معرفی
Federico Vigolo is a Junior Professor in pure mathematics at the University of Göttingen's Mathematical Institute and a Principal Investigator of RTG 2491 - Fourier Analysis and Spectral Theory. He also serves as one of the Equal Opportunities Officers (Gleichstellungsbeauftragte) of the Mathematical Institute. His work bridges several areas of mathematics including coarse geometry, operator algebras, and geometric group theory.
Dr. Vigolo completed his PhD at the University of Oxford in 2018 with a thesis titled "Geometry of actions, expanders and warped cones". His academic journey has led him to become a prominent researcher in coarse geometry and its interactions with other mathematical fields.
His primary research focuses on Coarse Geometry and its rich interactions with operator algebras, index theory, and group theory. Specific topics he has extensively worked on include Roe algebras, Expander Graphs, coarse Baum–Connes conjecture, actions on metric and measure spaces, and CAT(0) and Hyperbolic Cube Complexes. His work often explores the connections between large-scale geometric properties and algebraic structures, with significant contributions to understanding coarse groups and warped cones.
An analysis of his publication record reveals a strong focus on the intersection of coarse geometry with operator algebras and group theory. His work consistently explores how coarse geometric properties manifest in algebraic structures like Roe algebras, and how these connections can be used to prove rigidity results or construct counterexamples to important conjectures. A notable trend is his development of frameworks that unify previously disparate concepts in coarse geometry, such as his work on coarse geometric modules and rigidity frameworks for Roe-like algebras. His 2023 monograph "An Invitation to Coarse Groups" represents a foundational contribution to this emerging field.
Professional Activities
- Organizer of the "Autumn School on Large Scale Geometry" (2023, Göttingen)
- Organizer of the "Random walks and related random topics" workshop (2022, Göttingen)
- Organizer of the YMC*A conference (2021, Münster)
- Organizer of the "Interactions between expanders, groups and operator algebras" mini-workshop (2021, Münster)
Dr. Vigolo actively supervises students, with Christos Kitsios currently pursuing a PhD under his guidance. He welcomes bachelor's and master's students interested in topics related to coarse geometry, geometric group theory, group actions on measure spaces, and operator algebras. He teaches a variety of courses including "Analytische Geometrie und Lineare Algebra," "Introduction to algebraic topology," and specialized seminars on topics like "Gender and Mathematics" and "topological K-theory."
His research has led to significant contributions in multiple areas, particularly in developing the theory of coarse groups and exploring the connections between coarse geometry and C*-algebras. His work on warped cones and asymptotic expanders has provided new counterexamples to the coarse Baum-Connes conjecture and advanced our understanding of coarse geometric invariants.
