Decomposition of Lagrangian classes on K3 surfaces

We study the decomposability of a Lagrangian homology class on a K3 surface into a sum of classes represented by special Lagrangian submanifolds, and develop criteria for it in terms of lattice theory. As a result, we prove the decomposability on an arbitrary K3 surface with respect to the Kähler classes in dense subsets of the Kähler cone. Using the same technique, we show that the Kähler classes on a K3 surface which admit a special Lagrangian fibration form a dense subset also. This implies that there are infinitely many special Lagrangian 3-tori in any log Calabi-Yau 3-fold.https://arxiv.org/abs/2001.00202Othe

Twitter in Academic Conferences: Usage, Networking and Participation over Time

Twitter is often referred to as a backchannel for conferences. While the main conference takes place in a physical setting, attendees and virtual attendees socialize, introduce new ideas or broadcast information by microblogging on Twitter. In this paper we analyze the scholars' Twitter use in 16 Computer Science conferences over a timespan of five years. Our primary finding is that over the years there are increasing differences with respect to conversation use and information use in Twitter. We studied the interaction network between users to understand whether assumptions about the structure of the conversations hold over time and between different types of interactions, such as retweets, replies, and mentions. While `people come and people go', we want to understand what keeps people stay with the conference on Twitter. By casting the problem to a classification task, we find different factors that contribute to the continuing participation of users to the online Twitter conference activity. These results have implications for research communities to implement strategies for continuous and active participation among members

Surface and Edge States in Topological Semi-metals

We study the topologically non-trivial semi-metals by means of the 6-band Kane model. Existence of surface states is explicitly demonstrated by calculating the LDOS on the material surface. In the strain free condition, surface states are divided into two parts in the energy spectrum, one part is in the direct gap, the other part including the crossing point of surface state Dirac cone is submerged in the valence band. We also show how uni-axial strain induces an insulating band gap and raises the crossing point from the valence band into the band gap, making the system a true topological insulator. We predict existence of helical edge states and spin Hall effect in the thin film topological semi-metals, which could be tested with future experiment. Disorder is found to significantly enhance the spin Hall effect in the valence band of the thin films