The Event Horizon Telescope (EHT) has mapped the central compact radio source of the elliptical galaxy M87 at 1.3 mm with unprecedented angular resolution. These images show a prominent ring with a diameter of ~40 micro-arcsecond, consistent with the size and shape of the lensed photon orbit encircling the “shadow” of a supermassive black hole. The ring is persistent across four observing nights and shows enhanced brightness in the south. Here we consider the physical implications of the asymmetric ring seen in the 2017 EHT data. To this end, we construct a large library of models based on general relativistic magnetohydrodynamic simulations and synthetic images produced by general relativistic ray tracing. We compare the observed visibilities with this library and confirm that the asymmetric ring is consistent with earlier predictions of strong gravitational lensing of synchrotron emission from a hot plasma orbiting near the black hole event horizon. Overall, the observed image is consistent with expectations for the shadow of a spinning Kerr black hole as predicted by general relativity. If the black hole spin and M87’s large scale jet are aligned, then the black hole spin vector is pointed away from Earth. Models in our library of non-spinning black holes are inconsistent with the observations as they do not produce sufficiently powerful jets. We also briefly discuss the possibility of the alternatives to a black hole for the central compact object.

Plan of the seminar: we separate each talk into two. In the first 60 minutes the speaker gives an introductory talk for non-mathematicians. After a short break, the second 60 minutes is spent for a bit more detailed talk for mathematicians (working in other areas). We welcome you joining both parts of the seminar or only the first/second half.

Abstract: In this talk, I would like to talk about certain invariants that look like dimension. This talk has independent two parts.

In part 1, I will talk about finite metric spaces. In 2013, Leinster introduced the notion of magnitude of finite metric spaces. It measures effective number of points in finite metric spaces. Considering magnitude and scale transformation, Leinster and Willerton defined dimension of finite metric space with scale. I will explain the definition of magnitude of finite metric spaces and see examples.

In part 2, I will talk about derived categories of smooth projective varieties or finite dimensional algebras. In 2014, Dimitrov, Heiden, Katzarkov and Kontsevich introduced the notion of entropy of endofunctors of derived categories. It measures complexity of endofunctors under iteration. Serre functor is an autoequivalence of derived category, that describes Serre duality. Entropy of Serre functor looks like dimension of derived categories. I will talk about known results for entropy of Serre functors and some related topics.

GRIPS (Graduate-level Research in Industrial Projects for Students)-Sendai program was held last summer (June 18 - Aug. 10, 2018) with the support of iTHEMS as well as other institutions and companies. Two industrial projects were launched under the suggestion of TOYOTA and NEC, and two teams composed of US and Japanese students have worked intensively to find solutions of these problems. See for the details of the GRIPS program and the summary of activities at GRIPS-Sendai 2018.

This year, GRIPS-Sendai program will be held from June 17 through Aug. 9, 2019 with a larger scale under the support of iTHEMS. Stay tuned for further information.