Publications

  • Ma L. & Schwede K. (2020). A Kunz-type characterization of regular rings via alterations. (pp. 1124-1131). Vol. 224. Journal of Pure and Applied Algebra. Published, 03/01/2020.
  • Boix, Alberto F.; Hernández, Daniel J.; Kadyrsizova, Zhibek; Katzman, Mordechai; Malec, Sara; Robinson, Marcus; Schwede, Karl; Smolkin, Daniel; Teixeira, Pedro; Witt, Emily E. The TestIdeals package for Macaulay2. J. Softw. Algebra Geom. 9 (2019), no. 2, 89–110. Boix, Alberto F.; Hernández, Daniel J.; Kadyrsizova, Zhibek; Katzman, Mordechai; Malec, Sara; Robinson, Marcus; Schwede, Karl; Smolkin, Daniel; Teixeira, Pedro; Witt, Emily E. The TestIdeals package for Macaulay2. J. Softw. Algebra Geom. 9 (2019), no. 2, 89–110. Published, 07/2019.
  • B. Bhatt, J. Carvajal-Rojas, P. Graf, K. Schwede, and K. Tucker, Etale fundamental groups of strongly F-regular schemes, Int. Math. Res. Not. IMRN 2019, no. 14, 4325–4339. Published online https://doi.org/10.1093/imrn/rnx253 10/2017. Published, 07/2019.
    https://doi.org/10.1093/imrn/rnx253
  • Ma L. & Schwede K. (2019). Recent applications of p-adic methods to commutative algebra. (pp. 820-831). Vol. 66. Notices of the American Mathematical Society. Published, 06/01/2019.
  • Ma L., Polstra T., Schwede K. & Tucker K. (2019). F-signature under birational morphisms. Forum of Mathematics, Sigma. Published, 01/01/2019.
  • Karl E Schwede & Zhaoning Yang (2018). Divisor package for Macaulay2. J. Softw. Algebra Geom. Vol. 8, 87-94. Published, 12/2018.
    http://www.math.utah.edu/~schwede/Divisor.pdf
  • Ma L. & Schwede K. (2018). Perfectoid multiplier/test ideals in regular rings and bounds on symbolic powers. (pp. 913-955). Vol. 214. Inventiones Mathematicae. Published, 11/01/2018.
  • Carvajal-Rojas J. & Schwede K., Tucker K. (2018). Fundamental groups of F-Regular singularities via F-signature. Annales Scientifiques de l'Ecole Normale Superieure. Vol. 51, 993-1016. Published, 07/01/2018.
  • Patakfalvi Z. & Schwede K., Zhang W. (2018). F-singularities in families. Algebraic Geometry. Vol. 5, 264-327. Published, 05/01/2018.
  • Bhatt B. & Ma L., Schwede K. (2018). The dualizing complex of F-injective and Du Bois singularities. Mathematische Zeitschrift. Vol. 288, 1143-1155. Published, 04/01/2018.
  • Chiecchio A. & Enescu F., Miller L. E., Schwede K. E. (2018). Test ideals in rings with finitely generated anti-canonical algebras. Journal of the Institute of Mathematics of Jussieu. Vol. 17, 171-206. Published, 01/01/2018.
  • Das, Omprokash and Schwede, Karl, The F-different and a canonical bundle formula. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 17 (2017), no. 3, 1173–1205. Published, 09/21/2017.
    http://annaliscienze.sns.it/index.php?page=Article...
  • Z. Patakfalvi, K. Schwede and K. Tucker, Positive characteristic algebraic geometry, Proc. Sympos. Pure Math., 95, Amer. Math. Soc., Providence, RI, 2017. Published, 07/2017.
    https://bookstore.ams.org/pspum-95/
  • Sandor Kovacs and Karl Schwede, Inversion of adjunction for rational and Du Bois pairs. Algebra Number Theory 10 (2016), no. 5, 969–1000. Published, 10/2016.
    http://msp.org/ant/2016/10-5/p02.xhtml
  • Kovács, Sándor J. and Schwede, Karl, Du Bois singularities deform in Minimal models and extremal rays (Kyoto, 2011), 49–65, Adv. Stud. Pure Math., 70, Math. Soc. Japan, 2016. Published, 10/2016.
