-
作者：Dahmani, Francois; Touikan, Nicholas
作者单位：Centre National de la Recherche Scientifique (CNRS); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); University of New Brunswick
摘要：We solve Dehn's isomorphism problem for virtually torsion-free relatively hyperbolic groups with nilpotent parabolic subgroups. We do so by reducing the isomorphism problem to three algorithmic problems in the parabolic subgroups, namely the isomorphism problem, separation of torsion (in their outer automorphism groups) by congruences, and the mixed Whitehead problem, an automorphism group orbit problem. The first step of the reduction is to compute canonical JSJ decompositions. Dehn fillings ...
-
作者：Erman, Daniel; Sam, Steven V.; Snowden, Andrew
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of California System; University of California San Diego; University of Michigan System; University of Michigan
-
作者：Li, Chunyi
作者单位：University of Warwick
摘要：We study the Clifford type inequality for a particular type of curves C-2,C-2,C-5, which are contained in smooth quintic threefolds. This allows us to prove some stronger Bogomolov-Gieseker type inequalities for Chern characters of stable sheaves and tilt-stable objects on smooth quintic threefolds. Employing the previous framework by Bayer, Bertram, Macri, Stellari and Toda, we construct an open subset of stability conditions on every smooth quintic threefold in P-C(4).
-
作者：Skipper, Rachel; Witzel, Stefan; Zaremsky, Matthew C. B.
作者单位：University of Gottingen; University of Bielefeld; State University of New York (SUNY) System; University at Albany, SUNY
摘要：We show that for every positive integer n there exists a simple group that is of type Fn-1 but not of type Fn. For n3 these groups are the first known examples of this kind. They also provide infinitely many quasi-isometry classes of finitely presented simple groups. The only previously known infinite family of such classes, due to Caprace-Remy, consists of non-affine Kac-Moody groups over finite fields. Our examples arise from Rover-Nekrashevych groups, and contain free abelian groups of infi...
-
作者：Simmons, David; Weiss, Barak
作者单位：University of York - UK; Tel Aviv University
摘要：We extend results of Y. Benoist and J.-F. Quint concerning random walks on homogeneous spaces of simple Lie groups to the case where the measure defining the random walk generates a semigroup which is not necessarily Zariski dense, but satisfies some expansion properties for the adjoint action. Using these dynamical results, we study Diophantine properties of typical points on some self-similar fractals in R-d. As examples, we show that for any self-similar fractal K subset of R-d satisfying t...
-
作者：Montgomery, Richard
作者单位：University of California System; University of California Santa Cruz
摘要：For the Newtonian 4-body problem in space we prove that any zero angular momentum bounded solution suffers infinitely many coplanar instants, that is, times at which all 4 bodies lie in the same plane. This result generalizes a known result for collinear instants (syzygies) in the zero angular momentum planar 3-body problem, and extends to thed + 1 body problem in d-space. The proof begins by identifying the translation-reduced configuration space with real dxd matrices, the degeneration locus...
-
作者：Blair, Matthew D.; Sogge, Christopher D.
作者单位：University of New Mexico; Johns Hopkins University
摘要：We consider the problem of proving Lp bounds for eigenfunctions of the Laplacian in the high frequency limit in the presence of nonpositive curvature and more generally, manifolds without conjugate points. In particular, we prove estimates at the critical exponent pc=2(d+1)d-1, where a spectrum of scenarios for phase space concentration must be ruled out. Our work establishes a gain of an inverse power of the logarithm of the frequency in the bounds relative to the classical Lp bounds of the s...
-
作者：Aizenman, Michael; Duminil-Copin, Hugo; Tassion, Vincent; Warzel, Simone
作者单位：Princeton University; Universite Paris Saclay; University of Geneva; Swiss Federal Institutes of Technology Domain; ETH Zurich; Technical University of Munich
摘要：The known Pfaffian structure of the boundary spin correlations, and more generally order-disorder correlation functions, is given a new explanation through simple topological considerations within the model's random current representation. This perspective is then employed in the proof that the Pfaffian structure of boundary correlations emerges asymptotically at criticality in Ising models on Z2 with finite-range interactions. The analysis is enabled by new results on the stochastic geometry ...
-
作者：Sidoravicius, Vladas; Stauffer, Alexandre
作者单位：New York University; NYU Shanghai; University of Bath; Roma Tre University
摘要：We consider a stochastic aggregation model on Z(d). Start with particles distributed according to the product Bernoulli measure with parameter mu. In addition, start with an aggregate at the origin. Non-aggregated particles move as continuous-time simple random walks obeying the exclusion rule, whereas aggregated particles do not move. The aggregate grows by attaching particles to its surface whenever a particle attempts to jump onto it. This evolution is called multi-particle diffusion limite...
-
作者：Beliakova, Anna; Putyra, Krzysztof K.; Wehrli, Stephan M.
作者单位：University of Zurich; Syracuse University
摘要：Motivated by topology, we develop a general theory of traces and shadows for an endobicategory, which is a pair: bicategory and endobifunctor . For a graded linear bicategory and a fixed invertible parameter q, we quantize this theory by using the endofunctor sigma q such that sigma q:=q-deg sigma for any 2-morphism and coincides with sigma otherwise. Applying the quantized trace to the bicategory of Chen-Khovanov bimodules we get a new triply graded link homology theory called quantum annular...
