Integrated Calendar

Abstract: In my talk I will discuss some new features of conformal anomaly and entanglement entropy in the presence of boundaries. The talk is based on recent papers.This is a project to develop a wide expanse of new quantum field theories in 2n-dimensional space-time manifolds. For each 2d qft, there is to be a qft of extended objects in every 2n-dimensional space-time manifold M. The quantum fields live on ``quasi Riemann surfaces'', which are certain spaces of integral (n-1)-currents in M. The notion of integral current comes from Geometric Measure Theory. The quasi Riemann surfaces are complete metric spaces with analytic properties strictly analogous to Riemann surfaces. The new qfts are to be constructed on the quasi Riemann surfaces just as 2d qfts are constructed on ordinary Riemann surfaces. Local fields in space-time are obtained by restricting to small extended objects.
arXiv:1510.04566, arXiv:1601.06418 and arXiv:1604.07571

Abstract: I will present a general solution to the problem of determining all S-dual descriptions for a specific (but very rich) class of N=1 SCFTs. These SCFTs are indexed by decorated toric diagrams, and can be engineered in string theory by probing orientifolds of isolated toric singularities with D3 branes. The S-dual phases are described by quiver gauge theories coupled to specific types of conformal matter which I will describe explicitly.

Epigenetics is the study of heritable changes in phenotype that are not encoded in an organism’s DNA. Epigenetic effects due to persistent changes in gene transcription have been linked to chemical modification of DNA and the proteins that package and regulate DNA in the nucleus, histones. One of the major post-translational modifications of histones is acetylation of lysine residues prevalent in histone tails. The principal readers of histone acetyl lysine marks are bromodomains (BRDs), which are a diverse family of over sixty evolutionary conserved protein-interaction modules. Proteins that contain BRDs have been implicated in the development of a large variety of diseases, including cancer and inflammation. In order to decipher the complex biology of bromodomains and provide evidence linking specific bromodomain targets to disease, we are discovering selective, cell active small molecule inhibitors of bromodomains.

Kernel methods constitute a mathematically elegant framework for general-purpose infinite-dimensional non-parametric statistical inference. By providing a principled framework to extend classical linear statistical techniques to non-parametric modeling, their applications span the entire spectrum of statistical learning. However, training procedures naturally derived via this framework scale poorly and with limited opportunities for parallelization. This poor scalability poses a significant barrier for the use of kernel methods in big data applications. As such, with the growth in data across a multitude of applications, scaling up kernel methods has acquired renewed and somewhat urgent significance.

Random feature maps, such as random Fourier features, have recently emerged as a powerful technique for speeding up and scaling the training of kernel-based methods. However, random feature maps only provide crude approximations to the kernel function, so delivering state-of-the-art results requires huge amount of random features. Nevertheless, in some cases, even when the number of random features is driven to be as large as the training size, full recovery of the generalization performance of the exact kernel method is not attained. In the talk I will show how random feature maps can be used to efficiently perform non-approximate kernel ridge regression, and thus there is no need to compromise between quality and running time. The core idea is to use random feature maps to form preconditioners to be used in solving kernel ridge regression to high accuracy. I will describe theoretical conditions on when this yields an effective preconditioner, and empirically evaluate the method and show it is highly effective for datasets of up to one million training examples.