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In this talk, I will discuss two of our recent results on three-dimensional (3D) packing problems: the 3D Knapsack problem and the 3D Bin Packing problem. In both settings, we are given a collection of axis-aligned cuboids. In the Knapsack problem, each cuboid is associated with a profit, and the objective is to pack a subset of cuboids non-overlappingly into a unit cube to maximize total profit. In contrast, the Bin Packing problem seeks to pack all the cuboids using the minimum number of unit cubes (bins). Both problems are NP-hard and unlike their two-dimensional counterparts that have been extensively studied, the 3D variants have received much less attention. The previously best-known approximation ratios for 3D Knapsack and 3D Bin Packing are 7 + ε and (T_∞)^2 + ε ≈ 2.86, respectively for any constant ε > 0, where T_∞ ≈ 1.691 is the well-known Harmonic constant in Bin Packing. We provide improved approximation ratios of 139/29 + ε ≈ 4.794, and 3T_∞/2 + ε ≈ 2.54, for 3D Knapsack and 3D Bin Packing, respectively. Our key technical contribution is container packing -- a structured packing in 3D wherein all items are assigned into a constant number of containers, and each container is packed using a specific strategy based on its type. I shall also discuss few extensions of our techniques to related 3D packing problems.

This talk will provide a basic introduction to the three dimensional Dirac equation that describes an electron interacting with a magnetic field. Over the years a lot of work has gone into constructing zero energy solutions, also known as zero modes, for said equation. In this talk I will explain the importance of zero modes e.g. I will show how they relate to the stability of the hydrogen atom. After presenting explicit examples, I will state necessary conditions for the magnetic field so that zero modes exist. Here, of particular interest is a sharp inequality that is optimized by a magnetic field whose field lines are interlinking circles. This inequality relates to sharp inequalities for spinors of which some more examples will be given. _____________________ Invited by Prof. Christian Hainzl

Quantum mechanics, now about a century old, is a very successful physical theory of matter on a small scale. From its first description until today, it has surprised scientists and laypersons alike by the strange behaviour it attributes to particles, atoms, and molecules. This behaviour can be characterized by the keywords Uncertainty, Superposition, and Entanglement. It took about sixty years before it was realized that these three characteristics do not just express a certain vagueness and strangeness of matter on a small scale but can actually be USEd to our advantage. In 1994 Peter Shor made this idea concrete by devising an algorithm that would enable large arrays of quantum systems to perform specific calculations (factoring large integers), which are impossible to do in practice on any classical device. With this algorithm, present-day cryptographic schemes can be broken, provided such "quantum computers” can be made to work. Starting from a discussion of the "two-slit experiment”, we sketch the working of Shor's algorithm and discuss the possibilities of future quantum computers. About the speaker: Hans Maassen is a dutch mathematical physicist and emeritus professor specializing in quantum probability and quantum information theory. Standing out among his discoveries is the entropic uncertainty relation, named after himself and Jos Uffink, a fundamental  inequality in quantum mechanics. This talk is open to the general public and all interested persons, and is presented by the SFB TRR352 "Mathematics of Many-Body Quantum systems and their collective phenomena" in cooperation with the TUM-IAS Workshop "Beyond IID in Information Theory".

Please register for the workshop. More information can be found at s. https://www.fm.math.lmu.de/en/news/events-overview/event/frontiers-in-mathematical-finance-between-theory-and-applications.html