Joint equidistribution of adelic torus orbits and families of twisted L-functions

Farrell Brumley
Université Sorbonne Paris Nord
May 28, 2020
The classical Linnik problems are concerned with the equidistribution of adelic torus orbits on the homogeneous spaces attached to inner forms of GL2, as the discriminant of the torus gets large. When specialized, these problems admit beautiful classical interpretations, such as the equidistribution of integer points on spheres, of Heegner points or packets of closed geodesics on the modular surface, or of supersingular reductions of CM elliptic curves.

Mirrors of curves and their Fukaya categories

Denis Auroux
Harvard University
May 22, 2020
Homological mirror symmetry predicts that the derived category of coherent sheaves on a curve has a symplectic counterpart as the Fukaya category of a mirror space. However, with the exception of elliptic curves, this mirror is usually a symplectic Landau-Ginzburg model, i.e. a non-compact manifold equipped with the extra data of a "stop" in its boundary at infinity.

Victorian Fiction and the Location of Experience

Adela Pinch
Visitor, School of Social Science
May 22, 2020
What do we mean by “experience”? How have philosophers sought to help us understand this essential category of human existence? And how have novelists and literary critics grappled with this category? This talk brings the tools of literary analysis to both Victorian novels and Victorian philosophy, in order to enrich our appreciation of “experience.” Authors featured included Charlotte Brontë and William James, but you will also be introduced to some lesser-known figures, such as Shadworth Hodgson and May Sinclair.

Iwasawa theory and Bloch-Kato conjecture for unitary groups

Xin Wan
Morningside Center of Mathematics, Chinese Academy of Sciences
May 21, 2020
We describe a new method to study Eisenstein family and Iwasawa theory on unitary groups over totally real fields of general signatures. As a consequence we prove that if the central L-value of a cuspidal eigenform on the unitary group twisted by a CM character is 0, then the corresponding Selmer group has positive rank. The method also has a byproduct the p-adic functional equations for p-adic L-functions and p-adic families of Eisenstein series on unitary groups.

Forecasting Epidemics and Pandemics

Roni Rosenfeld
Carnegie Mellon University
May 21, 2020
Epidemiological forecasting is critically needed for decision making by national and local governments, public health officials, healthcare institutions and the general public. The Delphi group at Carnegie Mellon University was founded in 2012 to advance the theory and technological capability of epidemiological forecasting, and to promote its role in decision making, both public and private. Our long term vision is to make epidemiological forecasting as useful and universally accepted as weather forecasting is today.

Neural SDEs: Deep Generative Models in the Diffusion Limit

Maxim Raginsky
University of Illinois Urbana-Champaign
May 19, 2020
In deep generative models, the latent variable is generated by a time-inhomogeneous Markov chain, where at each time step we pass the current state through a parametric nonlinear map, such as a feedforward neural net, and add a small independent Gaussian perturbation. In this talk, based on joint work with Belinda Tzen, I will discuss the diffusion limit of such models, where we increase the number of layers while sending the step size and the noise variance to zero.

The Non-Stochastic Control Problem

Elad Hazan
Princeton University
May 18, 2020
Linear dynamical systems are a continuous subclass of reinforcement learning models that are widely used in robotics, finance, engineering, and meteorology. Classical control, since the work of Kalman, has focused on dynamics with Gaussian i.i.d. noise, quadratic loss functions and, in terms of provably efficient algorithms, known systems and observed state. We'll discuss how to apply new machine learning methods which relax all of the above: efficient control with adversarial noise, general loss functions, unknown systems, and partial observation.

Reflections on Cylindrical Contact Homology

Jo Nelson
Rice University
May 15, 2020
This talk beings with a light introduction, including some historical anecdotes to motivate the development of this Floer theoretic machinery for contact manifolds some 25 years ago. I will discuss joint work with Hutchings which constructs nonequivariant and a family Floer equivariant version of contact homology. Both theories are generated by two copies of each Reeb orbit over Z and capture interesting torsion information.

Entanglement Entropy in Flat Holography

Wei Song
Member, School of Natural Sciences, Institute for Advanced Study; Tsinghua University
May 15, 2020
The appearance of BMS symmetry as the asymptotic symmetry of Minkowski spacetime suggests a holographic relation between Einstein gravity and quantum field theory with BMS invariance, dubbed BMSFT. With a three dimensional bulk, the dual BMSFT is a non-Lorentz invariant, two dimensional field theory with infinite-dimensional symmetries. In this talk, I will argue that entanglement entropy in BMSFT can be described by a swing surface in the bulk.