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We show that the Hamiltonian Lagrangian monodromy group, in its homological version, is trivial for any weakly exact Lagrangian submanifold of a symplectic manifold. The proof relies on a sheaf approach to Floer homology given by a relative…

Over function fields of p-adic curves, we construct stably rational varieties in the form of homogeneous spaces of SL_n with semisimple simply connected stabilizers and we show that strong approximation away from a non-empty set of places…

Let E be a locally compact second countable Hausdorff space and F the pertaining family of all closed sets. We endow F respectively with the Fell-topology, the upper Fell topology or the upper Vietoris-topology and investigate weak…

We propose a new weak convergence theorem for martingales, under gentler conditions than the usual convergence in probability of the sequence of associated quadratic variations. Its proof requires the combined use of Skorohod's…

We show that the image of repeated differentiation on weak cusp forms is precisely the subspace which is orthogonal to the space of weakly holomorphic modular forms. This gives a new interpretation of the weakly holomorphic Hecke…

We identify the weak closures of the ranges of certain Calkin representations for $L^{p}$, $1<p<\infty$. As a consequence, assuming the continuum hypothesis, we show that the commutant of $B(L^{p})$, $1<p<\infty$, in its ultrapower may or…

Let $\mathfrak g$ be a simple Lie algebra with Cartan subalgebra $\mathfrak h$ and Weyl group $W$. We build up a graded map $(\mathcal H\otimes \bigwedge\mathfrak h\otimes \mathfrak h)^W\to (\bigwedge \mathfrak g\otimes \mathfrak…

Let G be a reductive p-adic group, H(G) its Hecke algebra and S(G) its Schwartz algebra. We will show that these algebras have the same periodic cyclic homology. This might be used to provide an alternative proof of the Baum-Connes…

We give a new proof of the recent K\"unneth theorem for periodic topological cyclic homology (TP) of smooth and proper dg categories over perfect fields of characteristic p>0 due to Blumberg and Mandell. Our result is slightly stronger and…

We match the electroweak chiral Lagrangian with two singlet scalars to the next-to-minimal composite Higgs model with $ SO(6)/SO(5) $ coset structure and extract the scalar divergences to one loop. Assuming the additional scalar to be…

We investigate the extent to which the weak equivalences in a model category can be equipped with algebraic structure. We prove, for instance, that there exists a monad T such that a morphism of topological spaces admits T-algebra structure…

Given a weak distributive law between algebras underlying two weak bialgebras, we present sufficient conditions under which the corresponding weak wreath product algebra becomes a weak bialgebra with respect to the tensor product coalgebra…

We use the theory of Condensed Mathematics to build a condensed cohomology theory for the Weil group of a $p$-adic field. The cohomology groups are proved to be locally compact abelian groups of finite ranks in some special cases. This…

We provide a construction of associating a de Rham subbundle to a Higgs subbundle in characteristic $p$ in the geometric case. As applications, we obtain a Higgs semistability result and a $W_2$-unliftable result.

We survey recent results about the Torelli question for holomorphic-symplectic varieties. Following are the main topics. A Hodge theoretic Torelli theorem. A study of the subgroup W, of the isometry group of the weight 2 Hodge structure,…

We introduce the $L$-series of weakly holomorphic modular forms using Laplace transforms and give their functional equations. We then determine converse theorems for vector-valued harmonic weak Maass forms, Jacobi forms, and elliptic…

We provide a geometric Hodge-Tate map giving generic description of the overconvergent modular symbols of some p-adic (accessible) weight k, base-changed to C_p, in terms of overconvergent modular forms of weight k+2.

We introduce a class of "weakly asymptotically hyperbolic" geometries whose sectional curvatures tend to $-1$ and are $C^0$, but are not necessarily $C^1$, conformally compact. We subsequently investigate the rate at which curvature…

A weakly reflective submanifold is a minimal submanifold of a Riemannian manifold which has a certain symmetry at each point. In this paper we introduce this notion into a class of proper Fredholm (PF) submanifolds in Hilbert spaces and…

Weak C* Hopf algebras can act as global symmetries in low-dimensional quantum field theories, when braid group statistics prevents group symmetries. Possibilities to construct field algebras with weak C* Hopf symmetry from a given theory of…