Conference

In this talk, I will describe a new technique—stochastic resonance magnetic force microscopy (SRMFM)—developed in my group for imaging the vortex dynamics in multiply connected superconducting devices. Unlike existing techniques, which directly image vortices, our technique relies on the mechanism of stochastic resonance to image the fluctuations between different vortex configurations. I will present data, taken using Josephson junction arrays and ring structures, that reveal striking geometric patterns which emerge when the energy of different vortex configurations become degenerate at well-defined positions of a magnetic tip that is scanned above the surface of the device. By analyzing the fluctuation rate as a function of temperature or external field, we obtain detailed information regarding the energy barriers connecting different vortex configurations, as well as energy scales associated with vortex-vortex interactions. The technique also provides a convenient means to manipulate vortices in multiply connected superconducting structures, which may prove useful in certain topological quantum-computing applications.

The kagome lattice in a mineral compound "Herbertsmithite" represents structurally the most ideal kagome Heisenberg antiferromagnet known to date. Herbertsmithite does not undergo a magnetic long-range order or spin freezing at least down to ~J/2000. We will present 17-Oxygen and 2-Deuterium single crystal NMR study of Herbertsmithite. We will demonstrate that the ground state of the kagome plane has a spin gap ~ 0.05J [1], and ~5% excess Cu2+ ions occupying the out-of-plane Zn2+ sites are the only defects [2]. [1] M. Fu et al., Science 350, 655 (2015). [2] T. Imai et al., Phys. Rev. B 84, 020411 (2011).

A many-body quantum system on the verge of instability between competing ground states exhibits emergent phenomena. Interacting electrons on triangular lattices are likely subjected to multiple instabilities in the charge and spin degrees of freedom, affording diverse phenomena related to the Mott physics. The molecular conductors are superior model systems for studying the Mott physics because of the designability and controllability of material parameters such as lattice geometry and bandwidth by chemical substitution and/or pressure. In this symposium, I first introduce the fundamentals of organic materials and then present various quantum manifestations that interacting electrons in triangular-lattice organics show under variable correlation on the verge of the Mott metal-insulator transition. The topics include i) the quantum criticality of the Mott transition revealed by the resistivity that obeys quantum-critical scaling, ii) the pseudo-gap-like behavior of the metallic state, which is found to originate from preformed Cooper pairs that persist up to twice as high as Tc, and iii) the spin liquid state that emerges in the Mott insulating state, depending on the lattice geometry. I may touch the recent finding on a doped triangular lattice that exhibits a possible BEC-to-BCS crossover in superconductivity. The work presented here was performed in collaboration with T. Furukawa, H. Oike, J. Ibuka, M. Urai, Y. Suzuki, K. Miyagawa (UTokyo), Y. Shimizu (Nagoya Univ.), M. Ito, H. Taniguchi (Saitama Univ.) and R. Kato (RIKEN)

In recent years, there has been much interest in honeycomb lattice quantum magnets described by Kitaev-Heisenberg Hamiltonian. For example, honeycomb lattice iridates, such as Na2IrO3 and Li2IrO3 have been intensely scrutinized. Recently, we proposed that a 4d honeycomb magnet α-RuCl3 is a promising candidate material in which Kitaev physics could be studied. I will give an overview of the physics of alpha-RuCl3, and talk about recent experimental and theoretical advances.

We have recently demonstrated an experimental platform to isolate 2D materials that are unstable in the ambient environment. I will discuss our recent studies of the charge density wave compound 1T-TaS2 and superconducting 2H-NbSe¬ in the atomically thin limit, made possible using this technique. In TaS2, we uncover a new surface charge density wave transition that is distinct from that in the bulk layers, as well as demonstrate continuous electrical control over this phase transition. In NbSe2, a small perpendicular magnetic field induces a transition to a quantum metallic phase, the resistivity of which obeys a unique field-scaling consistent with that predicted for a Bose metal. These methods and experiments open new doors for the study of other correlated 2D systems in the immediate future.

Beyond their deceptively featureless ground states, spin liquids are particularly remarkable in the exotic nature of their (fractionalised and gauge charged) excitations. Quenched disorder can be instrumental in nucleating or localising defects with unusual properties, revealing otherwise hidden features of these topological many-body states. This talk discusses how to turn the nuisance of disorder into a powerful probe and origin of new collective behaviour.

I will present a 'categorical' way of doing analytic geometry in which analytic geometry is seen as a precise analogue of algebraic geometry. Our approach works for both complex analytic geometry and p-adic analytic geometry in a uniform way. I will focus on the idea of an 'open set' as used in various geometrical theories and how it is characterized categorically. In order to do this, we need to study algebras and their modules in the category of Banach spaces. The categorical characterization that we need uses homological algebra in these 'quasi-abelian' categories which is work of Schneiders and Prosmans. In fact, we work with the larger category of Ind-Banach spaces for reasons I will explain. This gives us a way to establish foundations of derived analytic geometry (my joint project with Kobi Kremnizer). We compare this approach with standard standard notions such as the theory of affinoid algebras, Grosse-Klonne's theory of dagger algebras (over-convergent functions), the theory of Stein domains and others. I will formulate derived analytic geometry following the relative algebraic geometry approach of Toen, Vaquie and Vezzosi. This talk involves various joint work with Federico Bambozzi and Kobi Kremnizer.

I will define coisotropic structures in the setting of shifted Poisson geometry in two ways and show their equivalence. The interplay between the definitions allows one to produce nontrivial statements. I will also describe some examples of coisotropic structures. This is a report on joint work with V. Melani.

One of the key constructions in the PTVV theory of shifted symplectic structures is the construction, via transgression, of a shifted symplectic structure on the derived mapping stack from an oriented manifold to a shifted symplectic stack vastly generalizing the AKSZ construction (which was formulated in the context of super manifolds). I will explain local-to-global approach to this construction, which also generalizes the construction to shifted Poisson structures and shows that the AKSZ/PTVV construction is compatible with quantization in a strong sense. One pleasant consequence is that every deformation quantization problem reduces to a version of BV-quantization. Time permitting, I will describe several geometric applications of the theory.

Formal loop spaces are algebraic analogs to smooth loops. They were introduced and studied extensively in the 2000' by Kapranov and Vasserot for their link to chiral algebras. In this talk, we will introduced higher dimensional analogs of K. and V. formal loop spaces. We will show how derived methods allow such a definition. We will then study their tangent complexes: even though formal loop spaces are "of infinite dimension", their tangent has enough structure so that we can speak of symplectic forms on them.

I will describe a functorial construction of the free BV-quantization of chain complexes equipped with antisymmetric forms of degree 1 in the context of infinity-categories. This is joint work with Owen Gwilliam.

In this talk, we'll discuss what it means to be a cohomology theory for topological stacks, using a notion of local symmetric monoidal inversion of objects in families. While the general setup is abstract, it specializes to many cases of interest, including Schwede's global spectra. We will then go on to discuss various examples with particular emphasis on elliptic cohomology. It turns out that TMF sees more objects as dualizable (or even invertible) than one might naively expect.