    https://bookstore.ams.org/aspm-70/
  • P. Cascini, Y. Gongyo, and K. Schwede, Uniform bounds for strongly F-regular surfaces, Transactions of the American Mathematical Society, 368 (2016), no. 8, 5547–5563. Published, 08/2016.
    http://arxiv.org/abs/1402.0027
  • Y. Gongyo, Z. Li, Z. Patakfalvi, K. Schwede, H. Tanaka, H. R. Zong, On rational connectedness of globally F-regular threefolds, Adv. Math. 280 (2015), 47–78. Published, 08/2015.
    http://arxiv.org/abs/1307.8188
  • M. Blickle, K. Schwede, K. Tucker, F-singularities via alterations To appear in the American Journal of Mathematics. arXiv:1107.3807 doi: 10.1353/ajm.2015.0000. Published, 01/2015.
    http://muse.jhu.edu/journals/american_journal_of_m...
  • P. Cascini, C. Hacon, M. Mustata and K. Schwede, On the numerical dimension of pseudo-effective divisors in positive characteristic. Amer. J. Math. 136 (2014), no. 6, 1609–1628. MathSciNet review: 3282982 DOI: 10.1353/ajm.2014.0047. Published, 12/2014.
    http://muse.jhu.edu/journals/american_journal_of_m...
  • K. Schwede and K. Tucker, Test ideals of non-principal ideals: computations, jumping numbers, alterations and division theorems. J. Math. Pures Appl. (9) 102 (2014), no. 5, 891–929. MathSciNet review: 3271293 doi:10.1016/j.matpur.2014.02.009. Published, 11/2014.
  • K. Schwede, A canonical linear system associated to adjoint divisors in characteristic p > 0 J. Reine Angew. Math. 696 (2014), 69–87. MathSciNet review: 3276163 DOI: 10.1515/crelle-2012-0087. Published, 11/2014.
    http://www.degruyter.com/view/j/crelle.2014.2014.i...
  • K. Schwede and A. K. Singh, F-injectivity and depth. Appendix to Deformations of F -injectivity and local cohomology by J. Horiuchi, L. E. Miller and K. Shimomoto. Indiana Univ. Math. J. 63 (2014), no. 4, 1139-1157. MathSciNet review: 3263925 doi: 10.1512/iumj.2014.63.5313. Published, 09/2014.
    http://www.iumj.indiana.edu/oai/2014/63/5313/5313....
  • M. Katzman, K. Schwede, A. K. Singh and W. Zhang, Rings of Frobenius operators. Math. Proc. Cambridge Philos. Soc. 157 (2014), no. 1, 151–167. MathSciNet review: 3211813 http://dx.doi.org/10.1017/S0305004114000176. Published, 07/2014.
    http://journals.cambridge.org/action/displayAbstra...
  • K. Schwede and K. Tucker, On the behavior of test ideals under finite morphisms. J. Algebraic Geom. 23 (2014), 399-443 MathSciNet review: 3205587. DOI: http://dx.doi.org/10.1090/S1056-3911-2013-00610-4 DOI: http://dx.doi.org/10.1090/S1056-3911-2013-00610-4 - See more at: http://www.ams.org/journals/jag/2014-23-03/S1056-3911-2013-00610-4/#sthash.AzZDvpdc.dpuf DOI: http://dx.doi.org/10.1090/S1056-3911-2013-00610-4 - See more at: http://www.ams.org/journals/jag/2014-23-03/S1056-3911-2013-00610-4/#sthash.AzZDvpdc.dpuf. Published, 07/2014.
    http://www.ams.org/journals/jag/2014-23-03/S1056-3...
  • J. C. Hsiao, K. Schwede, and W. Zhang, Cartier modules on toric varieties. Trans. Amer. Math. Soc. 366 (2014), 1773-1795 MathSciNet review: 3152712 DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05856-4 DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05856-4 - See more at: http://www.ams.org/journals/tran/2014-366-04/S0002-9947-2013-05856-4/#sthash.elRsr1ya.dpuf. Published, 04/2014.
    http://www.ams.org/journals/tran/2014-366-04/S0002...
