Daniel Erman Curriculum Vitae

Department of Mathematics Phone: (608) 263–3055 Van Vleck Hall [email protected] University of Wisconsin http://www.math.wisc.edu/~derman/ Madison, WI 53706-1325 Employment 2018– University of Wisconsin, Associate Professor. 2013–18 University of Wisconsin, Assistant Professor. 2011–13 University of Michigan, Simons Postdoctoral Fellow. 2010–11 Stanford University, NSF Postdoctoral Fellow. 2003–05 Education Development Center, Mathematics Textbook Author.

Education 2005–10 University of California, Berkeley, Ph.D. Mathematics. Advisor: David Eisenbud. 1999–2003 Brown University, B.A. Mathematics.

Grants 2020 NSF conference grant DMS-2000390, CA+: a Midwestern conference in commutative algebra, $30,000 (co-PI). 2019–22 NSF grant DMS-1902123, New structures in homological commutative algebra, $253,500. 2018 NSF conference grant DMS-1812462, Macaulay2 at Wisconsin, $15,000. 2016–19 NSF grant DMS-1601619, Asymptotic Commutative Algebra and Multigraded Syzygies, $205,000. 2017 NSF conference grant, DMS-1702114, A view towards algebraic geometry, $40,000 (co-PI). 2015–21 NSF grant DMS-1502553, RTG: Algebraic Geometry, Applied Algebra, and Number Theory at the University of Wisconsin, $2,000,000 (co-PI). 2015-16 NSF conference grant, DMS-1549554, Upper Midwest Commutative Algebra Colloquium, $7,100. 2015 NSF conference grant DMS-1501249, Theory and application of syzygies, $19,500. 2013–16 NSF grant DMS-1302057, The structure of free resolutions in commutative algebra and algebraic geometry, $132,562. 2011–14 Simons Postdoctoral Fellowship. 2010–11 NSF Postdoctoral Fellowship. 2007–10 NDSEG Fellowship from the Oﬃce of Naval Research.

Awards 2021 H.I. Romnes Faculty Fellowship University of Wisconsin. Campus wide research award. I was the ﬁrst awardee from math in over a decade. 2016 William H. Kiekhofer Award, University of Wisconsin. The oldest campus wide teaching award at Wisconsin, awarded to one professor. 2013-20 Honored Instructor Award, University of Wisconsin at Madison. Daniel Erman 2

Based on student nominations. I have received at least one award per year since 2013. 2010 Ken Ribet/Lisa Goldberg Award in Algebra. UC Berkeley thesis prize for top PhD student in algebra or number theory.

Research Interests Commutative algebra, algebraic geometry, computational algebra.

Publications 1. Small projective spaces and Stillman Uniformity for sheaves, (with Steven V Sam and Andrew Snowden). Algebraic Geometry (to appear). 15 pages. arXiv:1906.10870. 2. Interpolation over Z and torsion in class groups, (with John D. Berman). Journal of Commuta- tive Algebra (to appear). 6 pages. arXiv:1905.12097. 3. The SchurVeronese Package in Macaulay2, (with Juliette Bruce, Steve Goldstein, and Jay Yang). Journal of Software for Algebra and Geometry (to appear). 6 pages. arXiv:1905.12661. 4. Big polynomial rings with imperfect coefficient fields, (with Steven V Sam and Andrew Snowden). Michigan Math Journal (to appear). 20 pages. arXiv:1806.04208v1. 5. Strength and Hartshorne’s Conjecture in high degree, (with Steven V Sam and Andrew Snow- den). Mathematisches Zeitschrift (2020). 16 pages. 6. An equivariant Hilbert Basis Theorem (with Steven V Sam and Andrew Snowden), Mathematical Research Letters (to appear). 7 pages. arXiv: 1712.07532. 7. Generalizations of Stillman’s Conjecture via Twisted Commutative Algebra, (with Steven V Sam and Andrew Snowden). IMRN (2019). 16 pages. 8. Virtual resolutions for a product of projective spaces (with Christine Berkesch and Gregory G. Smith), Algebraic Geometry (to appear) arXiv: 1703.07631. 22 pages. 9. Big Polynomial Rings and Stillman’s Conjecture, (with Steven V Sam and Andrew Snowden). arXiv:1801.09852v4. Inventiones, 218, 413–439 (2019). 10. A probabilistic approach to systems of parameters and Noether normalization (with Juliette Bruce), Algebra Number Theory 13, 2081–2102, (2019). 11. Cubics in 10 variables vs. cubics in 1000 variables: Uniformity phenomena for bounded degree polynomials, (with Steven V Sam and Andrew Snowden), Bulletin of the AMS, 56, pp. 87- 114,(2019). 12. Random flag complexes and asymptotic syzygies (with Jay Yang), Algebra Number Theory 12, pp. 2151-2166 (2018). 13. Conjectures and computations about Veronese syzygies (with Juliette Bruce, Steve Goldstein, and Jay Yang), Experimental Mathematics (2018). 14. Divergent Series and Serre’s intersection formula for graded rings, Advances in Mathematics, 314, pp. 573-582 (2017). 15. Questions about Boij-Söderberg theory, in Surveys on Recent Developments in Algebraic Geom- etry (ed. Izzet Coskun, Tommaso de Fernex, Angela Gibney), Proceedings of Symposia in Pure Mathematics, 95, pp. 285–304 (2017). Daniel Erman 3

