Monday, Oct. 3  Tuesday, Oct. 4  Wednesday, Oct. 5  Thursday, Oct. 6  Friday, Oct. 7 

8:30 Registration 
9:00 Registration 
9:00 Pauli 

9:00 Pilloni 
10:00 Rapoport 
9:30 Fintzen 
10:30 Tamme 
9:30 Gee 
10:30 Hellmann 
11:30 Anschütz 
11:00 Ziegler 
11:45 Kerz 
11:00 Pappas 
11:45 Nicaise 
14:30 Registration 
14:30 Le Bras 
Excursion 


15:15 Caraiani 
16:00 Fargues 
Excursion 
15:00 Temkin 

16:45 Zhu 
17:15 Scholze 
Excursion 
16:30 Habegger 

18:30 Get together 

19:30 Conference dinner 


All talks will be 60 minutes long.
This talk will report on joint work in progress with ArthurCésar Le Bras and Ben Heuer. The aim of this project is a possible description of the category of $\mathbb{C}_p$semilinear Galois representations of a padic field $K$ via vector bundles on CartierWitt stacks of rings of integers of finite extensions of $K$.
I will survey how to prove the modularity of elliptic curves defined over the rational numbers, as pioneered by Wiles and TaylorWiles and completed by Breuil, Conrad, Diamond and Taylor. I will also mention the case of elliptic curves defined over real quadratic fields, more recently completed by Freitas, Le Hung and Siksek. I will then explain why the case of imaginary quadratic fields is qualitatively different from the previous ones. Finally, I will discuss joint work in progress with James Newton, where we prove a localglobal compatibility result in the crystalline case for Galois representations attached to torsion classes occurring in the cohomology of locally symmetric spaces. This has an application to the modularity of elliptic curves over imaginary quadratic fields, which also builds on recent work of Allen, Khare and Thorne.
I will explain how to define an extended Kottwitz set that contains the usual one and whose basic elements allows us to reach all inner forms of a given reductive $p$adic group, even if its center is not connected. This relies on the work of Kaletha. In particular I give a geometric interpretation of its gerb in terms of the curve. One can then define an extended stack of $G$bundles that contains the one we defined and studied with Scholze as a closed / open substack and whose points are the extended Kottwitz set. At the end this allows us to formulate a geometrization conjecture for any reductive group even if it's not an extended pure inner form of its quasisplit inner form.
I will attempt to explain what the categorical $p$adic Langlands program is, and how it connects to more classical questions about congruences between modular forms.
The categorical version of the local Langlands conjecture of FarguesScholze asserts, in the case of $GL_n$, that there is an equivalence between a certain category of $\ell$adic sheaves on the stack of rank $n$ vector bundles on the FarguesFontaine curve and a certain category of coherent sheaves on the stack of $n$dimensional WeilDeligne representations. We will give some evidence for this conjecture by showing that there is an isomorphism between the Kgroups (in particular: on Grothendieck groups) of these categories. In particular we will (rather explicitly) compute the Ktheory of the stack of $n$dimensional WeilDeligne representations.
In the study of semistable degeneration of Lefschetz pencils one is led to a generalization of the classical PicardLefschetz formula for certain perverse sheaves on normal crossing spaces. In the talk I will recall the formalism of nearby cycle and vanishing cycle functors and I will explain how Hodge theory allows one to obtain the normal crossing PicardLefschetz formula. Joint work with A. Beilinson and H. Esnault.
Results from motivic homotopy theory allow to answer questions in enumerative geometry over an arbitrary base field. In the talk I will explain how this works and give some examples.
Cherednik discovered that a Shimura curve attached to a quaternion algebra over a totally real field F admits padic uniformization by the Drinfeld padic upper half plane if is ramified at some $p$adic place. This observation is now almost 50 years old and there is finally the hope for a published proof. One of the main difficulties is that outside the case $F=\mathbb Q$ the Shimura curve does not represent a moduli problem of abelian varieties. This difficulty disappears when the multiplicative group of the quaternion algebra is replaced by the group of unitary similitudes of a binary hermitian space, but then other interesting problems arise. I will discuss work of BoutotZink, of KudlaRapoportZink, and of ScholzeWeinstein.
Until very recently we knew different descriptions of essentially the same method to canonically resolve singularities (in characteristic zero), but in the past few years a few new methods were found. Perhaps, this is already a good time to compare the methods, point out principles which are common to all of them, and pin down what was the main ingredient which changes from one method to another and essentially determines the method. In my talk I will suggest such a systematization and will give a panoramic view of the known desingularization algorithms.
The main theorem of complex multiplication describes how automorphisms of $\mathbb C$ act on CM abelian varieties and their torsion points. I will explain an extension of this theory to describe the action of $p$quasiisogenies between mod $p$ reductions of CM abelian varieties on primeto$p$ torsion points. Joint work with Liang Xiao.