Related papers: Weinstein Homotopies
Reply to Ikeda (arXiv:0712.3341).
This is an expository lecture, for the Abel bicentennial (Oslo, 2002), describing some recent work on the (small) quantum cohomology ring of Grassmannians and other homogeneous varieties.
In this short note we provide a review of some developments in the area of homotopy quantum field theories, loosely based on a talk given by the second author at the Xth Oporto Meeting on Geometry, Topology and Physics.
Motivated by a previous work of Zheng and the second named author, we study pinching constants of compact K\"ahler manifolds with positive holomorphic sectional curvature. In particular we prove a gap theorem following the work of Petersen…
The topology of digital images has been studied much in recent years, but no attempt has been made to exhaustively catalog the structure of binary images of small numbers of points. We produce enumerations of several classes of digital…
We present some questions and suggestion on the second part of the Hilbert 16th problem
This survey contains the main results in rational homotopy, from the beginning to the most recent ones. It makes the status of the art, gives a short presentation of some areas where rational homotopy has been used, and contains a lot of…
A solution is given to a long-standing open problem posed by Almgren.
Brief recollections of how the author interacted with Steve Weinberg over issues in quantum mevhanics
In this short note, we construct a class of models of an extension of homotopy type theory, which we call homotopy type theory with an interval type.
We present several results, including some remarks on the Hopf Lemma.
We describe recent progress on QH(G/P) with special emphasis of our own work.
Basic examples show that coincidence theory is intimately related to central subjects of differential topology and homotopy theory such as Kervaire invariants and divisibility properties of Whitehead products and of Hopf invariants. We…
We introduce the notion of (half) 2-adjoint equivalences in Homotopy Type Theory and prove their expected properties. We formalized these results in the Lean Theorem Prover.
One generally expects that the techniques of arboreal singularities and gluing of local differential graded categories will result in a useful global invariant for all Weinstein manifolds. In this paper we construct explicit models for the…
Homotopy limits and colimits are homotopical replacements for the usual limits and colimits of category theory, which can be approached either using classical explicit constructions or the modern abstract machinery of derived functors. Our…
In this paper we describe a general strategy for approaching the Weinstein conjecture in dimension three. We apply this approach to prove the Weinstein conjecture for a new class of contact manifolds (planar contact manifolds). We also…
We established existence of periodic Reeb orbits for a large class of tight contact structures on closed 3-manifolds, notably the Stein fillable structures, based on a fundamental theorem of Cliff Taubes on symplectic 4-manifolds.
We give a detailed exposition of the homotopy theory of equivalence relations, perhaps the simplest nontrivial example of a model structure.
In a recent paper, Vink et al. analyzed some spectropolarimetry data of O-type stars. Here we comment on our disagreement with some points presented in this paper, with the hope of helping to fully grasp the scientific implication of these…