相关论文: Thompson's conjecture for real semi-simple Lie gro…

We prove that higher-dimensional Thompson's groups have linear divergence functions. By the work of Dru\c{t}u, Mozes, and Sapir, this implies none of the asymptotic cones of $nV$ has a cut-point.

In this exposition we give a simple and complete treatment of A. Knutson and T. Tao's recent proof (http://front.math.ucdavis.edu/math.RT/9807160) of the saturation conjecture, which asserts that the Littlewood-Richardson semigroup is…

We prove new cases of the Hilbert-Smith conjecture for actions by natural homeomorphisms in symplectic topology. Specifically, we prove that the group of $p$-adic integers $\mathbb Z_p$ does not admit non-trivial continuous actions by…

We prove that Thompson's groups $F$ and $V$ are the geometry groups of associativity, and of associativity together with commutativity, respectively. We deduce new presentations of $F$ and $V$. These presentations lead to considering a…

We give lower bounds for the small moments of the sum of a random multiplicative function, which improve on some results of Bondarenko and Seip and constitute further progress towards (dis)proving a conjecture of Helson. We also prove…

We prove that LG models for minimal semisimple adjoint orbits satisfy the Katzarkov-Kontsevich-Pantev conjecture about new Hodge theoretical invariants.

We show that Thompson's $A\times B$-Lemma can be obtained as a consequence of the Brauer pair version of Brauer's Third Main Theorem.

We prove Simon's conjecture for 3-manifolds.

We prove a homological stability theorem for the subgroup of the mapping class group acting as the identity on some fixed portion of the first homology group of the surface. We also prove a similar theorem for the subgroup of the mapping…

We detect topological semigroups that are topological paragroups, i.e., are isomorphic to a Rees product of a topological group over topological spaces with a continuous sandwich function. We prove that a simple topological semigroup $S$ is…

In this paper, we use inductive methods similar to those employed in a 2025 paper by Alberts, Lemke Oliver, Wang and Wood in order to prove many new cases of the Twisted Malle's Conjecture. Previously, this conjecture had only been proven…

We give a simple proof of the Lalonde-McDuff conjecture for aspherical manifolds.

We prove a discretized Product Theorem for general simple Lie groups, in the spirit of Bourgain's Discretized Sum-Product Theorem.

We prove that Thompson's group F is not minimally almost convex with respect to any generating set which is a subset of the standard infinite generating set for F and which contains x_1. We use this to show that F is not almost convex with…

We show that a locally symmetric space of noncompact type and with finite volume is quasi-isometric to the euclidean cone over a finite simplicial complex. A detailed analysis of metric properties yields a proof of a conjecture of Siegel.

We give an elementary proof of the real section conjecture for quasi-projective hyperbolic curves and semi-abelian varieties. The underlying argument is essentially equivalent to the one given by J. Stix.

We extend a conjecture of Kimberley-Robertson on the abelianizations of certain square complex groups.

Liebeck, Nikolov, and Shalev conjectured that for every subset A of a finite simple group S with |A|>1, there exist O( log|S| / log|A| ) conjugates of A whose product is S. This paper is a companion to [Lifshitz: Completing the proof of the…

In this paper, we use the KK-theory of Kasparov to prove exactness of sequences relating the K-theory of a real C^*-algebra and of its complexification (generalizing results of Boersema). We use this to relate the real version of the…

In this survey, we discuss a series of linearization problems--for Poisson structures, Lie algebroids, and Lie groupoids. The last problem involves a conjecture on the structure of proper groupoids. Attempting to prove this by the method of…