For more information: https://scgp.stonybrook.edu/archives/39862
Title: Free fermions in disguise
Speaker: Paul Fendley
Abstract: TBA
Title: A framework for the curvature of $L^2$ metrics
Speaker: Pranav Upadrashta [Stony Brook University]
Abstract: A result of Berndtsson states that the Chern connection associated with the $L^2$ metric on certain infinite rank vector bundles has positive curvature in the sense of Nakano. Following the ideas of Lempert and Szőke, together with Varolin, we developed a framework to define the curvature of families of Hilbert spaces that might not fit together to form a holomorphic vector bundle. This enables us to derive curvature formulas for $L^2$ metrics on families of Hilbert spaces associated with a general holomorphic submersion $pi: X rightarrow B$ and a holomorphic hermitian vector bundle $(E, h) rightarrow X$.
In the first part of the thesis, we obtain a curvature formula for the $L^2$ metric on a family of Bergman spaces when the fibers of $pi$ are domains and $E$ is a line bundle. Additionally, we establish a lower bound on the curvature, from which we recover Berndtsson's aforementioned result when $X$ is a product and $pi$ is projection onto a factor.
In the second part, we get another curvature formula when the fibers of $pi$ are compact Kähler manifolds. We show that from this formula, well-known curvature formulas of $L^2$ metrics can be recovered, including the curvature of: (i) the $L^2$ metric on the direct image of a family of holomorphic vector bundles due to To and Weng, (ii) the $L^2$ metric on the higher direct images of a family of line bundles due to Berndtsson, Păun, and Wang (iii) the Weil-Petersson on the moduli space of Hermite-Einstein vector bundles due to Schumacher and Toma.
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Title: Understanding the Defining Ideal Through Cones
Speaker: Karina Cho [Stony Brook University]
Abstract: We study the degrees in which the ideal of a smooth projective variety is generated by cones. Our main results focus on the first nontrivial case when the variety is a finite set of points in the projective plane.
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Title: The sinh-Gordon model beyond the self-dual point and freezing transitions in disordered systems
Speaker: Andre Leclair
Abstract: TBA
Title: From Herman Rings to Herman Curves
Speaker: Willie Rush Lim [Stony Brook University]
Abstract: Given a non-trivial holomorphic map on a Riemann surface, an invariant connected set for which the map is conjugate to rigid rotation is either a disk (Siegel disk), an annulus (Herman ring), or a single Jordan curve (Herman curve). The last one is the least understood. In this dissertation, we study a family of rational maps admitting a Herman ring with bounded type rotation number. For such a family, we prove a priori bounds that are independent of their conformal moduli via careful analysis of near-degenerate surfaces in the spirit of Kahn, Lyubich, and D. Dudko. As a major application, we study the limits of degenerating Herman rings and obtain the first examples of Herman curves which are not equivalent to round circles. The rigidity properties of such Herman curves are also explored. This dissertation also initiates the study of renormalization theory of critical quasicircle maps, i.e. analytic self homeomorphisms of a quasicircle with a single critical point. We prove a rigidity theorem, which implies dynamical universality and exponential convergence of renormalizations towards a horseshoe attractor. Moreover, we prove the hyperbolicity of renormalization periodic points of critical quasicircle maps by developing an operator called Corona Renormalization, a doubly connected version of Pacman Renormalization for Siegel disks.
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Title: Quantum circuits and real time dynamics with free fermions in disguise
Speaker: Balázs Pozsgai
Abstract: TBA
Title: General Free Fermionic and Parafermionic Quantum Chains
Speaker: Francisco Alcaraz
Abstract: TBA
Title: Integrable and non-integrable quenches from AdS/CFT
Speaker: Charlotte Kristjansen
Abstract: TBA
Title: Group Discussion
Title: Tensor product random matrix theory
Speaker: Alexander Altland
Abstract: TBA
Title: A Universal Model of Floquet Operator Krylov Space
Speaker: Aditi Mitra
Abstract: TBA
Title: Arithmetic Electric-Magnetic Duality
Abstract: The Langlands program is a grand organizing vision for a large slice of number theory and representation theory.
A shockingly accurate metaphor for the Langlands program has emerged as electric-magnetic duality in four-dimensional gauge theory, but where the role of spacetime is played by objects from arithmetic. I will discuss this general picture and begin to describe recent work with Yiannis Sakellaridis and Akshay Venkatesh, in which we apply ideas from QFT (the Gaiotto-Witten electric-magnetic duality for boundary theories) to a fundamental problem in number theory, predicting the relation between L-functions of Galois representations and integrals of automorphic forms.
