Toric and Tropical Geometry: Tools for Understanding Algebraic Varieties - Matt
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Imagine an intricate puzzle - an algebraic variety, defined by complex equations. Toric and tropical geometry offer powerful tools to understand its hidden structure.Toric geometry builds a bridge between algebraic varieties and lattices, grids of points with specific properties. By translating the variety into a "toric variety" based on this lattice, we gain insights into its symmetries and behavior.Tropical geometry takes a different approach. It replaces the variety with a simpler object - a polyhedral complex, a collection of flat shapes glued together. This "tropicalization" captures the…mehr

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Produktbeschreibung
Imagine an intricate puzzle - an algebraic variety, defined by complex equations. Toric and tropical geometry offer powerful tools to understand its hidden structure.Toric geometry builds a bridge between algebraic varieties and lattices, grids of points with specific properties. By translating the variety into a "toric variety" based on this lattice, we gain insights into its symmetries and behavior.Tropical geometry takes a different approach. It replaces the variety with a simpler object - a polyhedral complex, a collection of flat shapes glued together. This "tropicalization" captures the essential geometric features of the original variety, making it easier to analyze its shape and interactions with other objects.Together, toric and tropical geometry provide a diverse toolbox for mathematicians. By switching between these perspectives, we can gain a deeper understanding of the intricate world of algebraic varieties.
Autorenporträt
Dr. Matt, for your Environmental Studies course, I propose "Karoo's Uneven Anthropocene Burden." This book tackles the environmental and social challenges faced by South Africa's Karoo region in our current epoch, the Anthropocene. The Karoo disproportionately bears the weight of human impact on the planet, from resource extraction to climate change, while its communities fight for a sustainable future. The book dives into how these issues unfold, examining the consequences for the Karoo's delicate ecosystems and its people. We'll also explore concepts of environmental justice, as the Karoo's unique position often makes it a target for unsustainable practices. But "Karoo's Uneven Anthropocene Burden" isn't all doom and gloom. It highlights ongoing efforts for a just transition. We'll explore innovative solutions, community-based conservation initiatives, and strategies for mitigating the negative impacts of the Anthropocene. This book is a valuable resource for anyone interested in the environmental challenges of the Karoo, the concept of environmental justice, and the fight for a sustainable future in a region burdened by human impact.