# Seminars & Events for 2017-2018

##### Compactification of moduli spaces of J-holomorphic maps relative to snc divisors

In this talk, I will describe an efficient way of compactifying moduli spaces of J-holomorphic maps relative to simple normal crossings (snc) symplectic divisors, including the holomorphic case.

##### Methods of network comparison

The topology of any complex system is key to understanding its structure and function. Fundamentally, algebraic topology guarantees that any system represented by a network can be understood through its closed paths. The length of each path provides a notion of scale, which is vitally important in characterizing dominant modes of system behavior.

##### Rare Region Effects and Many-Body Localization

Certain strongly disordered many-body quantum systems are incapable of reaching thermal equilibrium. The nature of this so-called many-body localized (MBL) phase has recently been an active area of research. The phenomenon can be understood through perturbative approximations, but rare regions with weak disorder (Griffiths regions) have the potential to bypass barriers to thermalization.

##### The Hodge decomposition for some non-Kahler threefolds with trivial canonical bundle.

We show that the \partial\bar{\partial}-lemma holds for the non-Kahler compact complex manifolds of dimension three with trivial canonical bundle constructed by Clemens as deformations of Calabi-Yau threefolds contracted along smooth rational curves with normal bundle of type (-1, -1), at least on an open dense set in moduli.

##### Iron Age Hebrew Epigraphy in the Silicon Age - An Algorithmic Approach To Study Paleo-Hebrew Inscriptions

Handwriting comparison and identification, e.g. in the setting of forensics, has been widely addressed over the years. However, even in the case of modern documents, the proposed computerized solutions are quite unsatisfactory. For historical documents, such problems are worsened, due to the inscriptions’ preservation conditions.

##### Cover time of trees and of the two dimensional sphere

I will begin by reviewing the general relations that exist between the cover time of graphs by random walk and the Gaussian free field on the graph, and explain the strength and limitations of these general methods.

##### New Faculty Talks, III

4:30 p.m. | Yueh-Ju Lin, Instructor |

4:50 p.m. | Casey Kelleher, Postdoctoral Research Fellow |

5:10 p.m. | Huy Nguyen, Postdoctoral Research Associate |

5:30 p.m. | Joe Waldron, Instructor |

##### New Faculty Talks, III

4:30 p.m. | Yueh-Ju Lin, Instructor |

4:50 p.m. | Casey Kelleher, Postdoctoral Research Fellow |

5:10 p.m. | Huy Nguyen, Postdoctoral Research Associate |

5:30 p.m. | Joe Waldron, Instructor |

##### Moment map formalism, DUY theorem and beyond

In this expository talk, I will introduce the basic ideas about identifying symplectic quotient and good quotient in the sense of geometric invariant theory. After presenting some finite-dimensional examples, I will discuss the renowned Donaldson-Uhlenbeck-Yau theorem relating slope-stable holomorphic bundle with Hermitian-Yang-Mills connections.

##### Homotopy Group Actions and Group Cohomology

Understanding the symmetries of a topological space is a classical problem in mathematics. In this talk we will consider the somewhat more flexible notion of a group action up to homotopy. This leads to interesting interactions between topology, group theory and representation theory. This is joint work with Jesper Grodal.

##### Ranks of matrices with few distinct entries

Many applications of linear algebra method to combinatorics rely on the bounds on ranks of matrices with few distinct entries and constant diagonal. In this talk, I will explain some of these application. I will also present a classification of sets L for which no low-rank matrix with entries in L exists.

##### Willmore Stability of Minimal Surfaces in Spheres

Minimal surfaces in the round n-sphere are prominent examples of surfaces critical for the Willmore bending energy W; those of low area provide candidates for W-minimizers. To understand when such surfaces are W-stable, we study the interplay between the spectra of their Laplace-Beltrami, area-Jacobi and W-Jacobi operators. We use this to prove: 1) the square Clifford torus in the 3-sphere is

##### Solutions after blowup in ODEs and PDEs: spontaneous stochasticity

We discuss the extension of solutions beyond a finite blowup time, i.e., the time at which the system ceases to be Lipschitz continuous. For larger times solutions are defined first by using a (physically motivated) regularization of equations and then taking the limit of a vanishing regularization parameter.

##### Mayer-Vietoris sequence for relative symplectic cohomology

I will first recall the definition of an invariant that assigns to any compact subset K of a closed symplectic manifold M a module SH_M(K) over the Novikov ring. I will go over the case of M=two sphere to illustrate various points about the invariant. Finally I will state the Mayer-Vietoris property and explain under what conditions it holds.

##### The arithmetic intersection conjecture

The Gan-Gross-Prasad conjecture relates the non-vanishing of a special value of the derivative of an L-function to the non-triviality of a certain functional on the Chow group of a Shimura variety. Beyond the one-dimensional case, there is little hope for proving this conjecture.

##### The semi-continuity problem of normalized volume of singularities

Motivated by work in differential geometry, Chi Li introduced the normalized volume of a klt singularity as the minimum normalized volume of all valuations centered at the singularity. This invariant carries some interesting geometric/topological information of the singularity.

##### High frequency back reaction for the Einstein equations

It has been observed by physicists (Isaacson, Burnett, Green-Wald) that metric perturbations of a background solution, which are small amplitude but with high frequency, yield at the limit to a non trivial contribution which corresponds to the presence of a stress-energy tensor in the equation for the background metric.

##### Mean estimation: median-of-means tournaments

One of the most basic problems in statistics is how to estimate the expected value of a distribution, based on a sample of independent random draws. When the goal is to minimize the length of a confidence interval, the usual empirical mean has a sub-optimal performance, especially for heavy-tailed distributions.

##### Wrapped Fukaya categories and Functors

Inspired by homological mirror symmetry for non-compact manifolds, one wonders what functorial properties wrapped Fukaya categories have as mirror to those for the derived categories of the mirror varieties, and also whether homological mirror symmetry is functorial.