Seminars and Colloquia by Series

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 McCartyUniversity 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 BlumenthalGeorgia 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 EngelFU 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 KnavelGeorgia 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 WagnerTel 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 UlleryEmory 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.

Applications of contact geometry to 3-dimensional Anosov dynamics

Series
Geometry Topology Seminar
Time
Monday, November 29, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
Online (also Skiles 006)
Speaker
Federico SalmoiraghiTechnion

Meeting link: https://bluejeans.com/722836372/4781?src=join_info

Anosov flows are an important class of dynamical systems due to their ergodic properties and structural stability. Geometrically, they are defined by two transverse invariant foliations with expanding and contracting behaviors. Much of our understanding of the structure of an Anosov flow relies on the study of the leaves space of the invariant foliations. In this talk we adopt a different approach: in the early 90s Mitsumatsu first noticed that and Anosov vector field also belongs to the intersection of two transverse contact structures rotating towards each other. After giving the necessary background I will use this point of view to address questions in surgery theory on Anosov flows and contact structures.

Model-free Feature Screening and FDR Control with Knockoff Features

Series
Applied and Computational Mathematics Seminar
Time
Monday, November 29, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
https://bluejeans.com/457724603/4379
Speaker
Yuan KeUniversity of Georgia

This paper proposes a model-free and data-adaptive feature screening method for ultra-high dimensional data. The proposed method is based on the projection correlation which measures the dependence between two random vectors. This projection correlation based method does not require specifying a regression model, and applies to data in the presence of heavy tails and multivariate responses. It enjoys both sure screening and rank consistency properties under weak assumptions.  A two-step approach, with the help of knockoff features, is advocated to specify the threshold for feature screening  such that the false discovery rate (FDR) is controlled under a pre-specified level. The proposed two-step approach enjoys both sure screening and FDR control simultaneously if the pre-specified FDR level is greater or equal to 1/s, where s is the number of active features.  The superior empirical performance of the proposed method is illustrated by simulation examples and real data applications. This is a joint work with Wanjun Liu, Jingyuan Liu and Runze Li.

Strong 4-colourings of graphs

Series
Graph Theory Seminar
Time
Tuesday, November 23, 2021 - 15:45 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Jessica McDonaldAuburn University

In this talk we’ll discuss strong 4-colourings of graphs and prove two new cases of the Strong Colouring Conjecture. Let H be a graph with maximum degree at most 2, and let G be obtained from H by gluing in vertex-disjoint copies of K_4. We’ll show that if H contains at most one odd cycle of length exceeding 3, or if H contains at most 3 triangles, then G is 4-colourable. This is joint work with Greg Puleo.

Local and Optimal Transport Perspectives on Uncertainty Quantification

Series
Applied and Computational Mathematics Seminar
Time
Monday, November 22, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
https://bluejeans.com/457724603/4379
Speaker
Dr. Amir SagivColumbia

Please Note: remote

In many scientific areas, deterministic models (e.g., differential equations) use numerical parameters. In real-world settings, however, such parameters might be uncertain or noisy. A more comprehensive model should therefore provide a statistical description of the quantity of interest. Underlying this computational problem is a fundamental question - if two "similar" functions push-forward the same measure, would the new resulting measures be close, and if so, in what sense? We will first show how the probability density function (PDF) of the quantity of interest can be approximated, using spectral and local methods. We will then discuss the limitations of PDF approximation, and present an alternative viewpoint: through optimal transport theory, a Wasserstein-distance formulation of our problem yields a much simpler and widely applicable theory.
 

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