The mathematical construction of non-trivial quantum field theory in four dimensions, known as the "Yang-Mills existence and mass gap problem", is a very important issue in mathematical sciences. There are many examples of rigorous quantum field theories in two dimensions, although the four dimensions have not yet been solved. In particular, two-dimensional conformal field theory, which is a quantum field theory with conformal symmetry, has good properties and can be formulated mathematically using algebraic structures formed by "products of a field and a field" (operator product expansion).

In this talk, this algebraic formulation (full vertex algebra) will be explained. Various construction methods and concrete examples (construction using codes, construction from quantum groups, and construction by deformation) will then be discussed.

All the talk here is mathematical, but I will try to speak in a way that is motivated by physics as much as possible throughout the talk. I hope to receive various comments from the viewpoints of other fields.

The widely acclaimed 1995/1996 papers by Ho, Perelson and others [1,2] demonstrated the important insights that come from mathematical modelling of virus infection kinetics within a person. But there are key dynamical differences between chronic and acute infections, namely whether the infection reaches or maintains some equilibrium or not. In this talk, I will introduce the equations used to describe a virus infection within a person. I will show some of the tricks used by mathematical modellers to extract important rate estimates from measurements in patients infected with chronic diseases, like HIV or Hepatitis C virus. I will explain why it is difficult to extract meaningful information from measurements in patients with an acute infection, like influenza or possibly COVID-19 [3]. I hope to hear from the audience if they have any thoughts about overcoming the issue to extract better rate information from limited data in patients with acute infections.

(This seminar is a joint seminar between Nonequilibrium working group and Biology study group)

Axion-like particles (ALPs) are a class of hypothetical bosons which feebly interact with ordinary matter. The hot plasma of stars and core-collapse supernovae is a possible laboratory to explore physics beyond the standard model including ALPs. Once produced in a supernova, some of the ALPs can be absorbed by the supernova matter and affect energy transfer. We recently calculated the ALP emission in core-collapse supernovae and the backreaction on supernova dynamics consistently. It is found that the stalled bounce shock can be revived if the coupling between ALPs and photons is as high as $g_{a\gamma}\sim 10^{-9}$ GeV$^{-1}$ and the ALP mass is 40-400 MeV.

Recently, the phase of the two-flavor quark matter with the new
pattern of color superconductivity was proposed so that the continuous
crossover from the hadronic to the quark phase is realized [1]; it is
in consonance with the recent observation of neutron stars.
In this talk, I will show the classification of the topological
vortices in this phase. We found that the stable vortices are what we
call the "non-Abelian Alice strings" [2]. They are superfluid
vortices carrying 1/3 quantized circulation and color magnetic fluxes.
I will discuss their properties in comparison to the well-established
CFL vortices in three-flavor symmetric setup, by putting some emphasis
on their peculiarity: the non-Abelian generalization of the Alice
property. I will then discuss in detail the possibility that these
vortices are confined as well as how the vortices in the quark phase
can be connected to those in the hadronic phase [3].

[1] Y. Fujimoto, K. Fukushima, W. Weise, PRD 101, 094009 (2020) [1908.09360].
[2] Y. Fujimoto, M. Nitta, PRD 103, 054002 (2021) [2011.09947]; JHEP 09 (2021) 192 [2103.15185].
[3] Y. Fujimoto, M. Nitta, PRD 103, 114003 (2021) [2102.12928].

We consider the infrared (IR) aspects of the gauge invariant S-matrix in QED. I will review the problem of IR divergences in QED, and introduce the dressed state formalism to obtain IR-safe S-matrix elements. I will show a condition for dressed states to obtain IR-safe S-matrix elements, and explain that this condition can be interpreted as the memory effect and is related to asymptotic symmetry. I also explain that IR divergences are necessary to prohibit the violation of asymptotic symmetry. We also argue that the difference between dressed and undressed states can be observed, even if we are able to observe an inclusive cross-section summing over soft photons.

Recent developments in statistical mechanics have revealed a tradeoff between heat current and dissipation [1,2]. In various situations, this current-dissipation tradeoff represents a relationship between thermal energy flow and entropy increase, similar to Joule’s law W=RI^2.

On the other hand, the coherence effect on the current-dissipation tradeoff has not been thoroughly analyzed. Here, we systematically analyze how coherence affects the current-dissipation tradeoff [3]. The results can be summarized in the following three rules: