Vorträge in der Woche 18.11.2024 bis 24.11.2024

Dienstag, 19.11.2024: Representation Theory of semisimple Lie groups II

Anton Deitmar

Mittwoch, 20.11.2024: Tropical refined curve counting and mirror symmetry

Qaasim Shafi (Heidelberg)

An old theorem, due to Mikhalkin, says that the number of rational plane curves of degree d through 3d-1 points is equal to a count of tropical curves (combinatorial objects which are more amenable to computations). There are two natural directions for generalising this result: extending to higher genus curves and allowing for more general conditions than passing through points. I’ll discuss a generalisation which does both, as well as recent work connecting it to mirror symmetry for log Calabi-Yau surfaces. This is joint work with Patrick Kennedy-Hunt and Ajith Urundolil Kumaran.

Donnerstag, 21.11.2024: A geometric choice of asymptotically Euclidean coordinates via STCMC-foliations

Olivia Vicanek Martinez (Universität Tübingen)

Asymptotically Euclidean 3-dimensional initial data sets were shown to carry asymptotic foliations of closed hypersurfaces with constant spacetime mean curvature (Cederbaum-Sakovich, 2021). In order to prove the inverse implication of this result and hence the geometric characterization of being asymptotically Euclidean, we start from the purely geometric foliation and construct asymptotic coordinates from it, exploiting the properties of the induced Laplacian of the foliation leaves via a delicate analysis. We show that these coordinates are asymptotically Euclidean, and moreover seem well-adapted to the center of mass. This is joint work with A. Piubello.

Donnerstag, 21.11.2024: Typical Quantum States of the Universe are Observationally Indistinguishable

Prof. Dr. Eddy Keming Chen (University of California at San Diego)

This paper is about the epistemology of quantum theory. We establish a new result about a limitation to knowledge of its central object -- the quantum state of the universe. We show that, if the universal quantum state can be assumed to be a typical unit vector from a high-dimensional subspace of Hilbert space (such as the subspace defined by a low-entropy macro-state as prescribed by the Past Hypothesis), then no observation can determine (or even just narrow down significantly) which vector it is. Typical state vectors, in other words, are observationally indistinguishable from each other. Our argument is based on a typicality theorem from quantum statistical mechanics. We also discuss how theoretical considerations that go beyond the empirical evidence might bear on this fact and on our knowledge of the universal quantum state. https://arxiv.org/abs/2410.16860 <https://urldefense.com/v3/__https://arxiv.org/abs/2410.16860__;!!Mih3wA!HvIKeMUNQ4UbbRQdeRx7ufHuiIFcZ5KL-U2i-RFzX6BB_JRJH6S4lzjbxbB6R7q-WSCGY9lzjU85rbublCRmyVcEqAHH-Xw$>

Freitag, 22.11.2024: Cellular Approximation and Whitehead's Theorem

Anastasios Papadopoulos