Kevin Tucker - Curriculum Vitae – October 2022
Contact Information
Department of Mathematics, Statistics, & Computer Science
University of Illinois at Chicago
Science and Engineering Offices, Mail Code 249
851 South Morgan Street, Chicago, Illinois 60607-7045
Email: kftucker@uic.edu
Web: http://kftucker.people.uic.edu

Education
University of Michigan - Doctor of Philosophy, Mathematics, May 2010
Dissertation: Multiplier Ideals and Jumping Numbers on Algebraic Surfaces
Advisor: Professor Karen Smith
University of Chicago - Bachelor of Science, Mathematics, June 2004

Appointments
Professor, 2020 - Present
Associate Head of Instruction, 2018 - 2021
Associate Professor, 2016 - 2020
Assistant Professor, 2013 - 2016
University of Illinois at Chicago
Program Associate, Spring 2013, Spring 2019
Mathematical Sciences Research Institute
Instructor/NSF Postdoctoral Fellow, 2011-2013
Princeton University
NSF Postdoctoral Fellow, 2010-2011
University of Utah
Visiting Scholar:•••

Johannes Gutenberg Universität (Germany), June 2010, 2011, 2012, and 2013
University of Jyväskylä (Finland), April 2010
Katholieke Universiteit Leuven (Belgium), March 2010

Graduate Student Program Associate, Spring 2009
Mathematical Sciences Research InstituteResearch Interests
Singularities and invariants arising in positive and mixed characteristic commutative
algebra (such as test ideals and F-signature) and birational complex algebraic geometry(including multiplier ideals and jumping numbers).

Publications
1. L. Ma, K. Schwede, K. Tucker, J. Waldron, and J. Witaszek: An analog of adjoint ideals and
PLT singularities in mixed characteristic, Journal of Algebraic Geometry, 2022. ~62 pages.
2. J. Carvajal-Rojas, L. Ma, T. Polstra, K. Schwede, K. Tucker: Covers of rational double points
in mixed characteristic, Journal of Singularities, 2021. ~24 pages.
3. R. Datta and K. Tucker: On some permanence properties of (derived) splinters, Michigan
Mathematics Journal, 2020. ~15 pages.
4. J. Carvajal-Rojas, K. Schwede, and K. Tucker: Bertini Theorems for F-signature and HilbertKunz Multiplicity, Mathematische Zeitschrift, 2021. ~22 pages.
5. L. Ma, T. Polstra, K. Schwede, and K. Tucker: F-signature under Birational Morphisms.
Forum of Mathematics, Sigma, 2019. ~15 pages.
6. T. Polstra and K. Tucker: F-signature and Hilbert-Kunz Multiplicity, A Combined Approach.
Algebra and Number Theory, 2018. ~33 pages.
7. J. Carvajal-Rojas, K. Schwede, and K. Tucker: Fundamental Groups of F-regular Singularities
via F-signature. Annales scientifiques de l’Ecole normalé supérieure, 2018. ~22 pages.
8. B. Bhatt, J. Carvajal-Rojas, P. Graf, K. Schwede, and K. Tucker: Étale Fundamental groups ofstrongly F-regular schemes. International Mathematics Research Notices, 2017. ~10 pages.
9. K. Smith and K. Tucker: Appendix to “Contribution of jumping numbers by exceptional
divisors” by H. Baumers and W. Veys, Journal of Algebra, 2018.~5 pages
10. K. Schwede, K. Tucker, and Z. Patakfalvi: Notes for the workshop on positive characteristic
algebraic geometry, arXiv:1412.2203. Proceedings of Symposia in Pure Mathematics
volume for the 2015 AMS Algebraic Geometry Bootcamp, 2017.~40 pages.
11. M. Blickle, K. Schwede, and K. Tucker: F-singularities via alterations, American Journal of
Mathematics 137 (1), 61-109, 2015.
12. T. de Fernex, R. Docampo, S. Takagi and K. Tucker, Comparing multiplier ideals to test
ideals on numerically Q-Gorenstein varieties, Bulletin of the London Mathematical Society
47 (2), 359-369, 2015.

