Seminars

Let $K/F$ be a Galois extension of number fields with Galois group $G$. We begin by examining the descent of real zeros of the Dedekind zeta function $zeta_K$ to the Dedekind zeta functions of subfields of $K$. This descent will allow us to get lower bound of residue of $\zeta_K(s)$ at $s = 1$ for certain number fields. In the next part, we explore the connection between the holomorphy of the Artin $L$-functions $L(s, \chi, K/F)$ at a point $s_0$ and order of $\zeta_K(s)$ at $s_0$ for any character $\chi$ of $G$.

We present the latest lattice results for the hadronic vacuum polarization from lattice QCD. In order to isolate the different origin of systematic errors in lattice computations, the observable is decomposed into several windows. The latest discrepancy between the data-driven theory prediction of the intermediate and long distance window of the hadronic vacuum polarization using the experimental input of e+e- to hadrons cross-section and the lattice predictions have sparked several new physics scenarios. We elaborate on the Mainz results for the intermediate and long distance windows and discuss the implications of the discrepancy. The anomalous magnetic moment of the muon (aµ) provides a stringent test of the Standard Model and Beyond, that too, interestingly on two independent fronts: the “aµ-test” and the “HVP-test”.We discuss a generic, light (∼ 100 MeV-1 GeV) Z′’s impact on both these tests in multiple ways making this arena an excellent probe of such models.

A key question about the QCD phase diagram is whether there is a critical point somewhere on the boundary between the hadron gas and quark-gluon plasma phases, and if so where. Heavy-ion collisions offer a unique opportunity to search for signatures of such a critical point by analyzing event-by-event fluctuations in particle multiplicities. To draw meaningful conclusions from experimental data,  a theoretical framework is needed to link QCD thermodynamics with the particle spectra and correlations observed in detectors. This is done in the least biased by maximizing the entropy associated with the hadron resonance gas ensemble, subject to matching conditions from the hydrodynamic description at freeze-out. We use maximum entropy freeze-out of fluctuations to make estimates for the factorial cumulants of proton multiplicities, assuming thermal equilibrium, for a family of EoSs with a 3D Ising-like critical point, varying the microscopic inputs that determine the location and strength of the critical point. The unknown Equation of State (EoS) of QCD near a critical point can be related to the universal Gibbs free energy of the 3D Ising model using four non-universal mapping parameters whose values are determined by the microscopic details of QCD. We quantify the effect of the non-universal mapping parameters, and the distance between the critical point and the freeze-out curve, on the factorial cumulants of proton multiplicities.

In the past couple of decades, there have been significant advances in measuring quantum prop- erties of light, such as quadratures of squeezed light and single-photon counting. Here, we explore whether such tools can be leveraged to probe electronic correlations in the many-body quantum regime. Specifically, we show that it is possible to probe certain spin, charge, and topological orders in an electronic system by measuring the correlation functions of scattered photons. We construct a mapping from the correlators of the scattered photons to those of a correlated insulator, par- ticularly for Mott insulators described by a single-band Fermi-Hubbard model at half-filling. We show how frequency filtering before photodetection plays a crucial role in determining this mapping. We find that if the ground state of the insulator is a gapped spin liquid, a photon-pair correlation function, i.e., G(2), can detect the presence of anyonic excitations with fractional mutual statistics. If the ground state is a gapless Dirac Spin Liquid (DSL), we propose a magnetic "Josephson" junction setup, which under Raman scattering leads to a sharp signature of a DSL. Moreover, we show that correlations between electromagnetic quadratures can be used to detect expectation values of static spin chirality operators on both the kagome and triangular lattices, thus being useful in detecting chiral spin liquids. More generally, we show that a series of hitherto unmeasured spin-spin and spin-charge correlation functions of the material can be extracted from photonic correlations. This work opens up access to probe correlated materials, beyond the linear response paradigm, by detecting quantum properties of scattered light.