Seminars Sorted by Series

Relative symplectic cohomology, an invariant of subsets in a symplectic manifold, was recently introduced by Varolgunes. In this talk, I will present a generalization of this invariant to pairs of subsets, which shares similar properties with the...

In 1987, Hofer and Zehnder showed that for any smooth function $H$ on $\mathbb{R}^{2n}$, almost every compact and regular level set contains at least one closed characteristic. I'll show that, when $n = 2$, almost every compact and regular level set...

Algebraic torsion is a means of understanding the topological complexity of certain homomorphic curves counted in some Floer theories of contact manifolds.  This talk focuses on algebraic torsion and the contact invariant in embedded contact...

I will introduce a new structure on (relative) Symplectic Cohomology defined in terms of a PROP called the “Plumber’s PROP.” This PROP consists of nodal Riemann surfaces, of all genera and with multiple inputs and outputs, satisfying a condition...

Symplectic manifolds exhibit curious behaviour at the interface of rigidity and flexibility. A non-squeezing phenomenon discovered by Gromov in the 1980s was the first manifestation of this. Since then, extensive research has been carried out into...

By the Birkhoff Ergodic Theorem, the asymptotic mean action of an area-preserving map is defined almost everywhere. Bramham and Zhang asked whether, if a map is a pseudo-rotation, its asymptotic mean action is defined everywhere and is constant. In...

I will explain the relationship between the cyclotomic structure on symplectic cohomology and the equivariant pants products. This relationship exists for any cohomology theory (in particular, I will give a definition of the equivariant pants...

Distinct Hamiltonian isotopy classes of monotone Lagrangian tori in $\mathbb{C} P^2$ can be associated to Markov triples. With two exceptions, each of these tori are symplectomorphic to exactly three Hamiltonian isotopy classes of tori in the ball...

Apart from the usual transversality problems in defining curve counting invariants, when defining the open Gromov-Witten invariants of a Lagrangian one has to deal with the fact that the moduli spaces have boundary. Thus a homological (virtual)...

I will discuss the occurrence of some notions and results from contact topology in the context of equilibrium and non-equilibrium thermodynamics. Based on joint works with Michael Entov and Lenya Ryzhik.

Consider a contact three-manifold, and within it a symplectic surface with boundary on Reeb orbits. We show that assuming a certain inequality on the rotation numbers of the boundary Reeb orbits, there must exist Reeb orbits which intersect the...

The growth of an autonomous Hamiltonian flow in Hofer's metric is not yet well understood. A result of Polterovich and Rosen shows that generically this growth is asymptotically linear, and in all known cases where it is not, it appears to be...

Let Y be a symplectic divisor of X, $\omega$. In the Kahler setting, Givental's Quantum Lefschetz formula relates certain Gromov-Witten invariants (encoded by the G function) of X and Y. Given an Lagrangian L in (Y, $\omega$|Y), we can lift it to a...

The spectral norm on the group of Hamiltonian diffeomorphisms of a symplectic manifold is defined via a homological min-max process on the filtered Floer homology. Based on the spectral norm one defines the spectral capacity of domains which is...

We show that skein valued counts of open holomorphic curves in a symplectic Calabi-Yau 3-fold with Maslov zero Lagrangian boundary condition are invariant under deformations and discuss applications (Ooguri-Vafa conjecture and simple recursion...

We will explore certain $C^0$-rigidity and flexibility phenomena in the study of contact transformations. In particular, we will show how the dichotomy between contact squeezing and non-squeezing is reflected in the group of contact homeomorphisms...

In a series of papers with Alexander Ritter, we construct a symplectic cohomology for open non-convex symplectic manifolds that admit pseudo-holomorphic C*-actions. Out of this construction, we get a filtration on ordinary cohomology of these...

The open Gromov-Witten (OGW) potential is a function defined  on the Maurer-Cartan space of a closed Lagrangian submanifold in a  symplectic manifold with values in the Novikov ring. From the values  of the OGW potential, one can extract so-called...

(joint work with Shaoyun Bai) Using a new version of transversality condition (the FOP transversality) on orbifolds, one can construct Hamiltonian Floer theory over integers for all compact symplectic manifolds. In this talk I will first describe...

