Participant Testimonials
The workshop provided me with a lot of fresh insight and alerted me to some new and exciting results in the area. The selection of speakers was excellent! Several ideas for new projects came to my mind after listening to the talks.
This workshop is the third in a series on related topis (the first two took place in 2005 at AIM in Paolo Alto, and in 2009 at the MFO Oberwolfach. What has made these workshops particularly interesting is that they have been very focused (on eigenvalue problems), yet have attracted researcher across several disciplines, most notably Mathematical Physics, Spectral Geometry, Functional Analysis and Convexity. I am particularly interested in the "ovals conjecture", which says that a certain geometric eigenvalue problem involving the curvature of a loop should assume its minimum at the circle. Significant progress on this conjecture was reported at both subsequent workshops. This time. Jochen Denzler showed that the problem has a solution given by a planar, convex, smooth curve with strictly positive curvature. This problem continues to intrigue me, and the above meeting at BIRS was the ideal place to discuss it. I hope to see a resolution in the coming years ! The community is especially welcoming to younger researchers and students, including several Canadians who have recently returned to the country. Sadly, a number of researchers from abroad were affected by the visa strike and could not attend.
The workshop gathered together some of the leading researchers in this area and I found it quite profitable to learn about the most recent results, as well as being able to discuss future directions with some of the participants. It is too early to say whether or not these will translate themselves into actual publications, but definitely the overall balance in this respect is quite positive. It is not possible to follow all the developments and publications in this area, so I believe that the workshop was quite useful in giving an overall view of what is going on, which of course also shapes future developments. Workshops are always useful to discuss the work of your students and postdocs with other researchers, finding out about positions, etc, and this one was no exception.
Although I knew the majority of the participants already, there were several valuable new contacts. In particular, new ideas for research directions grew out of discussions with Alessandro Savo and Lotfi Hermi, and the open problem sessions were thought-provoking. I am not currently either seeking a job or involved in hiring, but it could make a difference in future hiring that I met some bright young people in spectral theory.
At the BIRS program 13w5059, I reported on the work that originated in discussions at the 2010 BIRS workshop 10w5106; additional progress was achieved at a 2012 workshop 12w5072. This resulted in two publications: 1) Y. Canzani, D. Jakobson, R. Gover and R. Ponge. "Conformal invariants from nodal sets." pdf, arxiv:1208.3040. To appear in IMRN; 2) Nullspaces of Conformally Invariant Operators. Applications to Q_k-curvature." pdf, arxiv:1206.0517, published online in Electronic Research Announcements in Mathematical Sciences, Vol. 20 (2013), pp. 43-50. I am also involved in several projects extending those results. At the BIRS program 13w5040, I reported on a series of projects that were discussed at the workshop 09w5040. These projects resulted in 3 publications: 1) Y. Canzani, D. Jakobson and I. Wigman. "Scalar curvature and Q-curvature of random metrics." To appear in Journal of Geometric Analysis. DOI 10.1007/s12220-013-9406-9; 2) Short announcement: Electronic Research announcements in Mathematical Sciences, Volume 17, 2010, pp. 43-56. 3) L. Chen and D. Jakobson. "Gaussian free fields and KPZ relation in R^4." arxiv:1210.8051, to appear in Annales de l'institut Henri Poincare. Another project is nearing completion, and a series of related projects have been completed (Y. Canzani, D. Jakobson and J. Toth. "On the distribution of propagated Schrodinger eigenfunctions." arxiv:1210.4499, to appear in Journal of Spectral Theory), or are in progress.
Mathematics and Statistics, McGill University
