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In this talk, we will discuss an open Gromov-Witten invariant on hyperKahler surfaces, including K3 surfaces and certain Hitchin moduli spaces. The invariant is defined via the Lagrangian Floer theory and satisfy the Kontsevich-Soibelman wall-crossing formula and are expect to recover the generalized Donaldson-Thomas invariants studied in the work of Gaiotto-Moore-Neitzke.

More than a billion years ago, two black holes collided. In the final second of their long life together, the black holes banged out a rhythm like mallets on a drum, creating gravitational waves – ripples in the shape of spacetime. One hundred years ago, Albert Einstein predicted the existence of such waves, though it seemed improbable – if not outright impossible – that we’d ever be able to actually detect them. They were long considered too faint for any earthbound experiment to measure. Undaunted, experimentalists were determined to measure these Lilliputian ripples, and after many decades of work and collaboration, they built LIGO – the Laser Interferometer Gravitational-Wave Observatory. This incredible sophisticated and sensitive instrument was made to listen for the beat of that distant drum. In 2015, a billion years after the two black holes collided, their waves rippled through the LIGO detectors in Louisiana and Washington. With these remarkable new observatories, we can now capture the soundtrack to accompany the silent movie of the history of our universe.

Collisions at the Large Hadron Collider (LHC) are dominated by jets, collimated sprays of particles that arise from quantum chromodynamics (QCD) at high energies.  With the remarkable performance of the ATLAS and CMS detectors, jets can now be characterized not just by their overall direction and energy but also by their substructure.  In this talk, I highlight the increasingly important role that jet substructure is playing in searches for dark matter and other new physics at the LHC, especially when exploring extreme kinematic regimes involving large Lorentz boosts.

I also explain how innovative theoretical studies of jet substructure have taught us surprising lessons about QCD, revealing new probes of hot dense matter and universal features of gauge theories.

In the past few years we have witnessed a flurry of activity in the field of topological phases of matter. An outstanding theme in the field is the study of the interplay between geometry and topology of many-body wave functions, which has attracted the attention of condensed matter and high-energy physicists. In this talk, I will present the quantum field-theoretic descriptions of the fascinating novel phenomena emergent from intertwined geometry and topology, which are vividly exemplified by the geometric responses in fractional quantum Hall systems. For the strict topological limit, where only the global topology of space matters, the fractional quantum Hall systems are characterized by their universal properties such as fractional quantum Hall conductivity and a degeneracy on surfaces with the topology of a torus. Quite surprisingly, these topological fluids also couple to the geometry and have universal responses to the adiabatic deformations of the background geometry. These responses are given by a Wen-Zee term, Hall viscosity term, and gravitational Chern-Simons term. Through the field-theoretic approaches of the topological fluids, I will for the first time show how to derive all the universal geometric responses. To account for the coupling to the background geometry, I show that the concept of “flux attachment” must be modified in the curved space and use it to derive the responses from Chern-Simons theories for all the known fractional quantum Hall states. I also apply these results to the theory of the anisotropic quantum Hall systems, where the geometric responses play a central role in understanding their universal physics.

We derive in the framework of soft collinear effective field theory (SCET) a Lagrangian describing the t-channel exchange of Glauber quarks, which are incorporated through fermionic potential operators in the effective theory. The Wilson line structure of the operators, which is derived from matching calculations and the symmetries of the effective theory, describe additional soft and collinear emissions from a fermionic t-channel exchange in the forward scattering limit to all orders. Lightcone singularities in the fermionic potential are regulated using a rapidity regulator, whose corresponding renormalization group evolution gives rise to the quark reggeization at amplitude level.

The notion of Positive Representations is a new research program devoted to the representation theory of split real quantum groups, initiated in a joint work with Igor Frenkel. It is a generalization of the special class of representations considered by J. Teschner for Uq(sl(2,R)) in Liouville theory, where it exhibits a strong parallel to the finite-dimensional representation theory of compact quantum groups, but at the same time also serves some new properties that are not available in the compact case. In this talk, I will survey the recent developments and describe some of its relations to other areas of mathematics. 

Many-body entanglement can lead to exotic phases of matter beyond conventional symmetry breaking paradigm. Those exotic phases may contain fractionalized quasiparticles and emergent gauge fields. In this talk,  I will focus on a wide class of long-range entangled phases—quantum spin liquid. In quantum spin liquids, the spins are entangled in some intricate fashion giving rise to interesting physics such as emergent topological field theory and QED3 theory. I will show in detail how such exotic physics can emerge in simple spin systems.

I will discuss some results on double loop groups that point to geometric phenomena about double affine flag varieties and double affine Grassmannian. One result of this study is a definition of double affine Kazhdan-Lusztig polynomials.

It is commonly believed that quantum information is not lost in a black hole. Instead, it is encoded into non-local degrees of freedom in some clever way; like a quantum error-correcting code. In this talk, I will discuss how one may resolve some paradoxes in quantum gravity by using the theory of quantum error-correction. First, I will introduce a simple toy model of the AdS/CFT correspondence based on tensor networks and demonstrate that the correspondence between the AdS gravity and CFT is indeed a realization of quantum codes. I will then show that the butterfly effect/scrambling in black holes can be interpreted as non-local encoding of quantum information and can be quantitatively measured by out-of-time ordered correlations. Finally I will describe a simple decoding protocol for reconstructing a quantum state from the Hawking radiation and suggest a physical interpretation as a traversable wormhole in an AdS black hole. The decoding protocol also provides an attractive platform for laboratory experiments for measuring out-of-time ordered correlation functions as it clearly distinguishes unitary scrambling from non-unitary decoherence.