13. K. Schwede and K. Tucker: Explicitly Extending Frobenius Splittings over Finite Maps,
Communications in Algebra 10 (43), 4070-4079, 2015.
14. K. Schwede and K. Tucker: Test ideals of non-principal ideals: Computations, Jumping
Numbers, Alterations and Division Theorems, Journal de Mathématiques Pures etAppliquées (9) 102, no. 5, 891-929, 2014.
15. K. Schwede and K. Tucker: On the behavior of test ideals under finite morphisms, Journal of
Algebraic Geometry 23 (2014), no. 3, 399-443.
16. M. Blickle, K. Schwede, and K. Tucker: F -signature of pairs: Continuity, p-fractals andminimal log discrepancies, Journal of the London Mathematical Society (2) 87 (2013), no. 3,
802-818.
17. K. Tucker: F-signature exists, Inventiones Mathematicae 190 (2012), no. 3, 743-765.
18. M. Blickle, K. Schwede, and K. Tucker: F-signature of pairs and the asymptotic behavior of
Frobenius splittings, Advances in Mathematics 231 (2012), no. 6, 3232-3258.
19. K. Schwede, K. Tucker, and W. Zhang: Test ideals via a single alteration and discretenessand rationality of F -jumping numbers, Mathematical Research Letters 19 (2012), no. 01,
191-197.
20. K. Schwede and K. Tucker: A Survey of Test Ideals, Progress in Commutative Algebra(2011), deGruyter, Berlin, 2012, pp. 39–99.
21. K. Schwede and K. Tucker: On the number of compatibly Frobenius split subvarieties,
prime F -ideals, and log canonical centers, Annales de L’Institut Fourier (Grenoble) (60)2010, no. 5, 1515-1531.
22. K. Tucker: Jumping numbers on algebraic surfaces with rational singularities, Transactionsof the AMS 362 (2010), 3223-3241.
23. K. Tucker: Integrally closed ideals on log terminal surfaces are multiplier ideals,
Mathematical Research Letters (16) 2009, no. 5, 903–908.
Submitted/ preprints
24. B. Bhatt, L. Ma, Z. Patakfalvi, K. Schwede, K. Tucker, J. Waldron, and J. Witaszek: Globally +regular varieties and the minimal model program for threefolds in mixed characteristic.
~120 pages, arXiv:2012.15801, submitted. Under revision at Publications mathématiquesde l'IHÉS.
25. H. Cai, S. Lee, L. Ma, K. Schwede, and K. Tucker: Perfectoid signature, perfectoid HilbertKunz multiplicity, and an application to local fundamental groups. ~75 pages,
arXiv:2209.04046, submitted.
26. R. Datta and K. Tucker: Openness of splinter loci in prime characteristic. ~36 pages, arXiv:
2103.10525, submitted.

27. I. Smirnov and K. Tucker: Towards the theory of F-rational signature. ~20 pages,
arXiv:1911.02642, submitted.
28. J. Page, D. Smolkin, and K. Tucker: Symbolic and Ordinary Powers of Ideals in Hibi Rings.
~15 pages, arXiv:1810.00149.

Honors and awards•

Co-PI (with I. Coskun, D. Marker, J. Ross, L. Ein) National Science Foundation Research Training
Grant (RTG) in Algebraic Geometry and Arithmetic Geometry, $2,500,000, 2021-2026•

PI National Science Foundation Grant DMS 2200716, Singularities in Positive and Mixed
Characteristic Commutative Algebra, $200,000, 2022-2025•

PI National Science Foundation Grant DMS 1602070, Computing and Interpreting
Frobenius Invariants, $205,000, 2016 – 2021•

PI (with J. Park and W. Ho) National Science Foundation Conference Grant DMS 2006070,
Collaborative Research: Midwest Arithmetic Geometry and Number Theory Series,$20,000, 2020 – 2023•

Co-PI (with J. Ross) National Science Foundation Grant DMS 1707661, Computing andInterpreting Frobenius Invariants, $205,000, 2016 – 2020•

Alfred P. Sloan Foundation Fellowship, $55,000, 2016-2020•

Co-PI (with L. Ein, I. Coskun, R. Takloo-Bighash, D. Marker) National Science Foundation
Research Training Grant (RTG) in Algebraic Geometry and Arithmetic Geometry,$2,500,000, 2013-2018•

PI National Science Foundation Grant DMS 1419448, Frobenius singularities and related
invariants, $144,000, 2013 - 2016•

Co-PI (with W. Zhang and K. Schwede) National Science Foundation Conference Grant
1160927, Computational Workshop on Singularities and Invariants Defined by Frobenius,$10,000, 2012•

PI National Science Foundation Post Doctoral Research Fellowship Grant DMS 1004344,$135,000, 2010 - 2013•2010 University of Michigan Distinguished Dissertation Award- This award is presented annually to around ten graduating doctoral students at the
University of Michigan, and aims to recognize exceptional and unusually interesting
work produced by doctoral students in the last phase of their graduate work.

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2010 Sumner B. Myers Prize- This award is presented by the Mathematics Department at the University ofMichigan to recognize the best dissertation in a given year.

•2010 Wirt & Mary Cornwell Award- This award is presented by the Mathematics Department at the University ofMichigan to a student who, during the four previous years, has demon- strated thegreatest intellectual curiousity and has given the most promise of original study andcreative work in mathematics. The award is available to both undergraduate andgraduate students.

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2004 Paul R. Cohen Memorial Prize- This award is presented by the Mathematics Department at the University of
Chicago to the graduating seniors in the field of Mathematics who have achieved thehighest record in mathematics.
2003 - 2004 Student Marshal, University of Chicago- Student Marshals are third-year students who have excelled academically anddemonstrated outstanding commitment to significant extra-curricular activities on
campus and in the community.

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Academic Honor Societies, University of Chicago- Inducted into membership in Sigma Xi in 2004.
- Inducted into membership in Phi Beta Kappa in 2003.