16. Categorified duality in Boij–Söderberg Theory and invariants of free complexes (with David Eisenbud), Journal of the European Mathematical Society, 19, pp. 2657–2695, (2017). 1 17. Gauss Composition for P , and the universal Jacobian of the Hurwitz space of double covers (with Melanie Matchett Wood), Journal of Algebra, 470, pp. 320-352 (2017). 18. Supernatural analogues of Beilinson monads (with Steven V Sam), Compositio, 152, pp. 2545– 2562 (2016). 19. Furstenberg sets and Furstenberg schemes over finite fields (with Jordan S. Ellenberg), Algebra and Number Theory, 10, pp. 1415–1436 (2016). 20. A quick proof of nonvanishing of asymptotic syzygies, (with Lawrence Ein and Robert Lazars- feld), Algebraic Geometry, 3, pp. 211–222 (2016). 21. A heuristic for the distribution of point counts for random curves over a finite field (with Jeffrey D. Achter, Kiran S. Kedlaya, Melanie Matchett Wood, and David Zureick-Brown), Philosophical Transactions of the Royal Society A, 373, (2015). 22. The Betti table of a high degree curve is asymptotically pure, Recent advances in algebraic geometry (ed. Christopher Hacon, Mircea Mustata, and Mihnea Popa), pp. 200–206, London Mathematical Society Lecture Notes (No. 417), Cambridge University Press, Cambridge, 2015. 23. Tate Resolutions for Products of Projective Spaces (with David Eisenbud and Frank-Olaf Schreyer), Acta Mathematica Vietnamica, 40, pp 5-36 (2015). 24. Semiample Bertini Theorems over a finite field (with Melanie Matchett Wood), Duke Mathe- matical Journal, 164, pp. 1–38, (2015). 25. Asymptotics of random Betti tables (with Lawrence Ein and Rob Lazarsfeld), to appear in Journal für die reine und angewandte Mathematik (Crelle’s Journal), 702, (2015). 26. Tensor Complexes: Multilinear free resolutions constructed from higher tensors (with Christine Berkesch, Manoj Kummini, and Steven Sam), Journal of the European Mathematical Society, 15, pp. 2257–2295 (2013). 27. Three flavors of extremal Betti tables (with Christine Berkesch and Manoj Kummini), in Com- mutative algebra (ed. Irena Peeva), pp. 99-121, Springer, New York, 2013. 28. Filtering Free Resolutions (with David Eisenbud and Frank-Olaf Schreyer), Compositio Mathe- matica, 149, pp. 754-772 (2013). 29. Murphy’s Law for Hilbert function strata in the Hilbert scheme of points, Mathematical Research Letters, 19, pp. 1277-1281 (2012). 30. Shapes of free resolutions over a local ring (with Christine Berkesch, Manoj Kummini, and Steven Sam), Mathematische Annalen, 354, pp. 939-9545 (2012). 31. Poset structures in Boij-Söderberg theory (with Christine Berkesch, Manoj Kummini, and Steven Sam), International Mathematics Research Notices, 2012, pp. 5132-5160 (2012). 2 n 32. Secant Varieties of P × P embedded by O(1, 2) (with Dustin Cartwright and Luke Oeding), Journal of the London Mathematical Society, 85, pp. 121-141 (2012). 33. The cone of Betti diagrams over a hypersurface ring of low embedding dimension (with Christine Berkesch, Jesse Burke, and Courtney Gibbons), Journal of Pure and Applied Algebra, 16, pp. 2256-2268 (2012). Daniel Erman 4

