Programa de Pós-Graduação em Matemática
Pura e Aplicada - UFSC
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Colóquio de Matemática
Colóquio de Matemática
08/05/2026, 14h - sala 202 !
Universidade Federal de Minas Gerais
Título: The importance of being odd: why it is better not to commute
Título: The importance of being odd: why it is better not to commute
Resumo: The introduction of supersymmetry in physics (more specifically, in quantum field theory) and string theory motivated the development of a geometry where spaces are endowed with functions taking both commuting and anticommuting values. The physics underpinning this geometry remains a driving force for the field today, dictating the directions in which the theory is evolving. In this talk, I will sketch the origins of supersymmetry, provide an introduction to supergeometry from an algebro-geometric perspective, and outline some applications.
15/05/2026, 14h - Auditório Airton Silva
Technische Universität Bergakademie Freiberg, Alemanha
Título: What is... a continuous geometry?
Título: What is... a continuous geometry?
Resumo: In the 1930s, John von Neumann developed a continuous-dimensional model for finite-dimensional projective geometry. Inspired by conversations with Garrett Birkhoff as well as his collaboration with Francis Murray concerning rings of operators, von Neumann introduced and studied the notion of a continuous geometry, which is a complete complemented modular lattice possessing a certain continuity property. For these geometries, he proved a deep coordinatization theorem, generalizing the classical Veblen--Young theorem from projective geometry, and established a powerful dimension theory. In recent years, continuous geometries and their coordinate rings have found new applications in the study of group rings, operator algebras, and topological dynamics. The talk will provide an introduction to von Neumann's continuous geometry and, time permitting, discuss some of the latest advances in the area.
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