Browsing by Author "Xie, Zhizhang"

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Conference: International Workshop on Operator Theory and its Applications 2018
Mathematics; TAMU; https://hdl.handle.net/20.500.14641/232; National Science Foundation
This award provides funding to help defray the expenses of participants in the meeting "International Workshop in Operator Theory and its Applications" (IWOTA) a workshop that will take place during July 23-27, 2018, on the campus of the East China Normal University in Shanghai, China. Additional information about the conference can be found on the website http://iwota2018.fudan.edu.cn The 2018 IWOTA meeting will continue the tradition of past meetings in this series going back to 1981. The meeting will be focused on the latest developments in functional analysis, specifically, operator theory and and related fields. This includes applications in engineering and mathematical physics from areas such as differential and integral equations, interpolation theory, system and control theory, signal processing, and scattering theory. The IWOTA meeting will run the week before the international symposium "Mathematical Theory of Networks and Systems"(MTNS) and this pairing provide opportunities for analysts to get exposed to engineering problems. Priority for funding will be given to early career mathematicians, women, members of underrepresented groups and those without other means of support. This is an important conference in operator theory and its applications that will offer participants the opportunity to learn of state-of-the-art research in operator theory with applications to engineering and other sciences. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
K-theory of Operator Algebras and Invariants of Elliptic Operators
Mathematics; TAMU; https://hdl.handle.net/20.500.14641/232; National Science Foundation
A fundamental idea in classical geometry is the correspondence between geometric spaces and algebras of coordinate functions. Descartes' remarkable insight was that any equation gives rise to a geometric object. This insight was further developed, first notably in algebraic geometry, later progressing to geometry and topology. For a classical geometric space, the multiplication of its coordinates is commutative, namely, the multiplication does not depend on the order of operation. However, there are many natural "geometric objects" in both mathematics and physics, especially quantum mechanics, where the coordinates no longer commute. Noncommutative geometry is a branch of mathematics that is designed to handle just such noncommutative "geometric objects". Invariants of differential equations and more generally K-theory of operator algebras are a central part of noncommutative geometry. The principal investigator intends to study a certain class of invariants of differential equations and apply them to study problems in geometry and topology. A long term research goal of the principal investigator is to use methods from K-theory of operator algebras and more generally noncommutative geometry to study higher index theoretic invariants of elliptic operators and their applications to geometry and topology. The principal investigator was able to use these methods to obtain various geometric applications such as in the case of positive scalar curvature metrics problems in geometry and in the case of the manifold rigidity problem in topology. In this project, the principal investigator plans to extend these methods to obtain new geometric and topological applications, which include (1) the higher homotopy groups of the space of positive scalar curvature metrics on a given spin manifold; (2) surgery theory of singular spaces; (3) the Grothendieck-Riemann-Roch theorem for singular varieties; (4) quantitative algebraic K-theory and its applications. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
Young Mathematicians in C*-Algebras 2020
Mathematics; TAMU; https://hdl.handle.net/20.500.14641/232; National Science Foundation
This award provides funding for US participation in the conference "Young Mathematicians in C*-Algebras" that will be held August 10-15, 2020 at the University of Münster, Germany. This conference is organized for and by Master's/Ph.D. students and postdocs in operator algebras and related areas, with the goal of fostering scientific interaction between young researchers. Young Mathematicians in C*-Algebras focuses on recent developments in operator algebras (both von Neumann and C*-algebras), noncommutative geometry, and related areas of mathematical analysis, with a particular emphasis on the interplay between operator algebras and the fields of geometric group theory, logic, and dynamical systems. The conference will feature three mini-courses by established researchers (Jesse Peterson, Astrid an Huef, and Christopher Schafhauser) alongside many contributed talks by participants, as well as mentoring activities designed to increase retention of underrepresented groups in operator algebras and a keynote address by Betül Tanbay. This award gives US-based early career researchers and members of underrepresented groups an opportunity to attend and participate in this conference. The organizing committee will strive to make this funding opportunity known to target groups via advertising in a variety of venues. More information will be made available at: https://ymcstara.org/. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.