  • Mircea Mustaţă and Karl Schwede, A Frobenius variant of Seshadri constants. Math. Ann. 358 (2014), no. 3-4, 861–878. MathSciNet review: 3175143 http://dx.doi.org/10.1007/s00208-013-0976-4. Published, 03/2014.
    http://link.springer.com/article/10.1007/s00208-01...
  • N. Epstein and K. Schwede, A dual to tight closure theory. Nagoya Math. J. 213 (2014), 41–75. MathSciNet review: 3290685 doi:10.1215/00277630-2376749. Published, 03/2014.
    http://projecteuclid.org/euclid.nmj/1383240639
  • S. Kumar and K. Schwede, Richardson varieties have Kawamata log terminal singularities. Int. Math. Res. Not. IMRN 2014, no. 3, 842–864. MathSciNet review: 3163569 doi:10.1093/imrn/rns241. Published, 02/2014.
    http://imrn.oxfordjournals.org/content/2014/3/842....
  • Z. Patakfalvi and K. Schwede, Depth of F-singularities and base change of relative canonical sheaves. J. Inst. Math. Jussieu 13 (2014), no. 1, 43–63. MathSciNet review: 3134015 DOI: http://dx.doi.org/10.1017/S1474748013000066. Published, 01/2014.
    http://journals.cambridge.org/action/displayAbstra...

Presentations

  • University of Michigan, Algebraic Geometry Seminar. Presentation, Presented, 10/2019.
  • John's Hopkins University, Algebraic Geometry Seminar. Presentation, Presented, 10/2019.
  • Workshop on Algebraic Geometry, Fudan University, Shang- hai, China. Invited Talk/Keynote, Presented, 07/2019.
  • University of Hawaii AMS Meeting, Special Session on Commutative Algebra and its Environs, Honolulu Hawaii. Presentation, Presented, 03/2019.
  • Lecture Series, Introductory Workshop: Derived Algebraic Ge- ometry and Birational Geometry and Moduli Spaces, Math Science Research Institute (MSRI), Berkeley. Invited Talk/Keynote, Presented, 01/2019.
    https://www.msri.org/people/11129
  • University of Arizona, Algebraic Seminar, Tucson, Arizona. Invited Talk/Keynote, Presented, 11/16/2017.
    http://math.arizona.edu/events/8874
  • Conference talk, Algebraic Geometry: Birational Classification, Derived Cate- gories, and Moduli Spaces, Oberwolfach, German. Invited Talk/Keynote, Presented, 09/27/2017.
    https://www.mfo.de/occasion/1739/www_view
  • EPFL Lausanne, Algebraic Geometry Seminar . Invited Talk/Keynote, Presented, 09/20/2017.
    https://tan.epfl.ch/page-126880-fr.html
  • University of North Texas AMS Meeting, Special Session on Commutative Algebra, Denton, Texas. Presentation, Presented, 09/09/2017.
    http://www.ams.org/meetings/sectional/2249_program...
  • The Prospects for Commutative Algebra, Osaka, Japan. Invited Talk/Keynote, Presented, 07/11/2017.
    http://commalg2017.jp/index.html
  • Higher Dimensional Algebraic Geometry 2017, National Center for Theoretical Sciences, Taipei, Taiwan . Invited Talk/Keynote, Presented, 06/20/2017.
    http://www.ncts.ntu.edu.tw/events_2_detail.php?nid...
  • London Geometry and Topology Seminar, Imperial College, London. Invited Talk/Keynote, Presented, 05/19/2017.
    http://geometry.ma.ic.ac.uk/seminar/?page_id=1094
  • AGNES (Algebraic Geometry Northeastern Series), Stony Brook University. Invited Talk/Keynote, Presented, 04/23/2017.
    http://www.agneshome.org/stony-brook-2017
  • SLAM (Southwest Local Algebra Meeting). University of New Mexico. Invited Talk/Keynote, Presented, 03/04/2017.
    http://www.math.ttu.edu/~lchriste/slam2017.html
  • KUMUNU – regional commutative algebra conference. Invited Talk/Keynote, Presented, 10/2016.