34. Laurent polynomials and Eulerian numbers (with Greogry G. Smith and Anthony Várilly- Alvarado), Journal of Combinatorial Theory, Series A, 118, pp. 396-402 (2011). 35. A syzygetic approach to the smoothability of zero-dimensional schemes (with Mauricio Velasco), Advances in Mathematics, 224, pp. 1143-1166 (2010). 36. A special case of the Buchsbaum-Eisenbud-Horrocks rank conjecture, Mathematical Research Letters, 17, pp. 1079-1089 (2010). 37. Hilbert schemes of 8 points (with Dustin Cartwright, Mauricio Velasco, and Bianca Viray), Algebra and Number Theory, 3, pp. 763-795 (2009). 38. The semigroup of Betti diagrams, Algebra and Number Theory, 3, pp. 341-365 (2009).

Preprints 39. Tate Resolutions on Products of Projective Spaces: Cohomology and PushForward Complexes, (with David Eisenbud and Frank-Olaf Schreyer.) 12 pages. arXiv:1905.10230. 40. Heuristics for `-torsion in Veronese Syzygies (with Caitlyn Booms and Jay Yang). 22 pages. arXiv: 2007.13914. 41. Tate resolutions on toric varieties (with Michael K. Brown). arXiv: 2108.03345. 1 1 42. Syzygies of P × P : data and conjectures (with Juliette Bruce, Daniel Corey, Steve Goldstein, Robert P. Laudone, and Jay Yang). arXiv:2104.14598. 43. Minimal free resolutions of diﬀerential modules (with Michael K. Brown). arXiv: 2103.08471.

Software Packages All packages are for Macaulay2, a software system devoted to computations in algebraic geometry and commutative algebra. 1. SchurVeronese (with Juliette Bruce, Steve Goldstein, and Jay Yang). Submitted for future releases of Macaulay2, pending approval. 2. TateOnProducts (with David Eisenbud and Frank-Olaf Schreyer). Distributed with releases of Macaulay2 (2015). Updated with new functionality in 2018. 3. TensorComplexes (with David Eisenbud, Gregory G. Smith, and Dumitru Stamate). Distributed with releases of Macaulay2 (2012).

Multimedia 1. The Josephus Problem, Numberphile YouTube video, similar to a public lecture. Produced by Brady Haran. ≈ 5, 000, 000 views. 2. SyzygyData.com, (with Juliette Bruce, Steve Goldstein, and Jay Yang), a public database on large-scale Veronese syzygy computations.

Invited Lecture Series 2019 Max Planck Summer School, Leipzig, Germany: Random Monomial Ideals. 2018 CIMPA Research School - Latinamerica: “Commutative Algebra with Applications to Statistics and Coding Theory”. Syzygies and Monomial Ideals. 2011 MSRI Graduate Student Summer School: Commutative Algebra. Free resolutions and Boij– Söderberg Theory. Daniel Erman 5

