This Week's Seminars and Colloquia

Non-Parametric Estimation of Manifolds from Noisy Data

Series
Applied and Computational Mathematics Seminar
Time
Monday, December 6, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
https://bluejeans.com/457724603/4379
Speaker
Yariv AizenbudYale University
A common task in many data-driven applications is to find a low dimensional manifold that describes the data accurately. Estimating a manifold from noisy samples has proven to be a challenging task. Indeed, even after decades of research, there is no (computationally tractable) algorithm that accurately estimates a manifold from noisy samples with a constant level of noise.
 
In this talk, we will present a method that estimates a manifold and its tangent in the ambient space. Moreover, we establish rigorous convergence rates, which are essentially as good as existing convergence rates for function estimation.

A Taste of Extremal Combinatorics in AG

Series
Algebra Seminar
Time
Tuesday, December 7, 2021 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Robert WalkerUniversity of Wisconsin, Madison

In this talk, we survey known results and open problems tied to the dual graph of a projective algebraic F-scheme over a field F, a construction that apparently Janos Kollar is familiar with. In particular one can use this construction to answer the following question: if you consider the 27 lines on a cubic surface in P^3, how many lines meet a given line? The dual graph can answer this and more questions in enumerative geometry and intersection theory easily, based on work of Benedetti -- Varbaro and others.

Density and graph edge coloring

Series
Graph Theory Seminar
Time
Tuesday, December 7, 2021 - 15:45 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Guangming JingAugusta University

Given a multigraph $G=(V,E)$, the chromatic index $\chi'(G)$ is the minimum number of colors needed to color the edges of $G$ such that no two incident edges receive the same color. Let $\Delta(G)$ be the maximum degree of $G$ and let  $\Gamma(G):=\max \big\{\frac{2|E(U)|}{|U|-1}:\,\, U \subseteq V, \,\, |U|\ge 3 \hskip 2mm
{\rm and \hskip 2mm odd} \big\}$. $\Gamma(G)$ is called the density of $G$. Clearly, the density is a lower bound for the chromatic index $\chi'(G)$. Moreover, this value can be computed in polynomial time. Goldberg and Seymour in the 1970s conjectured that $\chi'(G)=\lceil\Gamma(G)\rceil$ for any multigraph $G$ with $\chi'(G)\geq\Delta(G)+2$, known as the Goldberg-Seymour conjecture. In this talk we will discuss this conjecture and some related open problems. This is joint work with Guantao Chen and Wenan Zang.

Canonical measures and equidistribution in the arithmetic of forward orbits

Series
Job Candidate Talk
Time
Thursday, December 9, 2021 - 11:00 for 1 hour (actually 50 minutes)
Location
online
Speaker
Nicole LooperBrown University

This talk is about the arithmetic of points of small canonical height relative to dynamical systems over number fields, particularly those aspects amenable to the use of equidistribution techniques. Past milestones in the subject include the proof of the Bogomolov Conjecture given by Ullmo and Zhang, and Baker-DeMarco's work on the finiteness of common preperiodic points of unicritical maps. Recently, quantitative equidistribution techniques have emerged both as a way of improving upon some of these old results, and as an avenue to studying previously inaccessible problems, such as the Uniform Boundedness Conjecture of Morton and Silverman. I will describe the key ideas behind these developments, and raise related questions for future research. 

https://bluejeans.com/788895268/8348

Open sets of partially hyperbolic systems having a unique SRB measure

Series
CDSNS Colloquium
Time
Friday, December 10, 2021 - 13:00 for 1 hour (actually 50 minutes)
Location
Zoom (see additional notes for link)
Speaker
Davi ObataU Chicago

https://us06web.zoom.us/j/83392531099?pwd=UHh2MDFMcGErbzFtMHBZTmNZQXM0dz09

For a dynamical system, a physical measure is an ergodic invariant measure that captures the asymptotic statistical behavior of the orbits of a set with positive Lebesgue measure. A natural question in the theory is to know when such measures exist.

It is expected that a "typical" system with enough hyperbolicity (such as partial hyperbolicity) should have such measures. A special type of physical measure is the so-called hyperbolic SRB (Sinai-Ruelle-Bowen) measure. Since the 70`s the study of SRB measures has been a very active topic of research. 

In this talk, we will see a new example of open sets of partially hyperbolic systems with two dimensional center having a unique SRB measure.  One of the key features for these examples is a rigidity result for a special type of measure (the so-called u-Gibbs measure) which allows us to conclude the existence of the SRB measures.