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This talk will focus on hypermultiplet moduli spaces of various N=2 supersymmetric gauge theories in (3+1)d. In the first part of the talk, we discuss the moduli space of instantons on C^2. For the classical groups, the ADHM construction of the moduli space can be realised on the Higgs branch of N=2 gauge theories on D3-branes probing D7-branes. No known construction is available for exceptional groups. We go over the computation of Hilbert series for the one instanton moduli space and show that it is possible to count all chiral operators on the moduli space even though a Lagrangian is not known for exceptional gauge groups. In the second part, we discuss a class of N=2 gauge theories on two M5-branes wrapping Riemann surfaces. This talk will go over Hilbert series for the hypermultiplet moduli space of such theories and show that it is possible to count all chiral operators on the hypermultiplet moduli space for any genus and any number of punctures of the Riemann surface.

We give a detailed derivation of a supersymmetric configuration of wrapped D5-branes on a two-cycle of a warped resolved conifold. Our analysis reveals that the resolved conifold should support a non-Kahler metric with an SU(3) structure. We use this as a starting point of the geometric transition in type IIB theory. A mirror, and a subsequent flop transition using an intermediate M-theory configuration with a G2 structure, gives rise to the complete IR geometric transition in type IIA theory. A further mirror transformation gives the type IIB gravity dual of the IR gauge theory on the wrapped D5-branes. Expectedly non-Kahler deformations of the resolved and the deformed conifolds appear as the gravity duals of the confining gauge theories in type IIA and type IIB theories respectively, although in more generic cases these manifolds could also be non-geometric. In the local limit we reproduce precisely the scenarios presented in our earlier works. Our present work should therefore be viewed as providing a supergravity proof of geometric transitions in the full global scenarios in type II theories.

Large mixing angles and a mild mass hierarchy are observed in neutrino oscillations, in stark contrast with the quarks and charged leptons sectors where very hierarchical masses come along with small mixings. We review and discuss the neutrino mass patterns that are technically natural, in the context of the seesaw mechanism and with a quark-lepton unification perspective. We show that a seesaw in six dimensions offers an elegant and unique solution to the flavor puzzle. An explicit model is constructed, with a vortex background on a sphere. It offers an explanation for the replication of families in the Standard Model, and predicts suppressed flavour violating interactions.

False vacua in QFT are liable to undergo spontaneous decay. Slowness of quantum tunneling can however allow a long lifetime to the false vacuum state. In supersymmetric theories this is a crucial criterion for obtaining a long lived universe with spontaneously broken supersymmetry. We have explored false vacua which admit topological defects, including in a supersymmetric model with O'Rafeartaigh type supersymmetry breaking. We show that the presence of topological defects significantly alters the stability of the false vacuum. For some values of parameters, it also results in the putative false vacuum being rendered unstable. Finally I report a formula derived for instanton assisted tunneling applicable to metastable vacua with monopoles.

Since the dawn of civilization, humans have attempted to dissect the world and uncover its fundamental constituents. Today, this quest continues in the field of particle physics, the study of the fundamental subatomic particle that make up everything in the universe. The Large Hadron Collider (LHC) is a massive underground particle accelerator that physicists hope will reveal new secrets about the physical world. Located just outside Geneva, Switzerland at CERN, it has a circumference of 27 km and is the product of a collaboration that involves thousands of scientists worldwide. This presentation will talk about the LHC and some of the exciting new ideas it may confirm.

Physics emerged from the twentieth century with two remarkably successful descriptions of nature which stand in striking contrast. Quantum mechanics describes the subatomic realm with intrinsic uncertainties and probabilities. On the other hand, Einstein's general relativity describe gravitational phenomena in an exacting geometric arena. Theoretical physicists have struggled for over fifty years trying to combine these views in a single unified framework. More recently, superstring theory has drawn a huge amount of interest as a leading contender to provide such a unification. Superstring theory is a theory of strings, branes, extra spacetime dimensions and much more. In my lecture, I will try to give a flavour for what superstring theory is all about and why physicists, like myself, continue to be so excited about this, perhaps the final theory.

The gauge mediation models with a gravitino mass in the eV range is a quite attractive scenario which causes no cosmological/astrophysical problems. The model construction with such a light gravitino is, however, quite challenging and in most cases ends up with the problems with the suppressed gaugino mass, the vacuum instability and the Landau pole problems of the Standard Model gauge coupling constants. In this talk, I explain our proposal in which a gauge mediation model with the gravitino whose mass in the eV range is realized without having those problems.

In this talk I shall describe a general formalism based on $AdS_2/CFT_1$ correspondence that allows us to systematically calculate the entropy, index and other physical observables of an extremal black hole taking into account higher derivative and quantum corrections to the action. I shall also describe precise microscopic computation of the same quantities for a class of supersymmetric extremal black holes and compare this with the prediction of $AdS_2/CFT_1$ correspondence.

In this talk I shall describe a general formalism based on $AdS_2/CFT_1$ correspondence that allows us to systematically calculate the entropy, index and other physical observables of an extremal black hole taking into account higher derivative and quantum corrections to the action. I shall also describe precise microscopic computation of the same quantities for a class of supersymmetric extremal black holes and compare this with the prediction of $AdS_2/CFT_1$ correspondence.

In this talk I shall describe a general formalism based on $AdS_2/CFT_1$ correspondence that allows us to systematically calculate the entropy, index and other physical observables of an extremal black hole taking into account higher derivative and quantum corrections to the action. I shall also describe precise microscopic computation of the same quantities for a class of supersymmetric extremal black holes and compare this with the prediction of $AdS_2/CFT_1$ correspondence.

We discuss holographic models for the inflationary epoch. We show how cosmological observables such as the primordial spectrum and non-Gaussianities can be computed via computations of correlation functions of a dual three dimensional QFT (without gravity!) We present a general class of models that have the following universal features: (i) they have a nearly scale invariant spectrum of small amplitude primordial fluctuations, (ii) the scalar spectral index runs as alpha_s = - (n_s-1), (iii) the three point function of density perturbations is exactly equal to the sum of the local and equilateral form with f_{NL}^{local} = 6 f_{NL}^{equil} = 20/3.