Thin films of transition metal oxides open up a gateway to nanoscale electronic devices beyond silicon characterized by novel electronic functionalities. While such films are commonly prepared in an oxygen atmosphere, they are typically considered to be ideally terminated with the stoichiometric composition. Using the prototypical correlated metal SrVO$_3$ as an example, it is demonstrated that this idealized description overlooks an essential ingredient: oxygen adsorbing at the surface apical sites. The oxygen adatoms, which persist even in an ultrahigh vacuum environment, are shown to severely affect the intrinsic electronic structure of a transition metal oxide film. Their presence leads to the formation of an electronically dead surface layer but also alters the band filling and the electron correlations in the thin films. These findings highlight that it is important to take into account surface apical oxygen or -- mutatis mutandis -- the specific oxygen configuration imposed by a capping layer to predict the behavior of ultrathin films of transition metal oxides near the single unit-cell limit.

Judith Gabel Matthias Pickem Philipp Scheiderer Lenart Dudy Berengar Leikert Marius Fuchs Martin Stübinger Matthias Schmitt Julia Küspert Giorgio Sangiovanni Jan M. Tomczak Karsten Held Tien-Lin Lee Ralph Claessen Michael Sing

Novel two-dimensional electron systems at the interfaces and surfaces of transition-metal oxides recently have attracted much attention as they display tunable, intriguing properties that can be exploited in future electronic devices. Here we show that a high-mobility quasi-two-dimensional electron system with strong spin-orbit coupling can be induced at the surface of a KTaO$_3$ (001) crystal by pulsed laser deposition of a disordered LaAlO$_3$ film. The momentum-resolved electronic structure of the buried electron system is mapped out by hard x-ray angle-resolved photoelectron spectroscopy. From a comparison to calculations it is found that the band structure deviates from that of electron-doped bulk KTaO$_3$ due to the confinement to the interface. Nevertheless, the Fermi surface appears to be clearly three-dimensional. From the $k$ broadening of the Fermi surface and core-level depth profiling we estimate the extension of the electron system to be at least 1 nm but not much larger than 2 nm, respectively.

Michael Zapf Matthias Schmitt Judith Gabel Philipp Scheiderer Martin Stübinger Berengar Leikert Giorgio Sangiovanni Lenart Dudy Sergii Chernov Sergey Babenkov Dmitry Vasilyev Olena Fedchenko Katerina Medjanik Yury Matveyev Andrei Gloskowski Christoph Schlueter Tien-Lin Lee Hans-Joachim Elmers Gerd Schönhense Michael Sing Ralph Claessen

This is a survey of recent developments in combinatorics. The goal is to give a big picture of its many interactions with other areas of mathematics, such as: group theory, representation theory, commutative algebra, geometry (including algebraic geometry), topology, probability theory, and theoretical computer science.

Cristian Lenart

Pipe dreams and bumpless pipe dreams for vexillary permutations are each known to be in bijection with certain semistandard tableaux via maps due to Lenart and Weigandt, respectively. Recently, Gao and Huang have defined a bijection between the former two sets. In this note we show for vexillary permutations that the Gao-Huang bijection preserves the associated tableaux, giving a new proof of Lenart's result. Our methods extend to give a recording tableau for any bumpless pipe dream.

Adam Gregory Zachary Hamaker

We present an explicit combinatorial realization of the commutor in the category of crystals which was first studied by Henriques and Kamnitzer. Our realization is based on certain local moves defined by van Leeuwen.

Cristian Lenart

By combining the DiPerna and Lions techniques for the nonrelativistic Boltzmann equation and the Dudy\'{n}ski and Ekiel-Je\.{z}ewska device of the causality of the relativistic Boltzmann equation, it is shown that there exists a global mild solution to the Cauchy problem for the relativistic Boltzmann equation with the assumptions of the relativistic scattering cross section including some relativistic hard interactions and the initial data satisfying finite mass, energy and entropy. This is in fact an extension of the result of Dudy\'{n}ski and Ekiel-Je\.{z}ewska to the case of the relativistic Boltzmann equation with hard interactions.

Zhenglu Jiang

Participatory Artificial Intelligence (PAI) has recently gained interest by researchers as means to inform the design of technology through collective's lived experience. PAI has a greater promise than that of providing useful input to developers, it can contribute to the process of democratizing the design of technology, setting the focus on what should be designed. However, in the process of PAI there existing institutional power dynamics that hinder the realization of expansive dreams and aspirations of the relevant stakeholders. In this work we propose co-design principals for AI that address institutional power dynamics focusing on Participatory AI with youth.

Michael Alan Chang Shiran Dudy

We propose a new approach to the multiplication of Schubert classes in the K-theory of the flag variety. This extends the work of Fomin and Kirillov in the cohomology case, and is based on the quadratic algebra defined by them. More precisely, we define K-theoretic versions of the Dunkl elements considered by Fomin and Kirillov, show that they commute, and use them to describe the structure constants of the K-theory of the flag variety with respect to its basis of Schubert classes.

Cristian Lenart

We present a simple combinatorial model for the characters of the irreducible integrable highest weight modules for complex symmetrizable Kac-Moody algebras. This model can be viewed as a discrete counterpart to the Littelmann path model. We describe crystal graphs and give a Littlewood-Richardson rule for decomposing tensor products of irreducible representations. The new model is based on the notion of a lambda-chain, which is a chain of positive roots defined by certain interlacing conditions.

Cristian Lenart Alexander Postnikov

A recent breakthrough in the theory of (type A) Macdonald polynomials is due to Haglund, Haiman and Loehr, who exhibited a combinatorial formula for these polynomials in terms of a pair of statistics on fillings of Young diagrams. Ram and Yip gave a formula for the Macdonald polynomials of arbitrary type in terms of so-called alcove walks; these originate in the work of Gaussent-Littelmann and of the author with Postnikov on discrete counterparts to the Littelmann path model. In this paper, we relate the above developments, by explaining how the Ram-Yip formula compresses to a new formula, which is similar to the Haglund-Haiman-Loehr one but contains considerably fewer terms.

Cristian Lenart