  • Differential forms in algebraic geometry (conference) – University of Freiburg, Germany. Invited Talk/Keynote, Presented, 09/2016.
  • University of Illinois at Chicago, algebraic geometry seminar. Invited Talk/Keynote, Presented, 04/2016.
  • Joint mathematical meetings in Seattle, special session on commutative algebra,. Invited Talk/Keynote, Presented, 01/2016.
  • Mini-course at the Multiplier ideals, Test ideals and Bernstein Sato polynomials, conference – Universitat Politcnica de Catalunya, Barcelona. Invited Talk/Keynote, Presented, 09/2015.
  • AMS summer institute in Algebraic Geometry – University of Utah. Invited Talk/Keynote, Presented, 07/2015.
  • Georgetown University AMS Meeting, Special Session on Closure Operations in Commutative Algebra. Invited Talk/Keynote, Presented, 03/2015.
  • Conference on Frobenius Operators and Cartier Algebras – Georgia State University. Invited Talk/Keynote, Presented, 03/2015.
  • Georgia algebraic geometry symposium, University of Georgia. Invited Talk/Keynote, Presented, 10/2014.
  • Western Algebraic Geometry Symposium, University of Idaho. Invited Talk/Keynote, Presented, 10/2014.
  • Algebra Seminar, Georgia Tech University. Invited Talk/Keynote, Presented, 10/2014.
  • Route 81 Conference, Cornell University. Invited Talk/Keynote, Presented, 09/2014.
  • Algebraic Geometry Seminar, University of Utah. Presentation, Presented, 09/2014.
  • Short lecture series on Cartier modules held at the Special FRG month on Higher Dimensional Algebraic Geometry at the University of Michigan. Contributed Talk, Presented, 06/2014.
    http://www.math.lsa.umich.edu/~mmustata/FRG_specia...
  • Seminar/Conference style talk held at the Special FRG month on Higher Dimensional Algebraic Geometry at the University of Michigan. Invited Talk/Keynote, Presented, 06/2014.
    http://www.math.lsa.umich.edu/~mmustata/FRG_specia...
  • Colloquium, Mathematics Department, George Mason University. Invited Talk/Keynote, Presented, 04/2014.
  • Combinatorics and algebra seminar, George Mason University. Invited Talk/Keynote, Presented, 04/2014.
  • Algebra and number theory seminar, Penn State University. Presentation, Presented, 04/2014.
  • Queens University, Algebraic Geometry Seminar. Invited Talk/Keynote, Presented, 03/2014.
  • Presentation at the Texas Algebraic Geometry Symposium. Invited Talk/Keynote, Presented, 03/2014.
  • Colloquium, Math Department, University of South Carolina. Invited Talk/Keynote, Presented, 03/2014.
  • Presentation at the conference Birational Geometry and Foliations workshop. Held at the Hausdorff Research Institute for Mathematic. Invited Talk/Keynote, Presented, 02/2014.
  • Colloquium, Mathematics Department, University of Utah. Invited Talk/Keynote, Presented, 02/2014.
  • Algebraic Geometry Seminar, University of Utah. Presentation, Presented, 02/2014.
  • Colloquium, Mathematics Department, University of California at Davis. Invited Talk/Keynote, Presented, 01/2014.
  • Colloquium, Mathematics Department, University of California at Irvine. Invited Talk/Keynote, Presented, 01/2014.

