# Seminars & Events for 2016-2017

##### Kernel-based methods for Bandit Convex Optimization

Please click on the following link to access the abstract for this talk: http://www.pacm.princeton.edu/pacm-colloquium

##### Strong cosmic censorship in spherical symmetry for two-ended asymptotically flat data

In this talk, I will present a recent work (joint with Jonathan Luk) on the strong cosmic censorship conjecture for the Einstein-Maxwell-(real)-scalar-field system in spherical symmetry for two-ended asymptotically flat data. For this model, it was previously proved (by M. Dafermos and I.

##### Concurrent Disjoint Set Union

The disjoint set union problem is a classical problem in data structures with a simple and efficient sequential solution that has a notoriously complicated analysis. One application is to find strongly connected components in huge, implicitly defined graphs arising in model checking. In this application, the use of multiprocessors has the potential to produce significant speedups. We explore

##### Rectification and the Floer complex: Quantizing Lagrangians in T^N

We shall give a construction of the quantized sheaf of a Lagrangian submanifold in T^N and explain a number of features and applications.

##### C^0 Hamiltonian dynamics and a counterexample to the Arnold conjecture

After introducing Hamiltonian homeomorphisms and recalling some of their properties, I will focus on fixed point theory for this class of homeomorphisms. The main goal of this talk is to present the outlines of a C^0 counterexample to the Arnold conjecture in dimensions four and higher. This is joint work with Lev Buhovsky and Vincent Humiliere.

##### On a problem of Kahane in higher dimensions

**Please note special day, time and room. **We characterise those real analytic mappings from T^k to T^d which map absolutely convergent Fourier series on T^d to uniformly convergent Fourier series via composition.

##### Nonlinear Fourier series via Blaschke products

**Please note different start time: 1:30. **Classical Fourier series may be interpreted as repeatedly adding and removing roots in the origin of the complex plane.

##### Finding and hiding the seed

I will present an overview of recent developments in source detection and estimation in randomly growing graphs and diffusions on graphs. Can one detect the influence of the initial seed graph? How good are root-finding algorithms? Can one engineer messaging protocols that hide the source of a rumor? I will explore such questions in the talk.

##### Proof of a Null Penrose Conjecture using a new Quasi-local Mass

We define an explicit quasi-local mass functional which is nondecreasing along all null foliations (satisfying a convexity assumption) of null cones. We use this new functional to prove the Null Penrose Conjecture under fairly generic conditions.

##### TBD - Paul Seidel

##### The Modularity Theorem

The Shimura–Taniyama–Weil conjecture, now known as the modularity theorem, states that all elliptic curves over the field of rational numbers are modular. In this talk we will not attempt to discuss the proof; instead, we will have a more modest goal — to understand the statement, i.e., what it means for an elliptic curve to be modular.

##### A Central Limit Theorem for a $\B$-free dynamical system

For a set $\mathcal{B} \subset \mathbb{N} \setminus \{1\}$, let $\mathcal{B}$-free integers be the set of integers that are not divisible by any element of $\mathcal{B}$ and let $X^{\mathcal{B}} \subset \{0,1\}^{\mathbb{Z}}$ be the closure of the orbit of the indicator of $\mathcal{B}$--free integers under the left shift $T$. One can equip $\left(X^{\mathcal{B}},T\right)$ with the $T$--invaria

##### Capsets, sunflower-free sets in {0,1}^n, and the slice rank method

We call a family of sets F "sunflower-free'' if for every three of its sets, some element belongs to exactly two of them.

##### Cobordism maps in link Floer homology

Given a (decorated) link cobordism between two links K and L (that is, an embedded surface in S^3 x [0,1] that K and L co-bound), Juhász defined a map between their link Floer homologies. We prove that when the surface is an annulus the map preserves the natural bigrading of HFL and is always non-zero.

##### Transport and mixing by viscous vortex rings

Biomixing is the study of fluid mixing caused by swimming organisms. The swimming of large organisms can lead to mixing by the turbulent flows in their wakes, but the wakes created by small swimming organisms are less turbulent. Instead, the main mechanism of mixing by smaller organisms is the net particle displacement (drift) induced by the swimmer. Several experiments have been performed t

##### Integral points on moduli schemes and Thue equations

We will explain a way how one can use moduli schemes and their natural forgetful maps in the study of certain classical Diophantine problems (e.g. finding all integral points on hyperbolic curves). To illustrate and motivate the strategy, we consider the case of cubic Thue equations and we discuss a joint project with Matschke in which we solved many cubic Thue equations.

##### CANCELLED: The Kakeya needle problem for rectifiable sets

* THIS SEMINAR HAS BEEN CANCELLED. *We show that the classical results about rotating a line segment in arbitrarily small area, and the existence of a Besicovitch and a Nikodym set hold if we replace the line segment by an arbitrary rectifiable set. This is a joint work with Alan Chang.

##### Turbulent weak solutions of the Euler equations

**This joint Math/PACM colloquium will be held at 4:00, Monday, December 5, in Fine 214.**

##### Turbulent weak solutions of the Euler equations

**This joint Math/PACM colloquium will be held at 4:00, Monday, December 5, in Fine 214.**

##### Contact manifolds with flexible fillings

In this talk, I will prove that all flexible Weinstein fillings of a given contact manifold have isomorphic integral cohomology. As an application, I will show that in dimension at least 5 any almost contact class that has an almost Weinstein filling has infinitely many different contact structures.