We present a modern formulation of Élie Cartan's structure theory for Lie pseudogroups and prove a reduction theorem that clarifies the role of Cartan's systatic system.

Uploaded March 2025

We study Hamiltonicity in random subgraphs of the hypercube Qn. Our first main theorem is an optimal hitting time result. Our techniques also show that, with high probability, for all fixed p ∈ (0, 1] the graph Qn p contains an almost spanning cycle. Our methods involve branching processes, the R¨odl nibble, and absorption.

Uploaded March 2025

In this paper, we complete the program on the (non-)construction of the focusing Hartree Gibbs measures in the three-dimensional setting. More precisely, we study a focusing Φ43-modelwith a Hartree-type nonlinearity, where the potential for the Hartree nonlinearity is given by the Bessel potential of order β.

Uploaded March 2025

For each positive integer t and each sufficiently large integer r, we show that the maximum number of elements of a simple, rank-r, C-representable matroid with no U₂, t+₃-minor is t(r2)+r. We derive this as a consequence of a much more general result concerning matroids on group-labeled graphs.

Uploaded March 2025

In this volume, we introduce a property of topological dynamical systems that we call finite dynamical complexity. For systems with this property, one can in principle compute the K-theory of the associated crossed product C*-algebra by splitting it up into simpler pieces and using the methods of controlled K-theory. The main part of the paper illustrates this idea by giving a new proof of the Baum-Connes conjecture for actions with finite dynamical complexity.

Uploaded March 2025

This monograph provides a foundation for the theory of Drinfeld modular forms of arbitrary rank r and is subdivided into three chapters. In the first chapter, we develop the analytic theory. In the second chapter, we compare the analytic theory with the algebraic one that was begun in a paper of the third author. In the third chapter, we construct and study some examples of Drinfeld modular forms.

Uploaded March 2025

We study maximal length collections of disjoint paths, or 'disjoint optimizers', in the directed landscape. We show that disjoint optimizers always exist, and that their lengths can be used to construct an extended directed landscape.

Uploaded March 2025

In this fascinating book Cryptography , Panos Louridas provides a broad and accessible introduction to cryptography, the art and science of keeping and revealing secrets. Louridas explains just how cryptography works to keep our communications confidential, tracing it back all the way to its ancient roots. Then he follows its long and winding path to where we are today and reads the signs that point to where it may go tomorrow.

Uploaded March 2025

In this paper, we investigate the asymptotic analysis and qualitative behaviour for a general sequence of Sacks-Uhlenbeck -harmonic maps from degenerating Riemann surfaces. This answers an open problem proposed by J. D. Moore, aiming at developing a partial Morse theory for closed parametrized minimal surfaces with arbitrary codimensions in compact Riemannian manifolds.

Uploaded March 2025

This book investigates the asymptotic analysis and qualitative behavior

for a general sequence of Sacks-Uhlenbeck α-harmonic maps from degenerating

Riemann surfaces. This answers an open problem proposed by J. D. Moore, aiming

at developing a partial Morse theory for closed parametrized minimal surfaces with

arbitrary codimensions in compact Riemannian manifolds