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Texas A&M University
Mathematics

Events for 04/08/2019 from all calendars

Geometry Seminar

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Time: 3:00PM - 3:50PM

Location: BLOC 628

Speaker: Bernd Siebert, University of Texas

Title: Toric degenerations - a finite element method in algebraic geometry

Abstract: Toric degenerations in the broad sense referred to here, are deformations with central fiber a union of toric varieties, intersecting pairwise along joint toric divisors. A typical example is a family of quartic hypersurfaces in projective 3-space with central fiber the union of four coordinate hyperplanes. The interesting thing about such degenerations is that there is a large class of examples that can be produced canonically out of discrete data, thus giving a vast generalization of toric geometry (joint work with Mark Gross). In the talk I will give an overview of such degenerations, the relation to tropical geometry and wall structures, the explanation of the mirror phenomenon in this framework and the appearance of special functions generalizing Riemannian theta functions.


Industrial and Applied Math

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Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Rachel Neville, University of Arizona

Title: Topological Techniques for the Characterization of Pattern Forming Systems

Abstract: Examples of complex spatial-temporal patterns are ubiquitous, but can be difficult to characterize quantitatively. Irregular time-varying structures, complexity of patterns, and sensitivity to initial conditions, among other things, can make quantifying and distinguishing patterns difficult. In recent years, topological data analysis has emerged as a promising field for characterizing such systems, providing a low-dimensional summary of the geometric and topological structure of data. This can be used to quantify of order, for parameters to be learned and studied, and for the evolution of pattern defects to be studied. In this talk, I will give a brief introduction to persistent homology and discuss how persistence can be leveraged to study pattern forming systems. In particular, I will highlight some of the utility of some of these techniques in studying the formation of disordered hexagonal arrays of nanodots and crystalline structures that emerge in ion bombarded surfaces.