Steve Trettel

13. June 2023

Geometry from the Inside

Geometry is one of the oldest ongoing projects of humanity, with an unbroken chain of deep thought over the twenty-five centuries spanning Pythagoras to Einstein and continuing ever stronger into the future.  Over this time, mathematics has ventured beyond the 3-dimensional Euclidean world around us and into a menagerie of curved and twisted worlds.  These new geometries have greatly expanded our mathematical universe, and found applications from describing the curvature of space-time to the geometry of data in machine learning.

In this talk, we will attempt a broad exploration of modern geometry from the human perspective, starting from the question of ‘what would it be like to live in a curved world?’  Thinking deeply about what it means to ‘see’, we will use computer graphics to explore several of the modern geometric spaces integral to the Geometry+Dynamics Research Station at HITS/Heidelberg University.


About HITS

HITS, the Heidelberg Institute for Theoretical Studies, was established in 2010 by physicist and SAP co-founder Klaus Tschira (1940-2015) and the Klaus Tschira Foundation as a private, non-profit research institute. HITS conducts basic research in the natural, mathematical, and computer sciences. Major research directions include complex simulations across scales, making sense of data, and enabling science via computational research. Application areas range from molecular biology to astrophysics. An essential characteristic of the Institute is interdisciplinarity, implemented in numerous cross-group and cross-disciplinary projects. The base funding of HITS is provided by the Klaus Tschira Foundation.

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