Seminars and Colloquia by Series

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 Looper – Brown 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

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 Jing – Augusta 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.

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 Walker – University 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.

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 Aizenbud – Yale 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.

Vertex-minors and structure for dense graphs

Series
Combinatorics Seminar
Time
Friday, December 3, 2021 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Rose McCarty – University of Waterloo –

Structural graph theory has usually focused on classes of graphs that are 'sparse' rather than 'dense' (that is, have few edges rather than many edges). We discuss this paradigm, focusing on classes with a forbidden vertex-minor. In particular, we discuss progress on a conjecture of Geelen that would totally characterize classes with a forbidden vertex-minor. This is joint work with Jim Geelen and Paul Wollan.

Ergodic theory: a statistical description of chaotic dynamical systems

Series
SIAM Student Seminar
Time
Friday, December 3, 2021 - 14:30 for 1 hour (actually 50 minutes)
Location
Skiles 169
Speaker
Alex Blumenthal – Georgia Tech

Dynamical systems model the way that real-world systems evolve in time. While the time-asymptotic behavior of many systems can be characterized by “simple” dynamical features such as equilibria and periodic orbits, some systems evolve in a chaotic, seemingly random way. For such systems it is no longer meaningful to track one trajectory at a time individually- instead, a natural approach is to treat the initial condition as random and to observe how its probabilistic law evolves in time. This is the core idea of ergodic theory, the topic of this talk. I will not assume much beyond some basics of probability theory, e.g., random variables. 

A traveling wave bifurcation analysis of turbulent pipe flow

Series
CDSNS Colloquium
Time
Friday, December 3, 2021 - 13:00 for 1 hour (actually 50 minutes)
Location
Online via Zoom
Speaker
Maximilian Engel – FU Berlin –

Please Note: Zoom link-- https://us06web.zoom.us/j/83392531099?pwd=UHh2MDFMcGErbzFtMHBZTmNZQXM0dz09

Using techniques from dynamical systems theory, we rigorously study an experimentally validated model by [Barkley et al., Nature, 526:550-553, 2015], which describes the rise of turbulent pipe flow via a PDE system of reduced complexity. The fast evolution of turbulence is governed by reaction-diffusion dynamics coupled to the centerline velocity, which evolves with advection of Burgers' type and a slow relaminarization term. Applying to this model a spatial dynamics ansatz, we prove the existence of a heteroclinic loop between a turbulent and a laminar steady state and establish a cascade of bifurcations of traveling waves mediating the transition to turbulence, with a focus on an intermediate Reynolds number regime.

This is joint work with Björn de Rijk and Christian Kuehn.

An introduction to Cork twists, Gluck twists, and Logarithmic transformations of 4-manifolds.

Series
Geometry Topology Student Seminar
Time
Wednesday, December 1, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006 (also in BlueJeans)
Speaker
Sierra Knavel – Georgia Tech

Please Note: BlueJeans link: https://bluejeans.com/609527728/0740

The main goal of manifold theory is to classify all n-dimensional topological manifolds. For a smooth 4-manifold X, we aim to understand all of the exotic smooth structures there are to the smooth structure on X. Exotic smooth structures are homeomorphic but not diffeomorphic. Cork twists, Gluck twists, and Log transforms are all ways to construct possible exotic pairs by re-gluing embedded surfaces in the 4-manifold. In this talk, we define these three constructions.  

Constructions in combinatorics via neural networks

Series
Graph Theory Seminar
Time
Tuesday, November 30, 2021 - 12:00 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Adam Zsolt Wagner – Tel Aviv University –

Please Note: Note the unusual time!

Recently, significant progress has been made in the area of machine learning algorithms, and they have quickly become some of the most exciting tools in a scientist’s toolbox. In particular, recent advances in the field of reinforcement learning have led computers to reach superhuman level play in Atari games and Go, purely through self-play. In this talk I will give a basic introduction to neural networks and reinforcement learning algorithms. I will also indicate how these methods can be adapted to the "game" of trying to find a counterexample to a mathematical conjecture, and show some examples where this approach was successful.

Cayley-Bacharach theorems and measures of irrationality

Series
Algebra Seminar
Time
Tuesday, November 30, 2021 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Brooke Ullery – Emory University –

If Z is a set of points in projective space, we can ask which polynomials of degree d vanish at every point in Z. If P is one point of Z, the vanishing of a polynomial at P imposes one linear condition on the coefficients. Thus, the vanishing of a polynomial on all of Z imposes |Z| linear conditions on the coefficients. A classical question in algebraic geometry, dating back to at least the 4th century, is how many of those linear conditions are independent? For instance, if we look at the space of lines through three collinear points in the plane, the unique line through two of the points is exactly the one through all three; i.e. the conditions imposed by any two of the points imply those of the third. In this talk, I will survey several classical results including the original Cayley-Bacharach Theorem and Castelnuovo’s Lemma about points on rational curves. I’ll then describe some recent results and conjectures about points satisfying the so-called Cayley-Bacharach condition and show how they connect to several seemingly unrelated questions in contemporary algebraic geometry relating to the gonality of curves and measures of irrationality of higher dimensional varieties.

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