaijie QianTitle: Some non-concave dynamic optimization problems in financeVenue: CMSA Room G10Member Seminar Speaker: Shuaijie Qian (Harvard CMSA) Title: Some non-concave dynamic optimization problems in finance Abstract: Non-concave dynamic optimization problems appear in many areas of finance and economics. Most of existing literature solves these problems using the concavification principle, and derives equivalent, concave optimization problems whose value functions are still concave. In this talk, I will present our recent work on some non-concave dynamic optimization problems, where the concavification principle may not hold and the resulting value function is indeed non-concave. The first work is about the portfolio selection model with capital gains tax and a bitcoin mining model with exit options and technology innovation, where the average tax basis and the average mining cost serves as an approximation, respectively…. |
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Speaker: David ZuckermanTitle: Explicit Ramsey Graphs and Two Source ExtractorsVenue: CMSA Room G10Speaker: David Zuckerman, Harvard CMSA/University of Texas at Austin Title: Explicit Ramsey Graphs and Two Source Extractors Abstract: Ramsey showed that any graph on N nodes contains a clique or independent set of size (log N)/2. Erdos showed that there exist graphs on N nodes with no clique or independent set of size 2 log N, and asked for an explicit construction of such graphs. This turns out to relate to the question of extracting high-quality randomness from two independent low-quality sources. I’ll explain this connection and our recent exponential improvement in constructing two-source extractors. |
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Speaker: Leonid RybnikovTitle: Quantum magnet chains and Kashiwara crystalsVenue: CMSA Room G10Speaker: Leonid Rybnikov, Harvard CMSA/National Research University Higher School of Economics Title: Quantum magnet chains and Kashiwara crystals Abstract: Solutions of the algebraic Bethe ansatz for quantum magnet chains are, generally, multivalued functions of the parameters of the integrable system. I will explain how to compute some monodromies of solutions of Bethe ansatz for the Gaudin magnet chain. Namely, the Bethe eigenvectors in the Gaudin model can be regarded as a covering of the Deligne-Mumford moduli space of stable rational curves, which is unramified over the real locus of the Deligne-Mumford space. The monodromy action of the fundamental group of this space (called cactus group) on the eigenlines can be described very explicitly in purely combinatorial terms of Kashiwara crystals –… |
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Speaker: Zhigang YaoTitle: Principal flow, sub-manifold and boundaryVenue: CMSA Room G10Member Seminar Speaker: Zhigang Yao Title: Principal flow, sub-manifold and boundary Abstract: While classical statistics has dealt with observations which are real numbers or elements of a real vector space, nowadays many statistical problems of high interest in the sciences deal with the analysis of data which consist of more complex objects, taking values in spaces which are naturally not (Euclidean) vector spaces but which still feature some geometric structure. I will discuss the problem of finding principal components to the multivariate datasets, that lie on an embedded nonlinear Riemannian manifold within the higher-dimensional space. The aim is to extend the geometric interpretation of PCA, while being able to capture the non-geodesic form of variation in the data. I will… |
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Speaker: Jie WangTitle: Kahler geometry in twisted materialsVenue: CMSA Room G10Member Seminar Speaker: Jie Wang Title: Kahler geometry in twisted materials Abstract: Flatbands are versatile platform for realizing exotic quantum phases due to the enhanced interactions. The canonical example is Landau level where fractional quantum Hall physics exists. Although interaction is strong, the fractional quantum Hall effect is relatively well understood thanks to its model wavefunction, exact parent Hamiltonian, conformal field theory analogous and other exact aspects. In generic flatbands, the interacting physics is controlled by the interplay between the interaction scale and intrinsic quantum geometries, in particular the Berry curvature and the Fubini-Study metric, which are in general spatially non-uniform. It is commonly believed that the non-uniform geometries destroy these exact properties of fractional quantum Hall physics, making… |
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Speaker: Ben McKennaTitle: Random determinants, the elastic manifold, and landscape complexity beyond invarianceVenue: CMSA Room G10Member Seminar Speaker: Ben McKenna Title: Random determinants, the elastic manifold, and landscape complexity beyond invariance Abstract: The Kac-Rice formula allows one to study the complexity of high-dimensional Gaussian random functions (meaning asymptotic counts of critical points) via the determinants of large random matrices. We present new results on determinant asymptotics for non-invariant random matrices, and use them to compute the (annealed) complexity for several types of landscapes. We focus especially on the elastic manifold, a classical disordered elastic system studied for example by Fisher (1986) in fixed dimension and by Mézard and Parisi (1992) in the high-dimensional limit. We confirm recent formulas of Fyodorov and Le Doussal (2020) on the model in the Mézard-Parisi setting, identifying the boundary… |
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Speaker: Shai ChesterTitle: Derivation of AdS/CFT for Vector ModelsVenue: CMSA Room G10Member Seminar Speaker: Shai Chester Title: Derivation of AdS/CFT for Vector Models Abstract: We derive an explicit map at finite N between the singlet sector of the free and critical O(N) and U(N) vector models in any spacetime dimension above two, and a bulk higher spin theory in anti-de Sitter space in one higher dimension. For the boundary theory, we use the bilocal formalism of Jevicki et al to restrict to the singlet sector of the vector model. The bulk theory is defined from the boundary theory via our mapping, and is a consistent quantum higher spin theory with a well defined action. Our mapping relates bilocal operators in the boundary theory to higher spin fields in the bulk, while single trace local operators… |
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Speaker: Uri KolTitle: Duality in Einstein’s GravityVenue: CMSA Room G10Title: Duality in Einstein’s Gravity Abstract: Electric-Magnetic duality has been a key feature behind our understanding of Quantum Field Theory for over a century. In this talk I will describe a similar property in Einstein’s gravity. The gravitational duality reveals, in turn, a wide range of new IR phenomena, including aspects of the double copy for scattering amplitudes, asymptotic symmetries and more. |
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Speaker: Juven WangTitle: Cobordism and Deformation Class of the Standard Model and Beyond: Proton Stability and Neutrino MassVenue: VirtualMember Seminar Speaker: Juven Wang Title: Cobordism and Deformation Class of the Standard Model and Beyond: Proton Stability and Neutrino Mass Abstract: ‘t Hooft anomalies of quantum field theories (QFTs) with an invertible global symmetry G (including spacetime and internal symmetries) in a d-dim spacetime are known to be classified by a d+1-dim cobordism group TPd+1(G), whose group generator is a d+1-dim cobordism invariant written as a d+1-dim invertible topological field theory. Deformation class of QFT is recently proposed to be specified by its symmetry G and a d+1-dim invertible topological field theory. Seemly different QFTs of the same deformation class can be deformed to each other via quantum phase transitions. We ask which deformation class controls the 4d ungauged… |
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Speaker: Sergiy VerstyukTitle: Machine Learning the Gravity Equation for International TradeVenue: virtualMember Seminar Speaker: Sergiy Verstyuk Title: Machine Learning the Gravity Equation for International Trade Abstract: We will go through modern deep learning methods and existing approaches to their interpretation. Next, I will describe a graph neural network framework. You will also be introduced to an economic analog of gravity. Finally, we will see how these tools can help understand observed trade flows between 181 countries over 68 years. [Joint work with Michael R. Douglas.] |