Grants, Contracts & Research Gifts

  • Computational Workshop on Singularities and Invariants Defined by Frobenius (1160927). PI: Zhang, Wenliang. Co-PI(s): KARL E SCHWEDE. National Science Foundation, 2012 - 02/28/2013. Total project budget to date: $10,000.00
  • Singularities in Characteristic Zero and Singularities in Positive Characteristic (1064485). PI: Schwede, Karl. National Science Foundation, 2010 - 08/31/2013. Total project budget to date: $105,420.00
  • PostDoctoral Research Fellowship (0703505). PI: Schwede, Karl. National Science Foundation, 2007 - 08/31/2011. Total project budget to date: $108,000.00
  • PART SUPP FOR 58502697. PI: SCHWEDE,KARL E. NATIONAL SCIENCE FOUNDATION, 06/01/2019 - 05/31/2024. Total project budget to date: $1,506,970.00
  • ALGEBRA, GEOMETRY, & TOPOLOGY. PI: SCHWEDE,KARL E. NATIONAL SCIENCE FOUNDATION, 06/01/2019 - 05/31/2024. Total project budget to date: $188,735.00
  • SINGULARITIES. PI: SCHWEDE,KARL E. NATIONAL SCIENCE FOUNDATION, 09/01/2018 - 08/31/2021. Total project budget to date: $182,000.00
  • CAREER: TEST IDEALS AND THE... PI: SCHWEDE,KARL E. NATIONAL SCIENCE FOUNDATION, 08/01/2014 - 08/31/2018. Total project budget to date: $328,995.00
  • FRG: COLLABORATIVE RESEARCH. PI: SCHWEDE,KARL E. NATIONAL SCIENCE FOUNDATION, 08/01/2014 - 06/30/2017. Total project budget to date: $94,451.00
  • SCHWEDE SLOAN FELLOWSHIP. PI: SCHWEDE,KARL E. ALFRED P SLOAN FOUNDATION, 07/15/2014 - 10/18/2015. Total project budget to date: $16,198.77

Software Titles

  • FastLinAlg. A Macaulay2 package that . Release Date: 10/21/2019. Inventors: Boyana Martinova, Marcus Robinson, Karl Schwede, Yuhui Yao. Distribution List: https://github.com/Macaulay2/M2/blob/master/M2/Macaulay2/packages/FastLinAlg.m2.
  • FrobeniusThresholds Package. A Macaulay2 package for computing F-(pure)-thresholds and related invariants. Release Date: 10/05/2018. Inventors: Erin Bela, Alberto F. Boix, Juliette Bruce, Drew Ellingson, Daniel Hernandez, Zhibek Kadyrsizova, Moty Katzman, Sara Malec, Matthew Mastroeni, Maral Mostafazadehfard, Marcus Robinson, Karl Schwede, Dan Smolkin, Pedro Teixeira, Emily Witt. Distribution List: https://github.com/Macaulay2/M2/blob/master/M2/Macaulay2/packages/FThresholds.m2.
  • Seminormalization. A Macaulay2 package for seminormalizing rings. Release Date: 03/14/2018. Inventors: Karl Schwede, Bernard Serbinowski. Distribution List: https://github.com/Macaulay2/M2/blob/master/M2/Macaulay2/packages/Seminormalization.m2.
  • TestIdeals. A package for computations of test ideals in positive characteristic rings. Release Date: 07/25/2017. Inventors: Erin Bela, Alberto F. Boix, David J. Bruce, Daniel Hernandez, Zhibek Kadyrsizova, Mordechai Katzman, Sara Malec, Karl Schwede, Pedro Teixeira and Emily Witt. Distribution List: https://github.com/Macaulay2/M2/blob/master/M2/Macaulay2/packages/TestIdeals.m2.
  • RationalMaps. A Macaulay2 package for computing rational maps. Release Date: 08/30/2016. Inventors: C.J. Bott, S. Hamid Hassanzadeh, Karl Schwede, AND Dan Smolkin.
  • Pullback. A Macaulay2 package for computing pullbacks in the category of rings. Release Date: 10/15/2015. Inventors: Drew Ellingson and Karl Schwede.
  • Divisor. A Macaulay2 package for doing computations with divisors in algebraic geometry. Release Date: 07/2014. Inventors: Karl Schwede, Zhaoning Yang. Distribution List: It is part of the Macaulay2 build tree on github.
  • PosChar. A Macaulay2 package for doing computations with F-singularities. Release Date: 06/2014. Inventors: Daniel Hernandez, Moty Katzman, Sara Malec, Karl Schwede, Pedro Teixeira and Emily Witt . Distribution List: The current version was uploaded to my website on June 10th 2014, earlier versions were available before this. http://www.math.utah.edu/~schwede/M2/PosChar.m2 This is not the final version by a long shot.