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  • Birkhoff’s conjecture on integrable billiards and Kac’s problem “hearing the shape of a drum”

    Abstract: Billiards on an elliptical billiard table are completely integrable: phase space is foliated by invariant submanifolds for the billiard flow. Birkhoff conjectured that ellipses are the only plane domains with integrable billiards. Avila-deSimoi- Kaloshin proved the conjecture for ellipses of sufficiently small eccentricity. Kaloshin-Sorrentino proved local results for all eccentricities. On the quantum level, the analogous […]

  • CMSA-QMMP-03.16.2022-1544x2048-1

    Summing Over Bordisms In 2d TQFT

    Virtual

    Abstract: Some recent work in the quantum gravity literature has considered what happens when the amplitudes of a TQFT are summed over the bordisms between fixed in-going and out-going boundaries. We will comment on these constructions. The total amplitude, that takes into account all in-going and out-going boundaries can be presented in a curious factorized form. […]

  • CMSA-QMMP-03.17.2022-1-1544x2048-1

     A Hike through the Swampland

    https://youtu.be/9Mq9Jvmo3ic Abstract: The Swampland program aims at uncovering the universal implications of quantum gravity at low-energy physics. I will review the basic ideas of the Swampland program, formal and phenomenological implications, and provide a survey of the techniques commonly used in Swampland research including tools from quantum information, holography, supersymmetry, and string theory.

  • CMSA-Interdisciplinary-Science-Seminar-03.17.2022-1583x2048

    On optimization and generalization in deep learning

    Abstract: Deep neural networks have achieved significant empirical success in many fields, including the fields of computer vision and natural language processing. Along with its empirical success, deep learning has been theoretically shown to be attractive in terms of its expressive power. However, the theory of expressive power does not ensure that we can efficiently find an optimal solution in […]

  • Moduli Space of Metric SUSY Graphs

    Virtual

    Member Seminar Speaker: Yingying Wu Title: Moduli Space of Metric SUSY Graphs Abstract: SUSY curves are algebraic curves with additional supersymmetric or supergeometric structures. In this talk, I will present the construction of dual graphs of SUSY curves with Neveu–Schwarz and Ramond punctures. Then, I will introduce the concept of the metrized SUSY graph and […]

  • 3/21/2022 – Swampland Seminar

    Open Mic Discussion Topic: Entropy bounds (species bound, Bekenstein bound, CKN bound, and the like)

  • Bulk-boundary correspondence for vacuum asymptotically Anti-de Sitter spacetimes

    Abstract: The AdS/CFT conjecture in physics posits the existence of a correspondence between gravitational theories in asymptotically Anti-de Sitter (aAdS) spacetimes and field theories on their conformal boundary. In this presentation, we prove rigorous mathematical statements toward this conjecture. In particular, we show there is a one-to-one correspondence between aAdS solutions of the Einstein-vacuum equations and a suitable space of data on […]

  • CMSA-Combinatorics-Physics-and-Probability-Seminar-3.15.2022-1

    Flip processes

    Abstract: We introduce a class of random graph processes, which we call \emph{flip processes}. Each such process is given by a \emph{rule} which is just a function $\mathcal{R}:\mathcal{H}_k\rightarrow \mathcal{H}_k$ from all labelled $k$-vertex graphs into itself ($k$ is fixed). The process starts with a given $n$-vertex graph $G_0$. In each step, the graph $G_i$ is obtained […]

  • Fluctuation scaling or Taylor’s law of heavy-tailed data, illustrated by U.S. COVID-19 cases and deaths

    Speaker: Joel E. Cohen (Rockefeller University and Columbia University) Title: Fluctuation scaling or Taylor’s law of heavy-tailed data, illustrated by U.S. COVID-19 cases and deaths Abstract: Over the last century, ecologists, statisticians, physicists, financial quants, and other scientists discovered that, in many examples, the sample variance approximates a power of the sample mean of each of a set […]

  • CMSA-QMMP-03.23.2022-1583x2048

    Non-zero momentum requires long-range entanglement

    Youtube Video   Abstract: I will show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has non-zero lattice momentum, i.e. if it is an eigenstate of the translation symmetry with eigenvalue not equal to 1. Equivalently, any state that can be connected with a non-zero momentum state through […]

  • CMSA-NTM-Seminar-03.23.2022-1553x2048-1

    Formal Mathematics Statement Curriculum Learning

    https://youtu.be/4zINaGrPc9M Speaker: Stanislas Polu, OpenAI Title: Formal Mathematics Statement Curriculum Learning Abstract: We explore the use of expert iteration in the context of language modeling applied to formal mathematics. We show that at same compute budget, expert iteration, by which we mean proof search interleaved with learning, dramatically outperforms proof search only.  We also observe that […]

  • CMSA-GR-Seminar-03.24.22

    Rough solutions of the $3$-D compressible Euler equations

    Abstract: I will talk about my work on the compressible Euler equations. We prove the local-in-time existence the solution of the compressible Euler equations in $3$-D, for the Cauchy data of the velocity, density and vorticity $(v,\varrho, \omega) \in H^s\times H^s\times H^{s’}$, $2<s'<s$.  The result extends the sharp result of Smith-Tataru and Wang, established in the irrotational […]