Quantum mechanics is a cornerstone of modern physics. Just as the 19th century was called the Machine Age and the 20th century the Information Age, the 21st century promises to go down in history as the Quantum Age. Quantum Computing promises unprecedented speed in solving certain classes of problems while Quantum Cryptography promises unconditional security in communications. In this talk, I will discuss the world of single and entangled photons and also discuss ongoing work towards quantum computing, quantum information and quantum cryptography in our Quantum Information and Computing lab at the Raman Research Institute, Bengaluru. I will end with our broad vision for the future, which includes establishment of long distance secure quantum communications in India and beyond involving satellite based, fibre based as well as integrated photonics based approaches towards the global quantum internet.

Zoom Link: https://pitp.zoom.us/j/94788493307?pwd=QTlUaTY4Nm1IS3hyeUFIbVFKV3RMQT09

We present a series of (partly proven) conjectures
describing geometric realizations of
categories of (finite-dimensional) representations of quantum
super-groups U_q(g) corresponding
to Lie super-algebras g with reductive even part and a non-degenerate
invariant form.
We shall also discuss the meaning of these conjectures from the point
of view of local geometric Langlands correspondence as well as a
connection to the work of Ben-Zvi, Sakellaridis and Venkatesh.
Based on joint works with M.Finkelberg, V.Ginzburg and R.Travkin as
well as the work of R.Travkin and R.Yang.

I will discuss a close parallel between Gaiotto and Witten's S-duality for supersymmetric boundary conditions in 4d N=4 SYM and the relative Langlands program, an enhancement of the Langlands program that was developed to provide a framework for the theory of integral representations of L-functions. A special and conjecturally self-dual class of boundary conditions is provided by quantizations of "small" or "multiplicity-free" hamiltonian spaces called hyperspherical varieties. I'll explain how a hyperspherical variety produces objects of interest in all the different settings of the Langlands program (local / global, geometric / arithmetic) and a collection of conjectures providing S-dual descriptions of these objects. The talk is based on forthcoming joint work with Yiannis Sakellaridis and Akshay Venkatesh.

In this lecture I'll discuss various aspects of 4d N=2 and 5d N=1 supersymmetric QFT's in the 1/2 Omega-background (and along the way try to emphasize some relations to the 3d N=2 theories discussed in this workshop). Central to this story is the Nekrasov instanton partition function (or topological string partition function) in this background, which we will obtain through abelianization as an integral of a ratio of Wronskians of certain special solutions to the relevant Schrodinger equation. We will argue that a slight generalization of the above partition function solves an associated Riemann-Hilbert problem and defines a section of a distinguished line bundle over the moduli space of flat connections.

New massive "dark" vector bosons are ubiquitous in BSM physics.  I'll discuss the effective theories, interactions, and applications of theories with a (single) massive vector boson with a Stückelberg mass, with the goal of providing a clear and self-consistent approach to the (sometimes confusing) subject.  The critical role of possible couplings of the longitudinal mode will be emphasized, demarcating when theories have amplitudes that grow with energy.  In such theories, I'll identify the cutoff scale, as well as show the potential of longitudinally-enhanced observables given specific couplings of the vector boson.  The Stückelbergian approach to massive vectors also provides insight into generalized dark vector boson theories; I'll demonstrate a specific application to an "electrophobic" vector field that can evade many terrestrial experiment constraints that would otherwise apply to a dark photon.

Zoom Link: https://pitp.zoom.us/j/96937794653?pwd=cjIvM0hxQmo2ZEhuamhxeWx3cVdoZz09

3d mirror symmetry predicts an equivalence between A- and B-twists of a pair of dual 3d N=4 theories. Essentially the strongest invariants one can produce of the resulting 3-dimensional topological field theories are their 2-categories of boundary conditions. The B-side 2-category was first described by Kapustin-Rozansky-Saulinas, but the 2-categorical structure on A-side boundary conditions has not previously been understood. For abelian gauge theories with matter, we propose a model for the 2-category of A-type boundary conditions using Kapranov-Schechtman's "perverse schobers," and we prove a 3d mirror equivalence between dual 2-categories. By reducing to lower-dimensions, we can recover both the BFN construction and the BLPW Koszul duality for hypertoric categories O. This is joint work with Justin Hilburn and Aaron Mazel-Gee.