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


News

Check out the Special month at the University of Michigan, May 8th - June 2nd, 2023.

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, 1952531, and 2139613.

    Programs and Activities

    Summer 2023

    We are holding a Special month at the University of Michigan, May 8th - June 2nd, 2023.

    Summer 2022

    We held a Learning Workshop and Conference on Algebraic Geometry and Singularities at the University of Washington, June 20 - June 26, 2022.

    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

  • Lim Ulrich sequences and Lech's conjecture, Linquan Ma, Invent. math. 231, 407-429 (2023).
  • Syntomic complexes and p-adic etale Tate twists. Bhargav Bhatt, Akhil Mathew. Forum Math. Pi 11 (2023), Paper No. e1, 26 pp.
  • The existence of the Kähler-Ricci soliton degeneration. Harold Blum, Yuchen Liu, Chenyang Xu, Ziquan Zhuang. Forum Math. Pi 11 (2023), Paper No. e9, 28 pp.
  • Hodge sheaves underlying flat projective families. Sándor Kovács, Behrouz Taji. Math. Z. 303 (2023), no. 3, 75.
  • Finite generation for valuations computing stability thresholds and applications to K-stability. Yuchen Liu, Chenyang Xu, Ziquan Zhuang. Ann. of Math. (2) 196 (2022), no. 2, 507-566.
  • Hodge filtration on local cohomology, Du Bois complex, and local cohomological dimension. Mircea Mustata, Mihnea Popa. Forum Math. Pi 10 (2022), Paper No. e22, 58 pp.
  • Lower bounds on the F-pure threshold and extremal singularities, Zhibek Kadyrsizova, Jennifer Kenkel, Janet Page, Jyoti Singh, Karen E. Smith, Adela Vraciu and Emily E. Witt. Trans. Amer. Math. Soc. Ser. B 9 (2022), 977-1005
  • The six functors for Zariski-constructible sheaves in rigid geometry. Bhargav Bhatt, David Hansen. Compos. Math. 158 (2022), no. 2, 437-482.
  • Openness of K-semistability for Fano varieties, Harold Blum, Yuchen Liu, Chenyang Xu. Duke Math. J. 171 (2022), no. 13, 2753-2797.
  • An analogue of adjoint ideals and PLT singularities in mixed characteristic, Linquan Ma, Karl Schwede, Kevin Tucker, Joe Waldron and Jakub Witaszek. J. Algebraic Geom. 31 (2022), 497-559.
  • A Buchsbaum theory for tight closure, Linquan Ma and Pham Hung Quy. Trans. Amer. Math. Soc. 375 (2022), 8257-8276.
  • Multiplicities and Betti numbers in local algebra via lim Ulrich points. Srikanth B. Iyengar, Linquan Ma, Mark E. Walker. Algebra Number Theory 16 (2022), no. 5, 1213-1257.
  • Generic vanishing in characteristic p>0 and the geometry of theta divisors. Christopher D. Hacon, Zsolt Patakfalvi. Boll. Unione Mat. Ital. 15 (2022), no. 1-2, 215-244.
  • F-stable secondary representations and deformation of F-injectivity. Alessandro De Stefani, Linquan Ma. Acta Math. Vietnam. 47 (2022), no. 1, 141-150.
  • Classification of Frobenius forms in five variables, Zhibek Kadyrsizova, Janet Page, Jyoti Singh, Karen E. Smith, Adela Vraciu and Emily E. Witt. Women in commutative algebra, 353-367, Assoc. Women Math. Ser., 29, Springer, Cham, [2021]
  • 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).
  • Cubic Surfaces of Characteristic Two. Zhibek Kadyrsizova, Jennifer Kenkel, Janet Page, Jyoti Singh, Karen E. Smith, Adela Vraciu, Emily E. Witt. Trans. Amer. Math. Soc. 374 (2021), no. 9, 6251-6267.
  • 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

  • (2023) ACC for generalized log canonical thresholds for complex analytic spaces, Christopher Hacon, Lingyao Xie.
  • (2023) Vanishing and non-negativity of the first normal Hilbert coefficient, Linquan Ma, Pham Hung Quy.
  • (2023) Remarks on the existence of minimal models of log canonical generalized pairs, Nikolaos Tsakanikas, Lingyao Xie.
  • (2022) The minimal exponent and k-rationality for locally complete intersectionsQianyu Chen, Bradley Dirks, Mircea Mustață.
  • (2022) Perfectoid signature, perfectoid Hilbert-Kunz multiplicity, and an application to local fundamental groups, Hanlin Cai, Seungsu Lee, Linquan Ma, Karl Schwede, Kevin Tucker.
  • (2022) Maximal skew sets of lines on a Hermitian surface and a modified Bron-Kerbosch algorithm, Anna Brosowsky, Haoyu Du, Madhav Krishna, Sandra Nair, Janet Page, Tim Ryan.
  • (2022) Contraction theorem for generalized pairs, Lingyao Xie.
  • (2022) K-stability for varieties with a big anticanonical class, Chenyang Xu.
  • (2022) On Postnikov completeness for replete topoi, Shubhodip Mondal, Emanuel Reinecke.
  • (2022) Semi-ampleness of generalized pairs, Jihao Liu, Lingyao Xie.
  • (2022) Du Bois property of log centers, János Kollár, Sándor J Kovács.
  • (2022) Lim Ulrich sequences and Boij-Söderberg cones, Srikanth B. Iyengar, Linquan Ma, Mark E. Walker.
  • (2022) Ind-étale vs Formally étale, Shubhodip Mondal, Alapan Mukhopadhyay.
  • (2022) An estimate for F-jumping numbers via the roots of the Bernstein-Sato polynomial, Mircea Mustață.
  • (2022) Smooth limits of plane curves of prime degree and Markov numbers, Kristin DeVleming, David Stapleton.
  • (2022) Fano hypersurfaces with no finite order birational automorphisms, Nathan Chen, Lena Ji, David Stapleton.
  • (2022) V-filtrations and minimal exponents for locally complete intersection singularities, Qianyu Chen, Bradley Dirks, Mircea Mustață, Sebastián Olano.
  • (2022) Movable cones of complete intersections of multidegree one on products of projective spaces, Michael Hoff, Isabel Stenger, José Ignacio Yáñez.
  • (2022) Values of the F-pure threshold for homogeneous polynomials, Karen E. Smith, Adela Vraciu.
  • (2022) Relative Nakayama-Zariski decomposition and minimal models of generalized pairs, Jihao Liu, Lingyao Xie.
  • (2022) On k-rational and k-Du Bois local complete intersections, Mircea Mustață, Mihnea Popa.
  • (2022) On a conjecture of Bitoun and Schedler, Mircea Mustață, Sebastian Olano.
  • (2022) Stable degenerations of singularities, Chenyang Xu, Ziquan Zhuang.
  • (2022) On the 4-dimensional minimal model program for Kahler varieties, Omprokash Das, Christopher Hacon, Mihai Paun.
  • (2022) Arakelov inequalities in higher dimensions, Sándor J Kovács, Behrouz Taji.
  • (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) The log canonical threshold and rational singularities, Raf Cluckers, János Kollár, Mircea Mustață.
  • (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) Rational singularities. Sándor Kovács.
  • (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) 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) 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) 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) 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) 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) Compatible ideals in Q-Gorenstein rings, Thomas Polstra, Karl Schwede.
  • (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.
  • People involved in this NSF FRG grant


    Graduate Students

  • Anna Brosowsky, University of Michigan, student of Karen Smith.
  • Hanlin Cai, University of Utah, student of Karl Schwede.
  • Zhiyuan Chen, Princeton University, student of Chenyang Xu.
  • Haoyang Guo, formerly a student at the University of Michigan, student of Bhargav Bhatt.
  • Kristine Hampton, University of Washington, student of Sándor Kovács
  • Kai Huang, MIT, student of Chenyang Xu.
  • Tafari James, University of Washington, student of Sándor Kovács
  • 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.
  • Cheng Meng, Purdue University, student of Linquan Ma.
  • Shubhodip Mondal, University of Michigan, student of Bhargav Bhatt.
  • Alapan Mukhopadhyay, University of Michigan, student of Karen Smith.
  • Lu Qi, Princeton University, student of Chenyang Xu.
  • 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

  • David Stapleton, University of Michigan.
  • Qianyu Chen, University of Michigan.
  • FRG PIs

    Bhargav
    Bhatt

    co-PI
    University of Michigan
    /Princeton University and IAS

    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