This grant will support a cooperative effort with the Mathematical Society of Japan and other Japanese funding sources to hold the International Summer School and Conference on Schubert Calculus from July 17-27, 2012, in Osaka, Japan. Schubert calculus is a wide-ranging mathematical discipline that blends many fields. It has been used to solve problems in computational geometry, optimization, mathematical biology, and cryptography, among other important applications. While Japanese mathematicians are not very active in Schubert calculus, many are experts in closely related fields. The conference will bring US researchers and open problems in Schubert calculus to Japan, and bring specialized Japanese expertise and techniques to questions in Schubert calculus; this synergy has the potential to transform the field. NSF funds will be used to support travel and limited local expenses for about 20 US mathematicians at early stages in their careers, when the potential impact on their mathematical development is highest.
This conference will foster mathematical leadership in the next generation of researchers, and also encourage established researchers into the the field, via educational programs like the summer school and resulting publications (online, video, and traditional conference proceedings). The conference webpage is located here: www.math.ed.okayama-u.ac.jp/msjsi12/
The International Summer School and Conference on Schubert Calculus was held July 17-27, 2012, in Osaka, Japan, and brought together a group of top-tier researchers from different parts of the world and at all stages of their careers. The project was an MSJ (Mathematical Society of Japan) official conference for the year 2012. Funding from NSF complemented the support from Japanese sources to support 18 graduate and postdoctoral students from US universities. We had three goals: 1) Connect: Inspire cross-cultural and interdisciplinary conversation. Few Japanese mathematicians describe themselves as Schubert calculators. However, they are experts in the mathematical fields that underlie Schubert calculus, including representation theory, algebraic geometry, toric topology, and transformation groups. Our goal was a two-way transmission of mathematics: bringing the specialized skills of Japanese experts to problems in Schubert calculus, and bringing the ideas and questions of Schubert calculus to Japanese mathematicians. This has the potential to transform Schubert calculus and energize other research programs. 2) Catalyze: Build a framework for the development of Schubert calculus in the next decade. A meeting devoted to Schubert calculus organized at Banff International Research Station in Canada in 2007 framed important new directions for the field. Five years later, the time was ripe for another framework-building conference with the top researchers in the field. We catalyzed progress in the field through a judicious choice of the most important developing areas in Schubert calculus. The summer school and workshop both focused on specific research themes in modern Schubert calculus that are critical to the field’s future. The high calibre of discussion and exchange of ideas expanded the international arena in which Schubert calculus is active, and brought new energy into the field by introducing a wide range of researchers at different stages in their careers to the beautiful web of ideas in Schubert calculus. 3) Inspire: Foster leadership in the next generation and encourage established researchers into entry into the field. Two essential ingredients in the health of an interdisciplinary and rapidly developing field such as Schubert calculus are (a) mentoring junior researchers and (b) recruiting more established researchers into the field. The key to both is to provide accessible and exciting entry points. Our summer school lecturers were superb expositors; their presentations provided broad surveys of important theoretical areas and computational techniques. The speakers for the research conference formed a ``Dream Team" of Schubert calculus, including combinatorialists, geometers, and algebraists from all over the world, while still reflecting the strong US presence in the field. We incorporated both traditional and innovative practices to help junior participants learn the material, advertise their work to the international community, and learn how to navigate their careers. In addition, we included many programs to support women, a distinct minority in math in the United States and even rarer in Japan. By all metrics, the grant was wildly successful, training US mathematicians and forging international collaborations, and simultaneously increasing the profile of US mathematicians. Of eight junior mathematicians selected to give research talks in an evening session, four were supported by this NSF grant. 23 junior participants participated in the poster session, which was attended by almost all of the conference participants. Jennifer Koonz, an American graduate student supported by this NSF grant, won the ``Best Poster Award" (selected by popular vote). Five of the 24 speakers were female, as were thirty of the 150 participants; the events for women in math were widely acclaimed. We'll give the NSF participants themselves the last word: "I loved the summer school. I learned a ton...The whole thing just made me feel so mathematically alive—so many great ideas floating around and so many wonderful people to talk to about them. At one point I asked Kaisa Taipale if she had intuition for what equivariant quantum Schubert calculus was measuring. She didn't, but we looked around the room, and there was Dave Anderson, who gave us a good answer to our question in a very few minutes of talking...These are amazing things that don't happen most days, since I usually don't have this collection of people around." "This meeting just gave me so much more context, and let me connect the ideas that I am thinking about with those that other people are thinking about. I feel like I have a much better idea of where I fit in the broader mathematical picture and how to pull ideas from more places to further my research." "I was surprised to see all the big names in Schubert calculus in one conference. I really appreciated the way the conference encouraged young participants, through the poster session, 10 minute talks, and the advice offered at the female participants' lunch." "The research conference was great, and I can think of no way to improve it...I'm really grateful to have had this opportunity!"