Teaching
Instructor
University of Illinois at Chicago•

Math 330, Undergraduate Algebra I, Fall 2022
- Proofs based course aimed at undergraduate mathematics majors, ~ 15 students•

Math 516, Graduate Algebra I, Fall 2022
- Graduate course for first year students, ~ 15 students•

Math 552, Algebraic Geometry I, Fall 2020
- Graduate course for second year students, ~ 16 students•

Math 320, Linear Algebra, Fall 2019
- Proofs based course aimed at undergraduate mathematics majors, ~ 32 students•

Math 552, Algebraic Geometry I, Fall 2018
- Graduate course for second year students, ~ 15 students•

Math 553, Algebraic Geometry II, Spring 2018
- Graduate course for second year students, ~ 15 students•

Math 517, Graduate Algebra II, Spring 2018
- Graduate course for first year students, ~ 12 students•

Math 571, Topics in Algebraic Geometry, Spring 2017

- Topics course on positive characteristics methods in algebraic geometry andcommutative algebra, ~15 students•

Math 516, Graduate Algebra, Fall 2016
- Graduate course for first year students, ~ 14 students•

Math 517, Graduate Algebra II, Spring 2016
- Graduate course for first year students, ~ 12 students•

Math 516, Graduate Algebra I, Fall 2015
- Graduate course for first year students, ~ 12 students•

Math 520, Commutative and Homological Algebra, Fall 2014
- Graduate course aimed at second year students, ~12 students•

Math 310, Applied Linear Algebra, Fall 2014
- Advanced lecture course for non-mathematics undergraduates, ~80 students•

Math 215, Introduction to Advanced Mathematics, Spring 2014
- A first proofs course aimed at undergraduate mathematics and computer science
majors, ∼ 20 students•

Math 552, Algebraic Geometry I, Fall 2013
- Graduate course aimed at second year students, ∼ 15 students

Princeton University•

Math 447, Commutative Algebra, Fall 2012
- Advanced undergraduate course for senior math majors, ∼ 20 students•

Math 189, Number, Shape, & Symmetry, Spring 2012
- Designed to give non-science majors a way to fulfill their general education
quantitative reasoning course requirement without calculus, this course covered
an introduction to elementary number theory and group theory, ∼ 15 students•

Math 201, Calculus III, Fall 2011
- Multivariable calculus course for freshman and sophomores, ∼ 35 students

University of Michigan••

Math 115, Calculus I, Fall 2005
Math 116, Calculus II, Winter 2006, Fall 2006
- First and second semester calculus courses, respectively, largely for freshman,∼30 students each semester

Course grader and assistant
University of Michigan•

Math 631, Algebraic Geometry I, Fall 2006, 2007, & 2009

••Math 632, Algebraic Geometry II, Winter 2008
Math 513, Graduate Linear Algebra, Fall 2004

University of Chicago•

Math 161-163, Honors Calculus I - III, 2003-2004

Mentoring
Postdoctoral Fellows•

Postdoctoral mentor at UIC: Rankeya Datta (2018-2021, currently TT at the University ofMissouri), Christopher Skalit (2015-2018)

Graduate Students•

Ph.D. Thesis advisor for Graduate Students at UIC: Janet Page (August 2018, currently TT at
the University of North Dakota), Samuel Shideler (August 2018, currently working as a
Data Scientist at NORAD), Austyn Simpson (Graduated 2022, currently an NSF postdoc at
the University of Michigan), Greg Taylor (current, expected 2023), Shravan Patankar(current, expected 2023)•

MS advisor for Graduate Students at UIC: Wesley Townsend (May 2018)•

Weekly meetings with Graduate Students at UIC: Zhehao Li (January 2021 – August 2021),
Samuel Shideler (Fall 2013 – August 2018), Christopher Perez (Fall 2013 – Spring 2014),
Janet Page (Spring 2014 – August 2018), Xudong Zheng (Spring 2014 – Spring 2015)•

Official Reading Courses with Graduate Students at UIC:- UIC Reading Course with Nathan Bliss and Jeff Sommars on Toric Varieties, Spring
2014- UIC Reading course with Amit Shah on Local Cohomology, Spring 2014
- UIC Reading course with Shuhang Yang on Algebraic Geometry, Spring 2013
- UIC Reading course with Xudong Zheng (doctoral student of Lawrence Ein) on
Positive Characteristic Methods in Algebraic Geometry, Fall 2013•

RTG Reading Seminars at UIC:
- RTG Reading Seminar on Toric Varieties, Fall 2022
- Co-organized (with Izzet Coskun and Lawrence Ein) an RTG Reading Seminar on
Important Examples in Algebraic Geometry, Spring 2016
- Co-organized (with Izzet Coskun) an RTG Reading Seminar on Algebraic Surfaces for~10 graduate students in Spring 2015
- Co-organized (with Izzet Coskun) an RTG Reading Seminar on Representation
Theory for ~10 graduate students in Fall 2014•

Teaching apprenticeship organizer for the graduate students at Princeton University in Fall
2012, supervising and mentoring ∼ 10 graduate students in giving guest lectures in various
undergraduate classes

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University of Utah Reading Course on Differential Geometry with Brian Mann and Sonya
Leibman (students of Mladen Bestvina), Spring 2011