Title: Controlling Chaos with Measurements and Feedback
Speaker: Jedediah Pixley
Abstract: TBA
Title: Measurement induced transition in long-range systems
Speaker: Rosario Fazio
Abstract: TBA
Title: A measurement-only approach for entanglement transitions in a projective gauge-Higgs model
Speaker: Tzu-Chieh Wei
Abstract: TBA
Title: No GT Seminar due to SCGP talk by David Ben-Zvi
Abstract:
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Title: Group Discussion
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Title: Quantum Simulation of Dynamical Phases of BCS Superconductors
Speaker: Ana Maria Rey
Abstract: TBA
Title: The Fate of Entanglement
Speaker: William Witczak-Krempa
Abstract: TBA
Title: Fixed points, traces and characters
Abstract: This talk will explore one of my favorite themes in mathematics: the abstract notion of a trace and its manifestation via fixed points in geometry and partition functions in quantum mechanics. This relation gives rise to a sequence of increasingly sophisticated character formulas, as well as a broader sense of what characters are. I will conclude with a perspective on L-functions of Galois representations as characters, developed in my joint work with Yiannis Sakellaridis and Akshay Venkatesh. (The talk is meant to be independent of the previous day's talk but with a closely related end-point.)
Title: Emergent Topology in Many-Body Dissipative Quantum Chaos
Speaker: Jacobus Verbaarschot
Abstract: TBA
Title: TBA
Speaker: David Ben-Zvi [University of Texas, Austin]
Abstract:
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Title: An Exceptional Approach to Kaluza-Klein Spectroscopy
Abstract: The spectrum of light single-trace operators of holographic CFTs at strong coupling and large N, can be mapped to the spectrum of Kaluza-Klein (KK) excitations over the dual AdS supergravity solutions. Computing these KK spectra is usually a difficult task even for the simplest AdS solutions. In this talk, I will review new spectral methods based on Exceptional Field Theory, a duality-covariant reformulation of the higher-dimensional supergravities. For certain AdS/CFT dual pairs, these methods bypass the difficulties and reduce the KK spectral problem to simple diagonalisation of suitable mass matrices. I will illustrate these methods for the class of AdS4 solutions of M-theory and type II string theory that uplift consistently from D=4 maximal gauged supergravities. Also, I will describe progress to extend these methods to AdS solutions that uplift from half-maximal supergravities.
Title: Integrability in the design and control of quantum devices
Speaker: Angela Foerster
Abstract: TBA
Title: TBA
Speaker: Eric Bedford [Stony Brook University]
Abstract: TBA
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Title: Steering far from equilibrium many-body quantum dynamics through chaos control
Speaker: Klaus Richter
Abstract: TBA
Title: Higher Fano manifolds
Speaker: Svetlana Makarova [Australian National University]
Abstract: Fano manifolds are projective manifolds whose anticanonical class (determinant of the tangent bundle) is ample. The positivity condition has far-reaching geometric implications, e.g., a Fano manifold over complex numbers is simply connected, which has an analogue on the algebro-geometric side: any Fano manifold is covered by rational curves, and in fact rationally connected, i.e., there are rational curves connecting any two of its points. In a series of papers, De Jong and Starr introduce and investigate possible candidates for the notion of higher rationally connectedness, inspired by the natural analogue in topology, and define that a projective manifold X is 2-Fano if it is Fano and the second Chern character ch2(T_X) is positive (intersects positively with every surface in X). In a similar way, one defines n-Fano manifolds for any n ≥ 2; for instance, P^n is n-Fano.
In this talk, I will give evidence for the analogy with higher connectedness and present certain classification results. In the second half of the talk, I will focus on the recent progress towards proving the conjecture that the only toric higher Fano manifolds are projective spaces.
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Title: Group Discussion
Title: Time evolution in isolated quantum systems out of equilibrium
Speaker: Gesualdo Delfino
Abstract: TBA
Title: Counterflow superfluids and transverse quantum fluids: When Mottness cooperates with supertransport
Speaker: Boris Svistunov
Abstract: TBA
Title: TBA
Speaker: Daniel Alvarez-Gavela [MIT]
Abstract: TBA
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Title: Super-and subdiffusion in classical spin chains
Speaker: Roderich Moessner
Abstract: TBA
Title: Revisiting Localization, Periodicity and Galois Symmetry
Speaker: Runjie Hu [Stony Brook University]
Abstract: It is known that two complex algebraic varieties can be algebraically isomorphic but not\r\nbe homeomorphic. Such examples can be obtained by changing the coefficients of the\r\ndefining equations by some field automorphism of a finite extension of the rationals Q.\r\nThis dissertation aims to understand how the entire Galois group of Q-bar, the algebraic\r\nclosure of Q, changes the underlying manifold structures of smooth complex varieties\r\ndefined by equations with coefficients in Q-bar. It is known by the theory of finite covering\r\nspaces (étale theory) that the Galois action does not change that aspect of the homotopy\r\ntype determined by finite group theory (the profinite homotopy type). Thus we can use the\r\nknown theory of manifolds in a given homotopy type to study the Galois conjugates of\r\nalgebraic varieties in a given étale homotopy type. We study three aspects of this problem:\r\n(1) what algebraic-topological data is sufficient to specify a topological manifold in a\r\nhomotopy type; (2) what might be the étale construction for manifolds; (3) how might one\r\nexpress the Galois action in terms of the algebraic-topological data. We suggest an approach\r\nusing the study in (2) in order to propose a geometric interpretation of the question in (3).
