SMS Spring Meeting 2024

Participants

• Olivier Benoist (Paris)
• Thomas Blomme (Neuchâtel)
• Francesca Carocci (Geneva)
• Alois Demory (Paris)
• Ilia Itenberg (Paris)
• Andres Jaramillo Puentes (Essen)
• Hannah Markwig (Tübingen)
• Gurvan Mével (Nantes)
• Grigory Mikhalkin (Geneva)
• Victoria Schleis (Tübingen)
• Antoine Toussaint (Geneva)

Schedule

Abstracts

O. Benoist - The Wu relations in real algebraic geometry.

I will describe and study relations between Chern classes and Galois cohomology classes in the Gal(C/R)-equivariant cohomology of real algebraic varieties with no real points. These relations have applications to sums of squares problems, in the spirit of Hilbert's 17th problem. For instance, one can use them to show that a nonnegative real polynomial in R[X_1,...,X_n] of degree at most n-1 is a sum of 2^{n-1} squares in the field R(X_1,...,X_n) of rational functions. This is joint work with Olivier Wittenberg.

H. Markwig - The moduli space of twisted canonical divisors and tropical leaky covers.

(Joint work with Renzo Cavalieri, Dhruv Ranganathan, Johannes Schmitt) The moduli space of twisted canonical divisors can be viewed as a variant of the Hurwitz space parametrizing genus g degree d covers of a line with two special ramification profiles fixed for 0 and infinity.
The Hurwitz space can be used to define the classical (double) Hurwitz numbers which count covers of Riemann surfaces satisfying fixed ramification data. There is a correspondence theorem showing that Hurwitz numbers can be determined by counting the analogous tropical covers. One can similarly define an intersection product on the moduli space of twisted canonical divisors, for which we prove that it equals a count of tropical covers which do not satisfy the balancing condition but leak at every vertex. We call these leaky tropical covers.
Properties of these leaky tropical covers can be studied with tropical methods.

How to Go to Meielisalp ?

The CFF/SBB app is your best friend ! Basically, you need to go to Spiez In Spiez, get out of the train station and take the bus B60 to Leissingen, where the hotel shuttle should wait for you. The bold ones may go by foot, which is approximately 25min walk.

If you are coming from Zürich, you have direct trains leaving at **h02 to Spiez but you may have to change in Bern.

If you are coming from Basel, take train at **h28 or **h56 going to Brig or Interlaken, and get out in Spiez.

If you are coming from Bern, take train at **h04 or **h34 going to Brig or Interlaken, and get out in Spiez.

If you are coming from Lausanne, you need to go to Bern first and change in Bern and follow the corresponding instructions.

Thomas Blomme (organizer)