Undergraduate Students•

UIC Honors College Faculty Fellow 2017-present•

Undergraduate research supervisor at UIC:- Mathematics Undergraduate Research Laboratory semester long project andreading course titled “Exploring Lattice Polytopes through Problems Inspired by
Combinatorial Commutative Algebra” with Leila Dahlia, Kim de Souza, and John Gut- LASURI Faculty Mentor and Honors Capstone Project Advisor for Michael Perlmann
2014-2015 on computations of limit F-signature functions•

Official Reading Courses with Undergraduate Students at UIC:- UIC Reading course with Michael Perlmann on Commutative Algebra, Fall 2014•

Senior thesis advisor for Samuel Shideler at Princeton University in 2013•

Junior paper advisor for Sarah Trebat-Leider at Princeton University in Spring 2012

ServiceCommittees
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UIC Mathematics Department Erdos Institute Facilitator, 2021-present
UIC Mathematics Department Postdoc Hiring Committee, 2022-2023
UIC Mathematics Department Graduate Admissions Committee, 2022-2023
UIC Mathematics Department Teaching Load Task Force 2022-2023
UIC University Steering Committee for the Center for the Integration of Teaching, Research,and Learning (CIRTL) 2020-present
UIC Mathematics Department Director of Academic Resources and Programs SearchCommittee Chair, 2020
UIC Mathematics Department Director of Advising, Outreach, and Math Placement Search,
Chair, 2020
UIC Mathematics Department Lecturer Search Committee Chair, 2018-2020
UIC Mathematics Department Clinical Assistant Professor Search Committee Chair, 2020
UIC University GEO Side Letter Taskforce on Appointment and Reappointment Guidelines,
2019-2020
UIC Mathematics Department Tenure Track Hiring Committee 2019-2020
UIC Senate Admissions, Recruitment, Retention Committee Chair, 2020
UIC Mathematics Department Student Grievance Committee, 2018-2021
UIC Mathematics Department Faculty Teaching Award Committee, 2018-2021
Interviewed candidates for the Executive Director of the Center for Teaching Excellence,
Spring 2019, Spring 2020
UIC Mathematics and Science Learning Center (MSLC) Advisory Committee, 2018-2019

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Interviewed candidates for the Director of the Mathematics and Science Learning Center(MSLC), Summer 2018
UIC Mathematics Department Undergraduate Studies Committee, 2018-2019
UIC Mathematics Department Calculus Committee, 2018-2019
UIC Mathematics Department Precalculus Committee, 2018-2019
UIC Mathematics Department Advisory Committee, Spring 2018 - 2021
UIC Senate Admissions, Recruitment, Retention Committee 2017-2020
UIC Mathematics Department Research Training Grant Coordinator 2016-2017, Spring
2018, Fall 2018
UIC Senate Student Recruitment Committee 2015-2017
UIC Mathematics Department Admissions, Fellowships, Assistantships Committee 20152016
UIC Mathematics Department Tenure-Track Hiring Committee 2014-2015
UIC Mathematics Department Graduate Studies Committee 2013 – 2015, 2017-2018, 20182019
UIC Mathematics Department Research Assistant Professor Hiring Committee 2013-2014

Referree & Editor
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Editor of the Proceedings of the conference “Local and global methods in algebraic
geometry” in honor of Lawrence Ein’s 60th birthday, Chicago, now in publication (with N.
Budur, R. Docampo, and T. de Fernex)
UIC Chancellor’s Award Fellowship Application Reviewer (2016)
Grant Reviewer for the National Science Foundation (2014, 2018, 2021)
Grant Reviewer for the National Security Agency (2012, 2013, 2014, 2015)
Referee for numerous articles for journals including Advances in Mathematics, Annals of
Mathematics, Inventiones, Transactions, Compositio, Proceedings of the AMS, Journal ofCommutative Algebra, Algebra & Number Theory, and Communications in Algebra

Conference Organizer
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Upcoming:o Co-organizer (with C. Polini, D. Cutkosky, S. Sam, C. Raicu, A. Conca, C. Voisin) MSRI program
semester in Spring 2024 on Commutative Algebrao Co-organizer (with C. Polini, D. Cutkosky, S. Sam, C. Raicu) MSRI Graduate Summer Schoolon “Commutative Algebra and its interaction with Algebraic Geometry” to be held at the
University of Notre Dame in June 2023
o “Undergraduate Mathematics Symposium” at UIC, November 2022 (Funded by NSF RTG
Grant DMS #1246844 and #1602070, with D. Dumas and J. Ross)
Midwest Algebraic Geometry and Number Theory Series at UIC, Fall 2022 (Funded by NSF Grant
DMS #2006070, with W. Ho, J. Park, R. Holowinsky)“Undergraduate Mathematics Symposium” at UIC (online), November, 2021 (Funded by NSF RTG
Grant DMS #1246844 and #1602070, with D. Dumas, J. Ross, and C. Sparber)“Undergraduate Mathematics Symposium” at UIC (online), November, 2020 (Funded by NSF RTG
Grant DMS #1246844 and #1602070, with D. Dumas, J. Ross, and C. Sparber)
Midwest Algebraic Geometry and Number Theory Series, Fall 2019 and 2020 (Funded by NSF Grant
DMS #2006070, with W. Ho, J. Park, R. Holowinsky)“Undergraduate Mathematics Symposium” at UIC, November, 2019 (Funded by NSF RTG
Grant DMS #1246844 and #1602070, with D. Dumas, J. Ross, and C. Sparber)
Midwest Algebraic Geometry Graduate Conference at UIC Faculty Sponsor, May 2018
(Funded by NSF RTG Grant DMS #1246844, with I. Coskun)