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Title: Quantum Mpemba effect
Speaker: Pasquale Calabrese
Abstract: TBA
Title: TBA
Speaker: Maxim Jeffs [Stony Brook University]
Abstract:
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Title: Robustness and eventual slow decay of bound states of interacting microwave photons in the Google Quantum AI experiment
Speaker: Olexei Motrunich
Abstract: TBA
Title: Group Discussion
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Title: The Kondo model at large spin
Speaker: Max Metlitski
Abstract: TBA
Title: Degeneration techniques in complex geometry
Speaker: Roberto Albesiano [Stony Brook University]
Abstract: In 2009, B. Berndtsson proved a theorem on the positivity of direct image bundles of\r\npositive line bundles. Berndtsson’s theorem has been successfully used to give radically\r\nnew proofs of some fundamental theorems in the part of complex geometry often referred\r\nto as $L^2$ methods; proofs that are based on the monotonicity of certain degenerations into\r\nsituations in which the results are obvious, and that reveal an unexpected underlying\r\nconvexity. Among these is a proof of the $L^2$ extension with sharp estimates. As a step\r\ntowards determining how much of the classical $L^2$ theory can be recovered by this\r\ntechnique, we will present a new proof of a Skoda-type $L^2$ division theorem.
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Title: Inhomogeneous quantum quench in (1+1)d conformal field theory
Speaker: Shinsei Ryu
Abstract: TBA
Title: The finite-area holomorphic quadratic differentials and the geodesic flow on infinite Riemann surface
Speaker: Dragomir Saric [Queens College CUNY]
Abstract: Let $X$ be an infinite Riemann surface with a conformally hyperbolic metric. The Hopf-Tsuji-Sullivan theorem states that the geodesic flow is ergodic iff the Poincare series is divergent iff the Brownian motion is recurrent, and many other equivalent conditions are given in the literature. We added an equivalent condition: the Brownian motion on $X$ is recurrent iff almost every horizontal leaf of every finite-area holomorphic quadratic differential is recurrent.
A finite-area holomorphic quadratic differential on $X$ is uniquely determined by the homotopy class of its horizontal foliation, uniquely represented by a measured geodesic lamination on $X$. Most measured geodesic laminations do not come from the horizontal foliations of finite-area differentials. The problem of intrinsically deciding which measured laminations are induced by finite-area differentials is highly transcendental. From now on, assume that $X$ is equipped with a geodesic pants decomposition whose cuffs are bounded. The space of finite-area holomorphic quadratic differentials on $X$ is in a one-to-one correspondence with the measured geodesic laminations on $X$ whose intersection numbers with the cuffs (and “adjoint cuffs”) are square summable. Using this parametrization, we establish that the Brownian motion on $X$ is recurrent iff the simple random walk on the graph dual to the pants decomposition is recurrent.
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Title: Negative tripartite information after quantum quenches in integrable systems
Speaker: Vincenzo Alba
Abstract: TBA
Title: Hydrodynamic transport of Dirac plasma in graphene
Speaker: Alex Levchenko
Abstract: TBA
Title: C^2 STRUCTURALLY STABLE RIEMANNIAN GEODESIC FLOWS OF CLOSED SURFACES ARE ANOSOV
Speaker: Marco Mazzucchelli [ENS Lyon]
Abstract: A celebrated claim of Poincaré asserts that any positively-curved Riemannian 2-sphere has a (possibly degenerate) elliptic closed geodesic. This claim has been confirmed generically by Contreras and Oliveira, without requirements on the curvature: a C^2 generic Riemannian metric on the 2-sphere has an elliptic closed geodesic. In this talk, I will present a generalization of this result to arbitrary closed surfaces: a C^2 generic Riemannian metric on a closed surface has either an elliptic closed geodesic or an Anosov geodesic flow. A consequence of this statement is a confirmation of the C^2 stability conjecture for Riemannian geodesic flows of closed surfaces: any such geodesic flow that is C^2 structurally stable within Riemannian geodesic flows must be Anosov. The proof is based on a new characterization of Anosov Reeb flows of closed contact 3-manifolds. This is joint work with Gonzalo Contreras.
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Title: Spectral Form Factors of attractively interacting fermions
Speaker: Victor Gurarie
Abstract: TBA
Title: Group Discussion
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