URTAGSPractical
This session is a two-day event! It will take place from Thursday to Friday October 8-9 2026 at the Saarland University,
Department of Mathematics, University of Saarland. Lecture Hall III in the building E2.5How to get there：
The best way to reach the campus from Saarbrücken is by public transport. From the bus stop Universität Mensa, it is a short walk downhill to the buildings E2.4 and E2.5.
You can use the buses
112 and 124 from the central station,
101, 102, and 109 from the bus stop Rathaus in the city centre,
101, 102, 111, 112 and 124 from the bus stop Haus der Zukunft in the city centre.
If you arrive by car, preferably use the car park P3 (Uni Ost) on the campus.
Registration (deadline 25 September)
Another related activities:
Before the URTAGS, there is a three-day conference (5-7 October):
Complex and Algebraic Geometry in Saarbrücken
Schedule
Thursday 8 October:
| 12:30–14:00 | Lunch (for those who have already arrived) |
| 14:00–15:00 | Simone Billi: On the L-equivalence of cubic fourfolds |
| 15:15–16:15 | Eduardo Alves da Silva: Log Calabi-Yau geometry and Cremona equivalence |
| 16:15–16:45 | coffee break |
| 17:00–18:00 | Qaasim Shafi: Hilbert schemes of points, quantum cohomology and tropical curves |
| Around 19:30 | Dinner |
Friday 9 October:
| 09:00–10:30 | Stefan Schreieder: Cubic threefolds that are not retract rational |
| 10:30–11:00 | coffee break |
| 11:00–12:00 | Daniela Paiva: Birational geometry of Fano 3-folds and anticanonical surfaces |
| 12:00– | Lunch (for those who haven’t left) |
Speakers, titles and abstracts
Simone Billi: On the L-equivalence of cubic fourfolds
Recent progress points to a possible tie between L-equivalence and properties of the derived category, we explore this in the case of cubic fourfolds. We show that two very general L-equivalent cubic fourfolds are isomorphic. This is false for some special cubic fourfolds, i.e., belonging to certain Hassett divisors C_d. If the cubic fourfolds are L-equivalent and very general in a Hassett divisor C_d with d not divisible by 9, then they are Fourier–Mukai partners. This is based on joint work with L. Li Bassi.
Eduardo Alves da Silva: Log Calabi-Yau geometry and Cremona equivalence
Log Calabi-Yau geometry is the study of log Calabi-Yau pairs. Among these, the notion of volume-preserving equivalence gives rise to interesting subgroups of birational automorphism groups and, in the case of the projective space, to Cremona equivalence. Such questions depend on the birational geometry of the pairs involved. In this talk, I will address and share some findings on the challenging problem of classifying log Calabi-Yau pairs (P^3, S) of coregularity 2. This problem turns out to be equivalent to understanding Cremona equivalence among canonical quartic surfaces. This is a joint work in progress with Daniela Paiva, Sokratis Zikas & Felipe Zingali Meira.
Qaasim Shafi: Hilbert schemes of points, quantum cohomology and tropical curves
For a smooth surface S, the Hilbert scheme of points on S gives a smooth compactification of the configuration space of n distinct points on S. Its cohomology is by now well understood and exhibits deep connections with representation theory. Understanding its quantum cohomology, a deformation of ordinary cohomology involving curve counting invariants, has since received a lot of attention. I will explain joint work with Georg Oberdieck and Aaron Pixton about how to determine this ring for an elliptic surface, with the help of tropical geometry.
Stefan Schreieder: Cubic threefolds that are not retract rational
A smooth variety over a field k is retract rational if for any field extension L of k its L-points can be parametrized by rational functions. If this parametrization is generically 1:1 then the variety is rational. I will explain that one can trace this notion back to Euler and give many examples, concentrating in particular on cubics. I will then sketch a proof that the very general complex cubic threefold is not retract rational. Joint work with Philip Engel and Olivier de Gaay Fortman.
Daniela Paiva: Birational geometry of Fano 3-folds and anticanonical surfaces
The problem of determining which automorphisms of a projective K3 surface S are induced by birational maps of an ambient space in which it is embedded remains open. This is known as Gizatullin’s problem.
In this seminar, I will provide a general background on the theory of K3 surfaces and the birational geometry of Fano 3-folds, and explain how the interplay between these areas can be exploited to address the problem. In particular, I will present a solution to Gizatullin’s problem in certain specific cases.
The results I will present are part of joint works with Carolina Araujo, Michela Artebani, Alice Garbagnati, Ana Quedo, and Sokratis Zikas.