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“Algebraic Geometry and its Broader Implications: A Conference in honor of Hartshorne’s
80th and the book’s 40th” at UIC, March 2018 (Funded by NSF RTG Grant DMS #1246844,
with L. Ein, C. Polini, and B. Ulrich)“Undergraduate Mathematics Symposium” at UIC, November, 2018 (Funded by NSF RTG
Grant DMS #1246844 and #1602070, with D. Dumas and J. Ross)“Undergraduate Mathematics Symposium” at UIC, November, 2017 (Funded by NSF RTG
Grant DMS #1246844 and #1602070, with D. Dumas)
Midwest Algebraic Geometry Graduate Conference at UIC Faculty Sponsor, April 2017
(Funded by NSF RTG Grant DMS #1246844, with I. Coskun)
RTG Graduate Student Workshop on the Homological Conjectures at UIC, November 18-20,
2016 (Funded by NSF RTG Grant DMS #1246844, with C. Skalit)
RTG Undergraduate REU on Topics in Commutative Algebra, May 23-June 3, 2016 (Fundedby NSF RTG Grant DMS #1246844, with L. Ein)
“Undergraduate Mathematics Symposium” at UIC, October 15, 2016 (Funded by NSF RTG
Grant DMS #1246844 and #1602070, with D. Dumas)“Undergraduate Mathematics Symposium” at UIC, October 24, 2015 (Funded by NSF RTG
Grant DMS #0952869, with D. Dumas, S. Hurder, A. Austin)
RTG Graduate Student Workshop on Syzygies of Algebraic Varieties at UIC, November 21 –November 22, 2015 (Funded by NSF RTG Grant DMS #1246844, with L. Ein)
RTG Graduate Student Workshop on Higher Codimension Cycles in Algebraic Geometry at
UIC, November 21 – November 22, 2015 (Funded by NSF RTG Grant DMS #1246844, with
I. Coskun, J. Lesieutre)“Local and Global Methods in Algebraic Geometry: A Conference in Honor of Lawrence Ein’s
60th Birthday” at UIC, May 12 – 15, 2016 (Funded by NSF RTG Grant DMS #1246844, with T
de Fernex, N. Budur, R. DoCampo)
AMS Special Session on ``The Geometry of Algebraic Varieties'' at the AMS Central Section
Meeting at Michigan State University in March 2015 (with B. Lehmann)
Graduate Student Workshop on Local Cohomology at UIC, February 27 – March 1, 2015
(Funded by NSF RTG Grant DMS #1246844, with W. Zhang, C. Raicu, U. Walther)“Undergraduate Mathematics Symposium” at UIC, October 18, 2014 (Funded by NSF RTG
Grant DMS #0952869, with D. Dumas, S. Hurder, A. Austin)
Graduate Student Workshop on Positive Characteristic Algebraic Geometry at UIC, March
19-21, 2014 (Funded by NSF RTG Grant DMS #1246844, with K. Schwede, Z. Patakfalvi)
Tight closure and Singularities focus period at the Mathematical Sciences ResearchInstitute (MSRI), April 29, 2013 to May 24, 2013 (with S. Takagi, H. Brenner)
Conference on ``Computational workshop on Frobenius singularities and invariants'' at the
University of Michigan, Ann Arbor, MI, May 2012. (Co-PI NSF Grant DMS #1160927, with
W. Zhang, K. Schwede)
American Institute of Mathematics workshop ``Relating Test Ideals and Multiplier Ideals''in Palo Alto, CA, August 2011 (with K. Schwede)
AMS Special Session on ``Birational Geometry and Moduli Spaces'' at the Joint Mathematics
Meetings, New Orleans, LA, scheduled January 2011 (with D. Chen, A. Knecht, D. Swinarski)

Seminar Organizer••••

Algebraic Geometry Seminar, UIC, 2013 – Present
Commutative Algebra Seminar, UIC, 2015 – Present
Algebraic Geometry Seminar, Princeton University, 2011-2012.
University of Michigan Student Algebraic Geometry Seminar during the Fall 2007, Winter2008, and Fall 2009 semesters.

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Graduate Student Seminar at the Spring 2009 program in Algebraic Geometry at the
Mathematical Sciences Research Institute (MSRI, with D. Erman)

Outreach Activities••••

Volunteered to lead a problem session in a continuing education program for mathematics
educators at the University of Utah, Spring 2011
Graduate assistant for the MMSS (Michigan Math and Science Scholars) program for highschool students in the summer of 2006.
Counselor in the YSP (Young Scholars Program) at the University of Chicago in the summerof both 2002 and 2004, working with children from grades 7 through 12.
Course assistant in the SESAME (Seminars for Endorsement of Science and Mathematics
Educators) program at the University of Chicago in the summer of both 2003 and 2004, a
continuing education and recertification program for middle school mathematics teachers.

