Working Groups for Women in Operator Theory 2021

This is the rescheduled workshop of 2020

Operator theory is at the root of several branches of mathematics and offers a broad range of challenging and interesting research problems. Many classical areas of analysis rely on techniques from operator theory, including Banach space theory, differential equations, and dynamical systems. The broad field of operator theory also provides powerful tools for the development of other scientific fields including quantum theory, physics, and mechanics. While the field is extremely prolific early-career mathematicians often feel at a loss with so many possible avenues to explore, all requiring mastery of numerous techniques, mathematical subtleties, and deep understanding of important results. In addition, a survey of recent conferences on related topics reveals that many have offered excellent talks on recent research advances in operator theory, but few have provided a visible component geared towards preparing a new generation of researchers from underrepresented groups or a broad background on prominent research topics within operator theory. The proposed workshop has the following main objectives:

• Learn recent research trends and useful techniques in operator theory;
• Discuss strategies and solve open problems in operator theory and related areas;
• Initiate solid and long lasting research collaborations among participants;
• Increase the number of women researchers in operator theory and related areas; and
• Create an active network of support for (female) researchers in operator theory and related areas.

Toward these objectives, we plan a workshop that includes a succinct overview of state-of-the-art techniques and recent trends in operator theory and its applications; intensive group problem-solving sessions with each working group led by 1-2 project leaders and involving graduate students/postdocs, early career researchers, and more experienced researchers to discuss possible strategies and solutions to open problems; structured conversations focused on career and research advancement and teaching pedagogy; and ample social periods for informal discussions. We hope to bring together women in operator theory and related fields to work collaboratively on research projects and to form a network of support through research collaborations and professional mentorship.

This is a list of possible research projects for the workshop:

1. Composition operators: A concrete approach to questions in general operator theory (PL: Eva A. Gallardo Gutiérrez, co-PL: Carl Cowen)
2. Compressions of the shift operator in one and several variables (PL: Pamela Gorkin, co-PL: Kelly Bickel)
3. An infinite dimensional inverse eigenvalue problem and related topics (PL: Dijana Ilisevic, co-PL: Fernanda Botelho)
4. *Semigroup methods for degenerated evolution equations (PL: Birgit Jacob, co-PL: Hafida Laasri) 
5. Complex symmetric operators and related topics (PL: Ji Eun Lee, co-PL: Hyun-Kyoung Kwon)
6. Multiplication operators and structural projections on JBW*-triples (PL: Lina Oliveira, co-PL pauline Mellon