I review the current controversial status of the so-called "maximum force conjecture" in general relativity, whose validity has recently been debated. Then I will discuss how maximum force conjecture can nevertheless be relevant for black hole thermodynamics.

The Workshop on Virus Dynamics is an international meeting held every 2 years. It brings virologists, immunologists, and microbiologists together with mathematical and computational modellers, bioinformaticians, bioengineers, virophysicists, and systems biologists to discuss current approaches and challenges in modelling and analyzing different aspects of virus and immune system dynamics, and associated vaccines and therapeutics. This 6th version of the workshop builds on the success of previous ones held in Frankfurt (2013), Toronto (2015), Heidelberg (2017), Paris (2019) and virtually (2021). It is supported by the Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS) program at RIKEN, by Nagoya University, and by the Japan Science and Technology Agency. Up-to-date information and registration is available via the website. The workshop is for in-person participation only (no virtual or hybrid option).

Part 1 (14:00-15:00): Introduction to braid groups

Braid groups are groups that are defined by figures formed by the entanglement of n strings. Besides this geometric realization, it is a very interesting field where algebra and analysis intersect. In the first half of this seminar, aimed mainly at those unfamiliar with braid groups, we will introduce three aspects of braid groups and review the history of the research. In particular, in the area of its relation to analysis, the relationship between KZ equations and braid groups will be introduced.

Part 2 (15:30-16:30): Representations of braid groups and the relationship between monodromy representations of KZ equations

In the second half of the talk, after a brief introduction to representation theory, we will introduce the Katz-Long-Moody construction, a method of constructing infinite series of representations of the semi-direct product of braid group and free group. We will also show that its special case is isomorphic to multiplicative middle convolution, a method for constructing monodromy representations of KZ equations. Lastly, we will also discuss the connection between representations of braid groups and knot invariants. The talk includes joint work with Kazuki Hiroe.

Iras 00500+6713 is a bright nebula in the infrared, and X-ray observations show it consists of diffuse region and strong illuminated central region. In addition, optical spectral observations have recently revealed that fast wind with about 15,000 km/s is blowing from the massive white dwarf at the center. The properties of this nebula and white dwarf are very similar to those theoretically predicted by the binary white dwarf merger. In addition, its position on the celestial sphere and the extent make it a prime candidate for the remnant of SN 1181, a historical supernova. In this study, we propose that such a multilayered structure is formed by the collision between the remnant of SN 1181 and the stellar wind blowing from the central white dwarf, and succeeded in constructing a model that is consistent with the multi-wavelength observations. The results show that the progenitor of SN 1181 is a binary white dwarf with 1.3-1.9 solar mass and that their merger triggered an explosion that ejected mass with 0.2-0.6 solar mass to form the present object. The extent of the X-ray source concentrated in the center reveals that these winds began blowing within the last 30 years, and we will discuss this property as well.

Machine learning techniques are powerful tools to tackle diverse tasks in current astroparticle physics research. For example, Bayesian neural networks provide robust classifiers with reliable uncertainty estimates, and are particularly well suited for classification problems that are based on comparatively small and imbalanced data sets, such as the gamma-ray sources detected by Fermi-Large Area Telescope (LAT).
About one third of the gamma-ray sources collected in the most recent catalogs remain currently unidentified. Intriguingly, some of these could be exotic objects such as dark subhalos, which are overdensities in dark matter halos predicted to form by cosmological N-body simulations. If they exist in the Milky Way, they could be detected as gamma-ray point sources due to the annihilation or decay of dark matter particles into Standard Model final states.
In this talk I will discuss our recent work* in which, after training on realistic simulations, we use Bayesian neural networks to identify candidate dark matter subhalos among unidentified gamma-ray sources in Fermi-LAT catalogs. Our novel framework allows us to derive conservative bounds on the dark matter annihilation cross section, by excluding unidentified sources classified as astrophysical-like.

Influenza viruses are typically considered a respiratory pathogen, but are nonetheless capable of causing ocular complications in infected individuals and establishing a respiratory infection following ocular exposure. While both human and zoonotic influenza A viruses can replicate in ocular tissue and use the eye as a portal of entry, many H7 subtype viruses possess an ocular tropism in humans, though the molecular determinants that confer a non-respiratory tropism to a respiratory virus are poorly understood. In this presentation, I will discuss the establishment of several mammalian models to study ocular exposure and ocular tropism, ongoing investigations conducted in vitro and in vivo to elucidate properties associated with ocular-tropic viruses, and ways in which this information can improve efforts to identify, treat, and prevent human infection following ocular exposure to influenza viruses. Continued investigation of the capacity for respiratory viruses to gain entry to the respiratory tract and to cause ocular complications will improve understanding of how these pathogens cause human disease, regardless of the virus subtype or exposure route.

In these lectures, we will shed light on modern tools of higher algebra, where the traditional structures of algebra yield themselves only after controlled deformations. We will introduce infinity-categories, spectra, operads, and other standard tools of the last decade. The main applications will be to encode various higher-algebraic structures that inevitably arise in, and shed light on, geometry and topology. If time permits, we will illustrate how spectra naturally arise in geometric invariants.

The audience is imagined to consist of mathematicians interested in applications of infinity-categorical tools -- so a broad range of geometers (including topologists) and algebraists. From Lecture Two onward, I will assume basic knowledge of algebraic topology (e.g., the material of Hatcher) and homological algebra.

These lectures will be held between July 31 and August 10, each from 10:30 to 12:00, for a total of 8 lectures.

1st Week: Jul 31(mon), Aug 1(tue) - 3(thu)
- Introduction to ideas of higher algebra in geometry, for a general audience.
- Introduction to infinity-categories and to spectra.

2nd Week: Aug 7(mon) - 10(thu)
- Examples in geometry and topology, including invariants of Legendrian links and generating functions.
- Future Directions.

Profile:
Hiro Lee Tanaka is an assistant professor in the Department of Mathematics. After receiving his Ph.D. from Northwestern University and completing postdoctoral work at Harvard University, he conducted research at the Mathematical Sciences Research Institute in Berkeley, California, and at the Isaac Newton Institute in Cambridge, England. His research aims to fuse the higher structures in modern algebra with geometries emerging from both classical mechanics and supersymmetric field theories. Beyond research, Tanaka engages in efforts to create more equitable and supportive environments throughout the mathematics community.