Presentations
Invited Conference Speaker
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Plenary speaker at the conference Spec Qbar at the Fields Institute, Toronto, Canada, July
2020 – “Recent Advances on Variants of the F-signature”
FRG Algebraic Geometry and Singularities Learning Workshop and Conference at the
University of Washington, Seattle, Washington, June 2022 – four lecture minicourse titled “Recent
developments in singularity theory in mixed and positive characteristic algebraic geometry”

ICTP Graduate Course on Tight Closure of Ideals and its Applications (in honor of Hochster& Huneke), May 2022 – online three lecture minicourse titled “Three lectures on test ideals”
BIRS-CMO Conference on Advances in Mixed Characteristic Commutative Algebra andGeometric Connections, Oaxaca, Mexico – “Global +-Regularity”
AMS Special Session on Commutative Algebra at AMS Central Section Meeting at Purdue
University, Online, March 2022 – “Dual F-signature Exists”
CIRM conference on Singularities in Positive Characteristic, CIRM - Online, Luminy, France,
July 2021 – “Openness of splinter loci in positive characteristic”
AMS Special Session on Positive Characteristic Commutative Algebra at the Joint
Mathematics Meetings, Online, January 2021 – “On some permanence properties of (derived)
splinters”

AMS Special Session on Recent Advances in Homological and Commutative Algebra at the
Joint Mathematics Meetings, Baltimore, MD, January 2019 – “The Behavior of F-signature under
Small Birational Morphisms”•••

Commutative Algebra Conference in honor of Bernd Ulrich’s 60th, June 2019 – “pg Vector
Bundles on Normal Surfaces”

Seventh Iberoamerican Congress on Geometry, Special Session on Algebraic Surfaces,
January 2018 – “pg Vector Bundles on Normal Surfaces”
Special Session on ``Commutative Algebra'' at University of North Texas, September 2017 –“F-signature of a Cartier Module”••

Oberwolfach conference on Algebraic Geometry: Birational Classification, Derived
Categories, and Moduli Spaces, Oberwolfach, Germany, September 2017
The Prospects for Commutative Algebra, Hotel Nikko Osaka, Osaka, Japan, July 2017 – “Fsignature of a Cartier Module”

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Oberwolfach conference on Asymptotic Phenomena in Local Algebra and Singularity
Theory, Oberwolfach, Germany, December 2016 – “Fundamental Groups of F-regular Singularities
via F-Signature”

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Differential forms in algebraic geometry, University of Frieburg, Frieburg, Germany,
September 2016 – “Fundamental Groups of F-regular Singularities via F-Signature”
CIRM conference on Higher dimensional algebraic geometry and characteristic p > 0” CIRM,
Luminy, France, September 2016 – “Fundamental Groups of F-regular Singularities via F-Signature”
Commutative Algebra and Its Interactions with Algebraic Geometry (in honor of Craig
Huneke’s 65th Birthday), University of Michigan, July 2016 – “Fundamental Groups of F-regular
Singularities via F-Signature”

Higher dimensional algebraic geometry, University of Utah, July 2016 – “Fundamental Groups of
F-regular Singularities via F-Signature”

Minischool on Invariants of Singularities in zero and positive characteristic, Stonybrook
University, December 2015 - “Frobenius invariants of singularities”
Upper Midwest Commutative Algebra Conference, University of Wisconsin, November
2015 – “Limits of Frobenius Invairants”
Special Session on Commutative Algebra at the AMS Central Section Meeting, Loyola
University, October 2015 – “On the limit as p goes to infinity of the Hilbert-Kunz Multiplicity”
Lecture Series speaker at the Multiplier Ideals, Test Ideals, and Bernstein Sato Polynomials
Conference, Facultat de Matemàtiques i Estadistica Universitat Politècnica de Catalunya,
Barcelona, Spain, September 2015 – “An Introduction to Multiplier Ideals” (three 90 minute lectures)
Midwest commutative algebra conference, Purdue University, August 2015 – “On the limit as p
goes to infinity of the Hilbert-Kunz Multiplicity”

Graduate student boot camp mentor and speaker for the AMS Summer Research Institutein Algebraic Geometry, University of Utah, July 2015 – “Recent Methods in Positive Characteristic
Algebraic Geometry”

Conference on Rings of Frobenius Operators and Cartier Algebras, Georgia State University,
March 2015 – “An Introduction to Cartier Algebras”
KUMUNU Commutative Algebra Conference, University of Missouri, September 2014 –“Limit F-signature Functions of Diagonal Hypersurfaces”

Meeting On Combinatorial Commutative Algebra (MOCCA 2014), Levico Terme, Italy,
September 2014 – “Limit F-signature Functions of Diagonal Hypersurfaces”
Special Session on ``Toric Varieties'' at University of Wisconsin Eau Claire, September 2014
– “The F-splitting Ratio of a Monoid Algebra”
RIMS Workshop on Commutative Algebra, December 2013 – “The rationality of the F-pureThreshold in a Power Series Ring”

Centre International de Rencontres Mathématiques (CIRM) conference on ``Commutative
algebra and its interactions with algebraic geometry,'' Luminy, France, July 2013 – “Positivityof the F-splitting Ratio”

Special Sessions on Algebraic Geometry and Commutative Algebra at the Joint Meeting of
the AMS and RMS, Alba Iulia, Romania, June 2103 – “F-splitting Ratio of Monoid Algebras” and “A
Uniform Description of Test Ideals and Multiplier Ideals”

Thematic program on Motivic Invariants and Singularities, Notre Dame University, May
2013 – “A Uniform Description of Test and Multiplier Ideals”
Mathematical Sciences Research Institute (MSRI) conference on ``The Commutative
Algebra of Singularities in Birational Geometry: Multiplier Ideals, Jets, Valuations, andPositive Characteristic Methods,'' May 2013 – “F-Signature and Relative Hilbert-Kunz Multiplicity”
Conference on ``Trends in Arithmetic Geometry'' at the Lorentz Center, Leiden, theNetherlands, January 2013 – “An Introduction to F-singularities” (three lectures)
Joint University of British Columbia (Vancouver) and University of Washington (Seattle)
Algebraic Geometry Conference, November 2012 – “A Uniform Description of Test and Multiplier
Ideals”

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Conference on ``Characteristic p and p-adic Geometry'' at Johannes Gutenberg Universität,
Mainz, Germany, June 2012 – “A Uniform Description of Test and Multiplier Ideals”
Special Session on ``Singularities in Commutative Algebra and Algebraic Geometry'' at the
AMS Central Section Meeting, Lawrence, KA, April 2012 – “On the Number of Compatibly F-split
Subvarieties and Log Canonical Centers”

Special Session on Commutative algebra at the AMS Western Section Meeting, Salt Lake
City, UT, October 2011 – “On the Number of Compatibly F-split Subvarieties and Log Canonical Centers”
Western Algebraic Geometry Seminar (WAGS), Colorado State University, October 2011 –“On the the behavior of multiplier ideals and test ideals under finite morphisms in positive characteristic”

Midwest Commutative Algebra and Geometry Conference, Purdue University, May 2011 –“On the the behavior of multiplier ideals and test ideals under finite morphisms in positive characteristic”
Show-Me Algebraic Geometry Meeting, University of Missouri, May 2011 – “On the the behaviorof multiplier ideals and test ideals under finite morphisms in positive characteristic”

Special Session on ``Commutative Algebra and its Interactions with Algebraic Geometry'' at
the AMS Central Section Meeting, South Bend, IN, November 2010 – “F-signature Exists”
Special Session on ``Singularity Theory and Algebraic Geometry'' at the joint meeting of the
AMS and the Sociedad Matematica Mexicana, Berkeley, CA, June 2010 – “F-signature Exists”
Frobenius splitting in algebraic geometry, commutative algebra, and representation theory,
University of Michigan, May 2010 – “On the behavior of multiplier ideals and test ideals under finite
morphisms in positive characteristic”

AMS Special Session on Commutative Algebra at the Joint Mathematics
Meetings, San Francisco, CA, January 2010 – “Jumping Numbers and Multiplier Ideals on Algebraic
Surfaces”

Invited Seminar Speaker
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University of Missouri Department Colloquium, Columbia, Missiouri, October 2022 –“Perfectoid signature”

University of Missouri Commutative Algebra Seminar, Columbia, Missouri, October 2022 “The theory of F-rational signature”

Johannes Gutenberg University Algebraic Geometry Seminar, Mainz, Germany, July 2022 four lecture minicourse titled “Recent developments in singularity theory in mixed and positive characteristic
algebraic geometry
University of Utah Commutative Algebra Seminar – “The theory of F-rational signature”
Princeton Algebraic Geometry Seminar, March 2022 – “The theory of F-rational signature”
University of Notre Dame Algebraic Geometry Seminar, October 2021 – “Splinter rings andglobal +-regularity”
Northwestern Algebraic Geometry Seminar, October 2021 – “Splinter rings and global +regularity”
MSRI Fellowship of the Ring, April 2021 – “Global + Regularity”
CAZoom Online Seminar, May 2020 – “An Analogue of adjoint ideals and PLT singularities in mixed
characteristic”
University of Notre Dame Mathematics Colloquium, October 2018 – “Symbolic and Ordinary
Powers of Ideals in Hibi Rings”
University of Edinburgh Algebra Seminar, United Kingdom, September 2017 – “Bertini
Theorems for F-signature”

Beijing International Center of Mathematical Research, Peking University, Beijing, China,
September 2017 – “Bertini Theorems for F-signature”
Purdue University Commutative Algebra Seminar, February 2016 – “Fundamental Groups of Fregular Singularities via F-Signature”

Texas A&M Geometry and Topology Seminar, January 2016 – “Fundamental Groups of F-regular
Singularities via F-Signature”

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École polytechnique fédérale de Lausanne (EPFL) Algebraic Geometry Seminar, Lausanne,
Switzerland, December 2016 – “Fundamental Groups of F-regular Singularities via F-Signature”
University of Michigan Commutative Algebra Seminar, October 2016 – “Transformation rules
for F-signature under finite morphisms”

