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.

In algebraic geometry, we study the geometry of algebraic varieties, which are sets defined by algebraic equations.
There are two types of algebraic varieties, they are varieties over characteristic zero and varieties over positive characteristic.
Algebraic geometry in characteristic zero is similar to analytic geometry, so it is related to many other subjects.
In this talk, I will introduce the notion of algebraic geometry in positive characteristic and relationships between positive characteristic and characteristic zero.
In order to study it, we consider families consisting of varieties over characteristic zero and varieties over positive characteristic, called mixed characteristic.

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].

The singularity theorem by Penrose shows that a spacetime singularity arises in certain universal situations. The existence of a spacetime singularity is thought to represent a breakdown in the validity of theories such as general relativity and the phenomenological models of the universe. Thus, if we could build a correct model that describes the beginning of the universe, the universe predicted by that model should be non-singular. In this talk, we will discuss general properties that a non-singular universe must satisfy in order to avoid the singularity theorem. In particular, we will see that the universe must be, in some sense, smaller than the corresponding closed de Sitter spacetime.

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: