Non-Archimedean Geometry Techniques in Mirror Symmetry
University of Copenhagen
NOTE ON 30 APRIL, 2020: We are unable to host the masterclass during June 22-26, 2020, due to the pandemic. It is possible that the course will be rescheduled for later in 2020, or for sometime in 2021. In either case, the class will be advertised again.
NOTE ON 7 APRIL, 2020: It is unclear whether or not this masterclass will run as planned. Those who would like to attend should register as usual and make sure that all reservations they make are fully refundable. The organizers will send an email to all those registered as soon as final decisions are made.
This Masterclass, will be an introduction to recent breakthroughs on the SYZ Conjecture accomplished using techniques from Non-Archimedean and Tropical Geometry. The course is designed for PhD students working in related areas, though others are welcome to attend if space permits.
The course will consist of lectures and problem and discussion sessions given over the span of five days. Participants are also asked to prepare in advance of the event using the following materials: [Con08], [Nic16], [Gro13].
It is possible to receive 2.5 ECTS points for successful participation in this course. To do this, students must register at phdcourses.ku.dk.
[Con08] Brian Conrad, Several approaches to non-archimedean geometry., p-adic geometry. Lectures from the 2007 10th Arizona winter school, Tucson, AZ, USA, March 10–14, 2007, Providence, RI: American Mathematical Society (AMS), 2008, pp. 9–63.
[GHK15] Mark Gross, Paul Hacking, and Sean Keel, Mirror symmetry for log Calabi-Yau surfaces. I., Publ. Math., Inst. Hautes Étud. Sci. 122 (2015), 65–168.
[GHKK18] Mark Gross, Paul Hacking, Sean Keel, and Maxim Kontsevich, Canonical bases for cluster algebras, J. Amer. Math. Soc. 31 (2018), no. 2, 497–608. MR 3758151
[Gro13] Mark Gross, Mirror symmetry and the Strominger-Yau-Zaslow conjecture, Current developments in mathematics 2012, Int. Press, Somerville, MA, 2013, pp. 133–191. MR 3204345
[GS11a] Mark Gross and Bernd Siebert, An invitation to toric degenerations., Geometry of special holonomy and related topics, Somerville, MA: International Press, 2011, pp. 43–78.
[GS11b] Mark Gross and Bernd Siebert, From real affine geometry to complex geometry, Ann. of Math. (2) 174 (2011), no. 3, 1301–1428. MR 2846484
[KS06] Maxim Kontsevich and Yan Soibelman, Affine structures and non-Archimedean analytic spaces, The unity of mathematics, Progr. Math., vol. 244, Birkhäuser Boston, Boston, MA, 2006, pp. 321–385. MR 2181810
[KX16] János Kollár and Chenyang Xu, The dual complex of Calabi-Yau pairs., Invent. Math. 205 (2016), no. 3, 527–557.
[KY19] Sean Keel and Tony Yue Yu, The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus, arXiv e-prints (2019), arXiv:1908.09861.
[MN15] Mircea Mustaţă and Johannes Nicaise, Weight functions on nonArchimedean analytic spaces and the Kontsevich-Soibelman skeleton., Algebr. Geom. 2 (2015), no. 3, 365–404.
[Nic16] Johannes Nicaise, Berkovich skeleta and birational geometry, Nonarchimedean and tropical geometry, Simons Symp., Springer, [Cham], 2016, pp. 173–194. MR 3702312
[Nic18] Johannes Nicaise, Igusa zeta functions and the non-archimedean SYZ fibration, Acta Math. Vietnam. 43 (2018), no. 1, 31–44. MR 3755796
[NX16] Johannes Nicaise and Chenyang Xu, The essential skeleton of a degeneration of algebraic varieties., Am. J. Math. 138 (2016), no. 6, 1645–1667.
[NXY19] Johannes Nicaise, Chenyang Xu, and Tony Yue Yu, The non-archimedean SYZ fibration, Compos. Math. 155 (2019), no. 5, 953–972. MR 3946280
[Yu16a] Tony Yue Yu, Enumeration of holomorphic cylinders in log Calabi-Yau surfaces. I., Math. Ann. 366 (2016), no. 3-4, 1649–1675.
[Yu16b] Tony Yue Yu, Enumeration of holomorphic cylinders in log Calabi-Yau surfaces. II. Positivity, integrality and the gluing formula, arXiv e-prints (2016), arXiv:1608.07651.
The Masterclass will take place at the Department of Mathematical Sciences, University of Copenhagen. See detailed instructions on how to reach Copenhagen and the conference venue.
Tickets and passes for public transportation can be bought at the Copenhagen Airport and every train or metro station. You can find the DSB ticket office on your right-hand side as soon as you come out of the arrival area of the airport. DSB has an agreement with 7-Eleven, so many of their shops double as selling points for public transportation.
A journey planner in English is available.
More information on the "find us" webpage.
We kindly ask the participants to arrange their own accommodation.
We recommend Hotel 9 Små Hjem, which is pleasant and inexpensive and offers rooms with a kitchen. Other inexpensive alternatives are CabInn, which has several locations in Copenhagen: the Hotel City (close to Tivoli), Hotel Scandivania (Frederiksberg, close to the lakes), and Hotel Express (Frederiksberg) are the most convenient locations; the latter two are 2.5-3 km from the math department. Somewhat more expensive – and still recommended – options are Hotel Nora and Ibsen's Hotel.
The original registration deadline was April 15.
If the masterclass is rescheduled, we will post a new registration form and notify those who have already registered of the update.
Please direct all inquiries to Cody Gunton (firstname.lastname@example.org).