We study magnetically charged classical solutions of a spontaneously broken gauge theory interacting with gravity. We show that nonsingular monopole solutions exist only if the Higgs field vacuum expectation value v is less than or equal to a critical value v cr , which is of the order of the Planck mass. In the limiting case, the monopole becomes a black hole, with the region outside the horizon described by the critical Reissner-Nordstrom solution. For v < v cr , we find additional solutions which are singular at r = 0, but which have this singularity hidden within a horizon. These have nontrivial matter fields outside the horizon, and may be interpreted as small black holes lying within a magnetic monopole. The nature of these solutions as a function of v and of the total mass M and their relation to the Reissner-Nordstrom solutions is discussed.

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Following recent work on the quantum Hall effect on S 4 , we solve the Landau problem on the complex projective spaces CP k and discuss quantum Hall states for such spaces. Unlike the case of S 4 , a finite spatial density can be obtained with a finite number of internal states for each particle. We treat the case of CP 2 in some detail considering both Abelian and nonabelian background fields. The wavefunctions are obtained and incompressibility of the Hall states is shown. The case of CP 3 is related to the case of S 4 .

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We review the canonical theory for perfect fluids, in Eulerian and Lagrangian formulations. The theory is related to a description of extended structures in higher dimensions. Internal symmetry and supersymmetry degrees of freedom are incorporated. Additional miscellaneous subjects that are covered include physical topics concerning quantization, as well as mathematical issues of volume preserving diffeomorphisms and representations of Chern-Simons terms (= vortex or magnetic helicity).

The Hamiltonian formulation for a non-Abelian gauge theory in two spatial dimensions is carried out in terms of a gauge-invariant matrix parametrization of the fields. The Jacobian for the relevant transformation of variables is given in terms of the WZW-action for a hermitian matrix field. Some gauge-invariant eigenstates of the kinetic term of the Hamiltonian are given; these have zero charge and exhibit a mass gap.

We show that the coefficient of the three-dimensional Chern-Simons action on the noncommutative plane must be quantized. Similar considerations apply in other dimensions as well.

There is an urgent need for antiviral agents that treat SARS-CoV-2 infection. We screened a library of 1,900 clinically safe drugs against OC43, a human beta-coronavirus that causes the common cold and evaluated the top hits against SARS-CoV-2. Twenty drugs significantly inhibited replication of both viruses in vitro. Eight of these drugs inhibited the activity of the SARS-CoV-2 main protease, 3CLpro, with the most potent being masitinib, an orally bioavailable tyrosine kinase inhibitor. X-ray crystallography and biochemistry show that masitinib acts as a competitive inhibitor of 3CLpro. Mice infected with SARS-CoV-2 and then treated with masitinib showed >200-fold reduction in viral titers in the lungs and nose, as well as reduced lung inflammation. Masitinib was also effective in vitro against all tested variants of concern (B.1.1.7, B.1.351 and P.1).