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The elliptic quantum (toroidal) group U_{q,p}(g) is an elliptic and dynamical analogue of the Drinfeld realization 
of the affine quantum (toroidal) group U_q(g). I will discuss an interesting connection of its representations with 
a geometry such as an identification of the elliptic weight functions derived by using  the vertex operators with 
the elliptic stable envelopes in [Aganagic-  Okounkov ’16] and correspondence between the Gelfand-Tsetlin bases 
of a finite dimensional representation of U_{q,p} with the fixed point classes in the equivariant elliptic cohomology.

Cosmic Microwave Background (CMB) is a powerful probe to the Universe which carries signatures of cosmic secrets over a vast range of redshifts. Along with spatial fluctuations, spectral distortions of CMB blackbody are also a rich source of cosmological information. In my talk, I will introduce a new kind of spectral distortion of CMB which can arise due to the conversion of CMB photons into Axion-Like Particles (ALPs) in the presence of an external magnetic field. This effect leads to both polarized and unpolarized spatially varying spectral distortion signal with a unique spectral shape when CMB photons undergo resonant and non-resonant conversion into ALPs in the presence of the magnetic field of Milky Way, galaxy clusters and voids. I will discuss the spatial structure of this distortion which can arise from Milky Way and galaxy clusters and will show its uniqueness from other known cosmological and astrophysical signals. I will present the first all-sky map of this distortion which is obtained using the data of Planck satellite and will discuss the capability of this new cosmological window to probe ALPs from the upcoming ground-based and space-based CMB experiments such as CMB-S4, LiteBIRD, Simons Observatory, etc.

Black holes are like bells; once perturbed they will relax through the emission of characteristic waves. The frequency spectrum of these waves is independent of the initial perturbation and, hence, can be thought of as a `fingerprint' of the black hole. Since the 1970s scientists have considered the possibility of using these characteristic modes of oscillation to identify astrophysical black holes. With the recent detection of gravitational waves, this idea has started to turn into reality.
Inspired by the black hole-fluid analogy, we demonstrate the universality of the black-hole relaxation process through the observation of characteristic modes emitted by a hydrodynamical vortex flow. The characteristic frequency spectrum is measured and agrees with theoretical predictions obtained using techniques developed for astrophysical black holes. Our findings allow for the first identification of a hydrodynamical vortex flow through its characteristic waves.
The flow velocities inferred from the observed spectrum agree with a direct flow measurement. Our approach establishes a non-invasive method, applicable to vortex flows in fluids and superfluids alike, to identify the wave-current interactions and hence the effective field theories describing such systems.

The detection of gravitational waves from mergers of compact binaries in the first two runs of the Advanced LIGO-Virgo have brought in valuable insights into fundamental physics and astrophysics. The coalescence process sweeping the components through a range of frequencies at highly relativistic velocities, have enabled some of the first tests of general relativity in its highly dynamical and extremely strong field regime. The recent detection of the binary neutron star merger has shed first light on the elusive neutron star equation of state. Furthermore, with its coincident electromagnetic counterpart, a first "standard-siren" measurement of the Hubble parameter has been made independent of a cosmic distance ladder. Subsequent detections are expected to give us a more direct understanding of the nature of the black holes and the composition of neutron stars, as well as bring in a plethora of results in astrophysics and possibly new insights into cosmology. I will go over some of these exciting new results and talk about future prospects of fundamental physics and cosmology from gravitational-wave observations.