A hypersurface in a contact manifold is convex if there is a contact vector field that is transverse to it. Convex surfaces have long been a fundamental tool in 3-dimensional contact topology. In higher dimensions, convex hypersurfaces remained...

In this talk we discuss a relation between the contact version 
of the Hofer norm and positive loops of contactomorphisms.
This leads to a new criterion for the existence of contractible positive 
loops in terms of open book decompositions and...

In this talk, we will present a proof of contact big fiber theorem, based on invariants read off from contact Hamiltonian Floer homology. The theorem concludes that any contact involutive map on a Liouville fillable contact manifold admits at least...

This talk is based on joint work with Yang Li. I will discuss the problem of counting special Lagrangians in Calabi-Yau 3-folds and Fueter sections to define new numerical and Floer-theoretic invariants. The key challenges are the non-compactness...

The purpose of the talk is to discuss a class of pseudo-metrics that can be defined on the set of objects of a triangulated category whose morphisms are endowed with a notion of weight. In case the objects are Lagrangian submanifolds (possibly...

I will explain recent joint work proving that the group of compactly supported area preserving homeomorphisms of the two-disc is not a simple group; this answers the ”Simplicity Conjecture” in the affirmative. Our proof uses new spectral invariants...

Compatible almost-complex structures on symplectic manifolds correspond to optimal quantizations. I will discuss this statement (joint with Louis Ioos and David Kazhdan), as well as some other geometric facets of uncertainty principles in quantum...

Modern machine learning algorithms often involve complicated models with tunable parameters, called hyperparameters, that are set during training. Hyperparameter tuning/optimization is considered an art. We give a simple, fast algorithm for...

I will describe recent efforts in using machine learning to control cooling in Google data centers, as well as related research in linear quadratic control.

Our goal is to create a convenient natural language interface for performing well-specified but complex actions such as analyzing data, manipulating text, and querying databases. However, existing natural language interfaces for such tasks are quite...

With the continuing successes of deep learning, it becomes increasingly important to better understand the phenomena exhibited by these models, ideally through a combination of systematic experiments and theory. In this talk I discuss some of our...

A fundamental problem in Bayesian statistics is sampling from distributions that are only specified up to a partition function (constant of proportionality). In particular, we consider the problem of sampling from a distribution given access to the...

The current successes of deep neural networks have largely come on classification problems, based on datasets containing hundreds of examples from each category. Humans can easily learn new words or classes of visual objects from very few examples...

Linear dynamical systems (LDSs) are a class of time-series models widely used in robotics, finance, engineering, and meteorology. I will present our "spectral filtering" approach to the identification and control of discrete-time LDSs with multi...

Machine learning techniques based on neural networks are achieving remarkable results in a wide variety of domains. Often, the training of models requires large, representative datasets, which may be crowd-sourced and contain sensitive information...

Conventional wisdom in deep learning states that increasing depth improves expressiveness but complicates optimization. In this talk I will argue that, sometimes, increasing depth can speed up optimization.

The effect of depth on optimization is...

We consider the problem of adversarial (non-stochastic) online learning with partial information feedback, where at each round, a decision maker selects an action from a finite set of alternatives. We develop a black-box approach for such problems...

Three fundamental factors determine the quality of a statistical learning algorithm: expressiveness, optimization and generalization. The classic strategy for handling these factors is relatively well understood. In contrast, the radically different...

Datasets are often used multiple times with each successive analysis depending on the outcomes of previous analyses on the same dataset. Standard techniques for ensuring generalization and statistical validity do not account for this adaptive...

We revisit the question of reducing online learning to approximate optimization of the offline problem. In this setting, we give two algorithms with near-optimal performance in the full information setting: they guarantee optimal regret and require...

In modern “Big Data” applications, structured learning is the most widely employed methodology. Within this paradigm, the fundamental challenge lies in developing practical, effective algorithmic inference methods. Often (e.g., deep learning)...

Deep learning builds upon the mysterious ability of gradient-based methods to solve related non-convex optimization problems. However, a complete theoretical understanding is missing even in the simpler setting of training a deep linear neural...