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Texas A&M University
Mathematics

Events for 12/03/2021 from all calendars

Seminar on Banach and Metric Space Geometry

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Time: 09:00AM - 10:00PM

Location: Zoom

Speaker: Kasia Wyczesany, Tel Aviv University

Title: On almost Euclidean and well-complemented subspaces of finite-dimensional normed spaces

Abstract: In this talk I will discuss a version of an old question of Vitali Milman about almost Euclidean and well-complemented subspaces. In particular, I will introduce a notion of ' ε-good points ', which allows for a convenient reformulation of the problem. Let (X,||·||X) be a normed space. It turns out that if a linear subspace Y ⊂ X consists entirely of ε-good points then the restriction of the norm ||·||X to Y must be approximately a multiple of the l2 norm and the operator norm of the orthogonal projection onto Y is close to 1. I will present an example of a normed space X of arbitrarily high dimension, whose Banach-Mazur distance from the l2dim X is at most 2, but such that non of its (even two-dimensional) subspaces consists entirely of ε-good points. The talk is based on joint work with Timothy Gowers.


Working Seminar on Banach and Metric Spaces

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Time: 1:00PM - 03:00AM

Location: BLOC302

Speaker: Garrett Tresch, Texas A&M University

Title: Rosenthal l1 theorem


Mathematical Physics and Harmonic Analysis Seminar

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Time: 1:50PM - 2:50PM

Location: Zoom

Speaker: Patricia Alonso Ruiz, TAMU

Title: Minimal eigenvalue spacing in the Sierpinski gasket

Abstract: In the 80s, the physicists Rammal and Tolouse observed that suitable series of eigenvalues in the finite graph approximations of the Sierpinski gasket produced an orbit of a particular dynamical system. That observation lead to a complete description of the spectrum of the standard Laplace operator by Fukushima and Shima. The study of this spectrum has since then revealed structures with many interesting features not seen in other more classical settings. For instance, it presents large exponential gaps (or spacings), whose existence and properties have extensively been studied. What happens with the small gaps? This fairly challenging question had eluded previous investigations and is the main subject of the present talk, where we discuss yet another remarkable fact: Any two consequent eigenvalues in the Dirichlet or in the Neumann spectrum of the Laplacian on the Sierpinski gasket are separated at least by the spectral gap.


Noncommutative Geometry Seminar

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Time: 2:00PM - 3:00PM

Location: ZOOM

Speaker: Chao Li , Courant Institute, NYU

Title: Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions

Abstract: In this talk, I will discuss some recent developments on the topology of closed manifolds admitting Riemannian metrics of positive scalar curvature. In particular, we will prove if a closed PSC manifold of dimension 4 (resp. 5) has vanishing $\pi_2$ (resp. vanishing $\pi_2$ and $\pi_3$), then a finite cover of it is homotopy equivalent to $S^n$ or connected sums of $S^{n-1}\times S^1$. A key step in the proof is a homological filling estimate in sufficiently connected PSC manifolds. This is based on joint work with Otis Chodosh and Yevgeny Liokumovich.

URL: Event link


Algebra and Combinatorics Seminar

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Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Zhanar Berikkyzy, Fairfield University

Title: Long cycles in Balanced Tripartite Graphs

Abstract: In this talk, we will survey the relevant literature, namely degree and edge conditions for Hamiltonicity and long cycles in graphs, including bipartite and $k$-partite results. We will then prove that if $G$ is a balanced tripartite graph on $3n$ vertices, $G$ must contain a cycle of length at least $3n-1$, provided that $e(G) \geq 3n^2-4n+5$ and $n\geq 14$. The result will be generalized to long cycles for 2-connected graphs when the minimum degree is large enough. Joint work with G. Araujo-Pardo, J. Faudree, K. Hogenson, R. Kirsch, L. Lesniak, and J. McDonald.


Colloquium - Caroline Moosmueller

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Time: 4:00PM - 5:00PM

Location: BLOC 117

Speaker: Caroline Moosmueller, University of California, San Diego

Description:
Title: Efficient learning algorithms through geometry, and applications in cancer research
Abstract: In this talk, I will discuss how incorporating geometric information into classical learning algorithms can improve their performance. The main focus will be on optimal mass transport (OMT), which has evolved as a major method to analyze distributional data. In particular, I will show how embeddings can be used to build OMT-based classifiers, both in supervised and unsupervised learning settings. The proposed framework significantly reduces the computational effort and the required training data. Using OMT and other geometric data analysis tools, I will demonstrate applications in cancer research, focusing on the analysis of gene expression data and on protein dynamics.