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Dartmouth’s capacity to advance its dual mission of education and research depends upon the full diversity and inclusivity of this community. We must increase diversity among our faculty, students, and staff. As we do so, we must also create a community in which every individual, regardless of gender, gender identity, sexual orientation, race, ethnicity, socio-economic status, disability, nationality, political or religious views, or position within the institution, is respected. On this close-knit and intimate campus, we must ensure that every person knows that they are a valued member of our community.
Noncommutative Geometry is a subfield of Functional Analysis with broad connections to several areas of mathematics. A foundational idea of the field, originating in quantum physics, is the notion that the quantization of a topological space is a noncommutative algebra. The theory of C*-algebras provides one way to make this precise. A celebrated theorem of Gelfand and Naimark implies that the category of commutative unital C*-algebras is equivalent to the category of compact Hausdorff topological spaces, while every noncommutative C*-algebra can be realized as an algebra of operators on Hilbert space. The research of members of this group focuses on diverse topics, such as the study of C*-algebras associated to dynamical systems, index theory of elliptic and hypoelliptic operators, groupoids, analytic and topological K-theory, Connes-Higson E-theory, and Fredholm manifolds.
