Over the past years, there has been substantial and rapid progress in the understanding of higher dimensional algebraic varieties in characteristic p > 0, specifically from the point of view of the minimal model program. Techniques first developed in commutative algebra and representation theory in the 1980s have begun to be employed extensively.
Further development and dissemination of these methods is still needed. It has become clear that in order for further progress to be made, connections with arithmetic aspects of varieties in characteristic p > 0 must be explored and addressed.
Recent applications of Berkovich spaces to birational algebraic geometry suggest one approach to deal with these arithmetic problems one encounters in characteristic p.

This workshop will bring together researchers from several distinct areas within algebraic geometry and arithmetic geometry with the goal of disseminating recent techniques and forging new research connections.

Scientific & Organizing Committee
Manuel Blickle  (Johannes Gutenberg University of Mainz)
Karl Schwede (University of Utah)
Chenyang Xu (Beijing International Center for Mathematical Research)

Lecture Series

• Christian Liedtke (TUM Munich)

Crystalline cohomology, period maps, and applications to K3 surfaces

• Johannes Nicaise (University of Leuven)

The non-archimedean SYZ bration and Igusa zeta functions

Speakers

• Bhargav Bhatt (University of Michigan)

The direct summand conjecture and its derived variant

• Paolo Cascini (Imperial College London)

Singularities of log pairs in characteristic two

• Tommaso de Fernex (University of Utah)

Towards a link theoretic characterization of smoothness

• Yoshinori Gongyo (University of Tokyo)

Rational points on log Fano 3-fold over a finite field

• Stefan Kebekus (Albert-Ludwigs University of Freiburg)

Higgs sheaves on singular spaces and the Miyaoka-Yau Inequality for
minimal varieties of general type

• Adrian Langer (University of Warsaw)

Endomorphisms of Drinfeld half-spaces over a finite field

• Linquan Ma (University of Utah)

Deformation of F-injectivity   (pdf)

• Mircea Mustatà (University of Michigan)

Hodge ideals

• Zsolt Patakfalvi (Princeton University)

On projectivity of the moduli space of stable surfaces in characteristic p > 5

• Sergey Rybakov (Russian Academy of Sciences and
  National Research University Higher School of Economics)

On zeta functions of cubic surfaces over finite fields

• Vasudevan Srinivas (Tata Institute of Fundamental Research, Mumbai)

Stratified vector bundles on simply connected varieties in positive
characteristic

• Roberto Svaldi (University of Cambridge)

Log birational boundedness of Calabi-Yau pairs

• Shunsuke Takagi (University of Tokyo)

General hyperplane sections of canonical 3-folds in positive characteristic

• Sofia Tirabassi (University of Bergen)

Fourier-Mukai partners of canonical covers in positive characteristic

• Kevin Tucker (University of Illinois at Chicago)

Fundamental Groups of F-regular Singularities via F-Signature

• Remy van Dobben de Bruyn (Columbia University)

The Hodge ring of varieties in positive characteristic

• ​Yuan Wang (University of Utah)

On the characterization of abelian Varieties for log pairs in characteristic
zero and p > 0.