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


News

Make sure to register for the Learning Workshop and Conference on Algebraic Geometry and Singularities June 20 - June 26, 2022 at the University of Washington in Seattle.

About

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
  • Princeton University
  • 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 2022

    We are holding a Learning Workshop and Conference on Algebraic Geometry and Singularities at the University of Washington, June 20 - June 26, 2022. You can register here.

    Summer 2021

    We held a Virtual Special Month at the University of Utah, May 17 - June 11th, 2021. Click on the link for more information and to watch the videos.

    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.
  • Maximal Cohen-Macaulay complexes and their uses: a partial survey. Srikanth B. Iyengar, Linquan Ma, Karl Schwede, Mark E. Walker, Commutative algebra, 475-500, Springer (2021).
  • F-stable secondary representations and deformation of F-injectivity. Alessandro De Stefani, Linquan Ma. Acta Math. Vietnam. 47 (2022), no. 1, 141-150.
  • Preprints

  • (2022) Variations of generalised pairs, Caucher Birkar, Christopher D. Hacon
  • (2022) On the fixed part of pluricanonical systems for surfaces. Jihao Liu, Lingyao Xie.
  • (2022) Syntomic complexes and p-adic etale Tate twists. Bhargav Bhatt, Akhil Mathew.
  • (2022) Absolute prismatic cohomology. Bhargav Bhatt, Jacob Lurie.
  • .
  • (2022) The prismatization of p-adic formal schemes. Bhargav Bhatt, Jacob Lurie.
  • (2022) Frobenius-Poincare function and Hilbert-Kunz multiplicity. Alapan Mukhopadhyay.
  • (2022) On generalized lc pairs with b-log abundant nef part. Junpeng Jiao, Jihao Liu, Lingyao Xie.
  • (2022) Boundedness of polarised Calabi-Yau fibrations. Junpeng Jiao
  • (2022) Uniform Lech's inequality. Linquan Ma, Ilya Smirnov.
  • (2021) A Buchsbaum theory for tight closure. Linquan Ma, Pham Hung Quy.
  • (2021) Rational singularities. Sándor Kovács.
  • (2021) Hodge sheaves underlying flat projective families. Sándor Kovács, Behrouz Taji.
  • (2021) The existence of the Kähler-Ricci soliton degeneration. Harold Blum, Yuchen Liu, Chenyang Xu, Ziquan Zhuang.
  • (2021) Birational automorphism groups and the movable cone theorem for Calabi-Yau complete intersections of products of projective spaces, José Ignacio Yáñez.
  • (2021) Rational nef and anti-nef polytopes are not uniform, Lingyao Xie.
  • (2021) Number of singular points on projective surfaces, Jihao Liu, Lingyao Xie.
  • (2021) Divisors computing minimal log discrepancies on lc surfaces, Jihao Liu, Lingyao Xie.
  • (2021) On the Boundedness of Canonical Models, Junpeng Jiao.
  • (2021) Totaro's inequality for classifying spaces. Bhargav Bhatt, Shizhang Li.
  • (2021) Finite generation for valuations computing stability thresholds and applications to K-stability. Yuchen Liu, Chenyang Xu, Ziquan Zhuang.
  • (2021) On the termination of the MMP for semi-stable fourfolds in mixed characteristic. Lingyao Xie, Qingyuan Xue.
  • (2021) Existence of flips for generalized lc pairs, Christopher D. Hacon, Jihao Liu.
  • (2021) On the existence of flips for threefolds in mixed characteristic (0,5). Lingyao Xie, Qingyuan Xue
  • (2021) Boundedness of semistable sheaves. Haoyang Guo, Sanal Shivaprasad, Dylan Spence, Yueqiao Wu.
  • (2021) Boundedness of elliptic Calabi-Yau threefolds. Stefano Filipazzi, Christopher D. Hacon, Roberto Svaldi.
  • (2021) Global generation of test ideals in mixed characteristic and applications. Christopher Hacon, Alicia Lamarche, Karl Schwede
  • (2021) Hodge filtration on local cohomology, Du Bois complex, and local cohomological dimension. Mircea Mustata, Mihnea Popa.
  • (2021) Prismatic F-crystals and crystalline Galois representations. Bhargav Bhatt, Peter Scholze.
  • (2021) The Du Bois complex of a hypersurface and the minimal exponent. Mircea Mustata, Sebastian Olano, Mihnea Popa, Jakub Witaszek
  • (2021) The six functors for Zariski-constructible sheaves in rigid geometry. Bhargav Bhatt, David Hansen.
  • (2021) Algebraic geometry in mixed characteristic. Bhargav Bhatt
  • (2021) Prismatic cohomology of rigid analytic spaces over de Rham period ring. Haoyang Guo.
  • (2021) Divisors computing minimal log discrepancies on lc surfaces. Jihao Liu, Lingyao Xie.
  • (2021) Multiplicities and Betti numbers in local algebra via lim Ulrich points. Srikanth B. Iyengar, Linquan Ma, Mark E. Walker
  • (2021) RandomPoints package for Macaulay2 Sankhaneel Bisui, Zhan Jiang, Sarasij Maitra, Thai Thanh Nguyen, 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 Kahler 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) 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.
  • (2020) Cohen-Macaulayness of absolute integral closures, Bhargav Bhatt.
  • (2019) Openness of K-semistability for Fano varieties, Harold Blum, Yuchen Liu, Chenyang Xu.
  • People involved in this NSF FRG grant


    Graduate Students

  • Hanlin Cai, University of Utah, student of Karl Schwede.
  • Haoyang Guo, formerly a student at the University of Michigan, student of Bhargav Bhatt.
  • Junpeng Jiao, University of Utah, student of Christopher Hacon.
  • Jihao Liu, formerly a student at the University of Utah, student of Christopher Hacon.
  • Seungsu Lee, University of Utah, student of Karl Schwede.
  • Shubhodip Mondal, University of Michigan, student of Bhargav Bhatt.
  • Alapan Mukhopadhyay, University of Michigan, student of Karen Smith.
  • Sandra Rodríguez-Villalobos, student of Karl Schwede.
  • Lingyao Xie, University of Utah, student of Christopher Hacon.
  • Qingyuan Xue, University of Utah, student of Christopher Hacon.
  • José Ignacio Yáñez, University of Utah, student of Christopher Hacon.
  • 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