University of Illinois Algebraic Geometry Seminar, April 2016 – “Test Ideals in F-regular rings”
Princeton Algebraic Geometry Seminar, March 2016 – “Test Ideals in F-regular rings”
University of Arkansas Mathematics Colloquium, October 2015 – “Limits of Frobenius Invariants”
University of Arkansas Algebra Seminar, October 2015 – “The F-splitting Ratio of a Monoid
Algebra”

University of Minnesota Mathematics Colloquium, October 2015 – “Limits of Frobenius
Invariants”

University of Minnesota Commutative Algebra Seminar, October 2015 – “The Rationality of theF-pure Threshold in Power Series Rings”

Georgia State University Colloquium, August 2015 – “Limit F-signature Functions of DiagonalHypersurfaces”

Utah Commutative Algebra Seminar, April 2015 – “Limit F-signature Functions of DiagonalHypersurfaces”

Queens University Algebraic Geometry Seminar, March 2015 – “Limit F-signature Functions of
Diagonal Hypersurfaces”

Notre Dame Commutative Algebra Seminar, January 2015 – “On the Limit of the F-signature
Function in Characteristic Zero”

Texas A&M Algebra and Combinatorics Seminar, January 2015 – “Limit F-signature Functions of
Diagonal Hypersurfaces”

Yale Algebraic Geometry Seminar, December 2014 – “Comparing multiplier ideals to test ideals on
numerically QQ-Gorenstein varieties”

Princeton Algebraic Geometry Seminar, March 2014 – “Comparing multiplier ideals to test ideals on
numerically QQ-Gorenstein varieties”

Purdue Algebraic Geometry and Commutative Algebra Seminars, March 2014 – “Comparing
multiplier ideals to test ideals on numerically QQ-Gorenstein varieties” and “On the Limit of the F-signature
Function in Characteristic Zero”
Wisconsin Algebraic Geometry Seminar, March 2014 – “Comparing multiplier ideals to test ideals
on numerically QQ-Gorenstein varieties”
Michigan Algebraic Geometry Seminar, October 2013 – “F-Signature of a Cartier Module”
Johns Hopkins Algebraic Geometry Seminar, October 2013 – “Rationality of the F-Pure Thresholdin Power Series Rings”
Algebraic Geometry Seminar, UCLA, May 2013 – “An Introduction to F-signature”
Algebraic Geometry Seminar, University of Illinois at Chicago, April 2012 – “A uniform
description of test and multiplier ideals”
Algebraic Geometry Seminar, Stony Brook University, October 2011 – “A uniform description oftest and multiplier ideals”
Commutative Algebra Seminar, University of Utah, September 2011 – “F-signature Exists”

Commutative Algebra Seminar, University of Osnabrück, Osnabrück, Germany, June 2011 –“F-signature Exists”

Algebraic Geometry Seminar, University of British Columbia, April 2011 – “On the behavior of
multiplier ideals and test ideals under finite morphisms in positive characteristic”

Algebraic Geometry Seminar, University of Washington, April 2011 – “On the behavior of
multiplier ideals and test ideals under finite morphisms in positive characteristic”

Commutative Algebra Seminar, University of Kansas, March 2011 – “F-signature Exists”
Commutative Algebra and Algebraic Geometry Seminars, University of Michigan, March
2011, September 2012 – “On the behavior of multiplier ideals and test ideals under finite morphisms inpositive characteristic” and “F-signature Exists”

Algebraic Geometry Seminar, Harvard University, October 2010 – “On the behavior of multiplierideals and test ideals under finite morphisms in positive characteristic”

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Algebraic Geometry Seminar, University of Illinois, January 2010 – “On the Number ofCompatibly F-split Subvarieties and Log Canonical Centers” and “Jumping Numbers and Multiplier Ideals on
Algebraic Surfaces”
Algebraic Geometry Seminar, Rice University, March 2008 and August 2012 – “Jumping
Numbers of Plane Curves” and “A uniform description of test and multiplier ideals”
Student Algebraic Geometry Seminar, Stanford University, March 2008 – “Jumping Number ofPlane Curves”

Other Conference & Workshop
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Oberwolfach conference on Algebraic Geometry: Singularities and Homological Aspects ofCommutative Algebra, Oberwolfach, Germany, February 2019
American Institute of Mathematics (AIM) Squares Participant, June 2017
American Institute of Mathematics (AIM) conference on ``The minimal model program incharacteristic p,'' May 2013
Participant in the AMS Mathematical Research Communities 2010 on Birational Geometry
and Moduli Spaces, Salt Lake City, Utah.
Poster contributor at the Pan-American Advanced Study Institute (PASI) 2009 conferencein Commutative Algebra and its Connections to Geometry, Olinda, Brazil.
Participant in the 2008 Park City Mathematics Institute (PCMI) / Institute for Advanced
Study (IAS) program titled ``Analytic and Algebraic Geometry: Common Problems –Different Methods.''
Attended the 2008 Summer School and Conference on the ``Aspects of Moduli'' at the De
Giorgi Center of the Scuola Normale Superiore in Pisa, Italy.
Attended the 2007 Summer School ``Geometry of Complex Projective Varieties and the
Minimal Model Program'' at the Fourier Institute, Grenoble, France.
Participant in the University of Chicago Research Experiences for Undergraduates (REU) in
the summer of both 2002 and 2003.