# Seminars & Events for 2017-2018

##### Well-posedness for Stochastic Continuity Equations with Rough Coefficients.

According to the theory of Diperna/ Lions, the continuity equation associated to a Sobolev (or BV) vector field with bounded divergence has a unique weak solution in L^p.

##### Unlikely intersections for algebraic curves in positive characteristic

Please follow this link for the abstract: http://www.math.ias.edu/seminars/abstract?event=131079

##### Geometric finite amalgamations of hyperbolic 3-manifold groups are not LERF

A group G is called LERF if the property that an element not lying in a finitely generated subgroup is visible via a finite quotient of G. LERFness of groups is closed related with low-dimensional topology: whether an immersed \pi_1-injective object can be lifted to embedding in some finite cover.

##### A proof of the instability of AdS spacetime for the Einstein–null dust system

The AdS instability conjecture, suggested by Dafermos and Holzegel in 2006, states that generic, arbitrarily small perturbations to the initial data of the AdS spacetime, under evolution by the vacuum Einstein equations with reflecting boundary conditions on conformal infinity, lead to the formation of black holes.

##### Maximal globally hyperbolic developments of subluminal and superluminal quasilinear wave equations

**Please note the different time.**

##### TBA - Veit Elser

##### Wrapped Floer theory and Homological mirror symmetry for toric Calabi-Yau manifolds

Abstract: Consider a Lagrangian torus fibration a la SYZ over a non compact base. Using techniques from arXiv:1510.04265, I will discuss the construction of wrapped Floer theory in this setting. Note that this setting is generally not exact even near infinity.

##### Progress in showing cutoff for random walks on the symmetric group

Cutoff is a remarkable property of many Markov chains in which they rapidly transition from an unmixed to a mixed state. Most random walks on the symmetric group, also known as card shuffles, are believed to mix with cutoff, but we are far from being able to proof this.

##### Singularities on general fibres

I shall describe a canonical bundle formula which is useful to study the failure of generic smoothness, and give an outline of its proof. This is joint work with Zsolt Patakfalvi.

##### Macroscopic loops in the loop O(n) model

A loop configuration on the hexagonal (honeycomb) lattice is a finite subgraph of the lattice in which every vertex has degree 0 or 2, so that every connected component is isomorphic to a cycle. The loop O(n) model on the hexagonal lattice is a random loop configuration, with the energy of of a loop configuration taken to be linear in the number of edges and the number of loops.

##### TBA - Veit Elser

##### Random interlacements and the Gaboriau-Lyons problem

Given a Cayley graph for a non-amenable group, can one find a factor of an IID process that gives a random forest in which the average degree is greater than 2? Gaboriau-Lyons proved that the answer is `yes’ and this has interesting applications to ergodic theory. However, they required a lower bound on the entropy of the IID process.

##### Deformations of Q-Curvature

Stability (local surjectivity) and rigidity of the scalar curvature have been studied in an early work of Fischer-Marsden on \vacuum static spaces". Inspired by this line of research, we seek similar properties for Q-curvature by studying \Q-singular spaces", which were introduced by Chang-Gursky-Yang.

##### New Faculty Talks, II

4:30 p.m. | Jonathan Hanselman, Assistant Professor |

4:50 p.m. | Theo Drivas, Postdoctoral Research Fellow |

5:10 p.m. | Henry Horton, Postdoctoral Research Associate |

5:30 p.m. | Ian Zemke, Postdoctoral Research Fellow |

##### Connected Components of Divisor Function Ranges

For each complex number c, the divisor function \sigma_c is the arithmetic function given by \sigma_c(n)=\sum_{d|n}d^c. We will touch upon a small sliver of the rich and exhilarating history behind these classical functions, leading into a discussion of recent questions concerning their ranges.

##### A Lagrangian Fluctuation-Dissipation Relation for Scalar Turbulence

A common approach to calculate the solution of a scalar advection-diffusion equation is by a Feynman-Kac representation which averages over stochastic Lagrangian trajectories going backward in time to the initial conditions and boundary data.

##### The optimal design of wall-bounded heat transport

Flowing a fluid is a familiar and efficient way to cool: fans cool electronics, water cools nuclear reactors, and the atmosphere cools the Earth. In this talk, we discuss a class of problems from fluid dynamics concerning the design of incompressible wall-bounded flows achieving optimal rates of heat transport for a given flow intensity budget.

##### On residues of Eisenstein series - through a cohomological lens

The cohomology of an arithmetic subgroup of a reductive algebraic group defined over a number field is closely related to the theory of automorphic forms. We discuss in which way residues of Eisenstein series contribute non-trivially to the subspace of square-integrable classes in these cohomology groups.

##### Palindromes in Teichmuller Theory

It is well known that every primitive word in a rank two free group is conjugate to either a palindrome or the product of two palindromes.

##### How to play with the three spheres theorem.

**Please note the different time.**