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FRG: Algebraic Geometry and Singularities in Positive and Mixed Characteristic NSF


This NSF Focus Research Grant award, FRG: Algebraic Geometry and Singularities in Positive and Mixed Characteristic is designed to study singularities in positive and mixed characteristic and to apply what is discovered to key questions in algebraic geometry and related fields.
This is a collaborative project involving the institutions:

  • Purdue University
  • The Massachussets Institute of Technology
  • The University of Michigan
  • The University of Utah
  • The University of Washington
  • Under NSF grants #1952366, 1951376, 1952399, 1952522, and 1952531.

    Programs and Activities

    Summer 2021

    We are holding a Virtual Special Month at the University of Utah, May 17 - June 11th, 2021. Click on the link for more information and to register!

    Published Papers

  • On positivity of the CM line bundle on K-moduli spaces. Chenyang Xu, Ziquan Zhuang. Annals of Mathematics. Vol. 192, No. 3, (November 2020), pp. 1005-1068.
  • Preprints

  • (2021) The six functors for Zariski-constructible sheaves in rigid geometry. Bhargav Bhatt, David Hansen.
  • (2021) Divisors computing minimal log discrepancies on lc surfaces. Jihao Liu, Lingyao Xie.
  • (2021) RandomRationalPoints package for Macaulay2 Sankhaneel Bisui, Zhan Jiang, Sarasij Maitra, Thái Thành Nguyên, Karl Schwede.
  • (2020) Globally +-regular varieties and the minimal model program for threefolds in mixed characteristic. Bhargav Bhatt, Linquan Ma, Zsolt Patakfalvi, Karl Schwede, Kevin Tucker, Joe Waldron, Jakub Witaszek.
  • (2020) The log minimal model program for Kähler 3-folds. Omprokash Das, Christopher Hacon.
  • (2020) Extremal Singularities in Positive Characteristic. Zhibek Kadyrsizova, Jennifer Kenkel, Janet Page, Jyoti Singh, Karen E. Smith, Adela Vraciu, Emily E. Witt
  • (2020) F-stable secondary representations and deformation of F-injectivity. Alessandro De Stefani, Linquan Ma
  • (2020) On the relative Minimal Model Program for fourfolds in positive characteristic. Christopher Hacon, Jakub Witaszek
  • (2020) Generic vanishing in characteristic p>0 and the geometry of theta divisors. Christopher D. Hacon, Zsolt Patakfalvi.
  • (2020) Cubic Surfaces of Characteristic Two. Zhibek Kadyrsizova, Jennifer Kenkel, Janet Page, Jyoti Singh, Karen E. Smith, Adela Vraciu, Emily E. Witt
  • (2020) Excellence, F-singularities, and solidity. Rankeya Datta, Takumi Murayama, Karen E. Smith.
  • (2020) Koszul and local cohomology, and a question of Dutta. Linquan Ma, Anurag K. Singh, Uli Walther.
  • (2020) Effective birationality for sub-pairs with real coefficients. Jingjun Han, Jihao Liu.
  • (2020) FastLinAlg package for Macaulay2. Boyana Martinova, Marcus Robinson, Karl Schwede, Yuhui Yao.
  • (2020) Asymptotic Lech's inequality. Craig Huneke, Linquan Ma, Pham Hung Quy, Ilya Smirnov.
  • People involved in this NSF FRG grant


    Graduate Students

  • Jihao Liu, University of Utah, Student of Christopher Hacon.
  • Seungsu Lee, University of Utah, Student of Karl Schwede.

    Postdocs

  • FRG PIs

    Bhargav
    Bhatt

    co-PI
    University of Michigan

    Christopher
    Hacon

    PI
    University of Utah

    Sándor
    Kovács

    PI
    University of Washington

    Linquan Ma

    PI
    Purdue University

    Mircea
    Mustaţă

    co-PI
    University of Michigan

    Karl
    Schwede

    co-PI
    University of Utah

    Karen
    Smith

    PI
    University of Michigan

    Chenyang Xu

    PI
    Princeton University