Conference Talks Since 2013 2022 JMM Special Session on “Commutative Algebra”. 2021 AMS Special Session, Plenary Talk, Omaha, NE. CIRM: Singularities in Positive Characteristic, Luminy, France. JMM Special Session on “Commutative Algebra meets Representation Theory”. 2020 Fellowship of the Ring, National Commutative Algebra Seminar (virtual). AMS Special Session on “Combinatorial algebra and geometry”, West Lafayette, IN. 1 JMM Special Session on “Commutative Algebra”, Denver, CO. 2019 Texas Algebraic Geometry Symposium, Texas A&M. AMS Special Session on “Commutative Algebra”, Madison, WI. Combinatorial Algebra meets Algebraic Combinatorics, University of Ottawa. JMM Special Session on “Commutative Algebra”, Baltimore, MD. 2018 AMS Special Session on “Combinatorial Commutative Algebra”, Bentonville, AR. 2017 The Structure of Free Resolutions and Applications, Texas Tech University. SIAM Conference on Applied Algebraic Geometry, Georgia Tech University. The Prospects for Commutative Algebra, (Osaka, Japan). Spring Lecture Series: Geometry and the Equations of Projective Varieties, University of Arkansas. 2016 Oberwolfach: Asymptotic Phenomena in Local Algebra and Singularity Theory (Germany). Fields Institute: on Convexity in Algebraic Geometry, (Toronto, Canada). Oberwolfach: Classical Algebraic Geometry (Oberwolfach, Germany). 2015 Midwest Commutative Algebra Meeting, Purdue University. Graduate Student Bootcamp for the 2015 Algebraic Geometry Summer Research Institute, Uni- versity of Utah. Theory and Applications of Syzygies, Universität des Saarlandes, (Saarbrücken, Germany). ICMS: Minimal free resolutions, Betti numbers, and combinatorics, (Edinburgh, Scotland). 2014 Simons Workshop on Tensors, University of California, Berkeley Macaulay2 Conference, University of Illinois, Urbana-Champaign Western Algebraic Geometry Seminar, University of Colorado, Boulder 2013 CIRM: Commutative Algebra and its Interactions with Algebraic Geometry (Luminy, France). Michigan Computational Algebraic Geometry Conference, Western Michigan University. JMM Special Session on Arithmetic Geometry and L-series San Diego, January 2013

Seminar and Colloquium Talks since 2013 2021 Colorado State University, Colloquium. University of Minnesota, Algebra Seminar. Cornell University, Colloquium. 2020 New Mexico State University, Colloquium. University of Wisconsin, Logic Seminar. Stony Brook University, Algebraic Geometry Seminar.

1Cancelled due to COVID-19. Daniel Erman 6

Humboldt-Universität zu Berlin, Algebraic Geometry Seminar. 2019 Stanford University, Algebraic Geometry Seminar. 2018 Rice University, Colloquium. University of Illinois at Chicago, Algebraic Geometry Seminar. Iowa State, Colloquium. Algebraic Geometry Seminar, Queen’s University. 2017 Stony Brook University Algebraic Geometry Seminar. 2016 University of Washington Algebra Seminar. University of South Carolina Algebraic Geometry Seminar. University of Virginia Commutative Algebra Seminar. University of Michigan Commutative Algebra Seminar. 2015 Notre Dame Algebra Seminar. University of Minnesota Commutative Algebra Seminar. University of Illinois at Chicago, Algebraic Geometry Seminar. 2013 University of Michigan Commutative Algebra Seminar University of Illinois at Urbana-Champaign, Colloquium University of Michigan Algebraic Geometry Seminar Rutgers University, Colloquium Rice University, Colloquium University of British Columbia, Colloquium University of British Columbia, Algebraic Geometry Seminar

Teaching since 2013 2021 Math 746: Commutative rings, University of Wisconsin Math 467: Elementary Number Theory, University of Wisconsin (designed course) 2020 Math 742: Abstract Algebra 2, University of Wisconsin. 2019 Math 222: Calculus 2, University of Wisconsin. (500 students in 2 lectures). Math 764: Algebraic Geometry 2, University of Wisconsin. 2017 Math 222: Calculus 2 (750 students in 3 lectures). Math 742: Abstract Algebra 2, University of Wisconsin. 2016 Math 567: Undergraduate Number Theory, University of Wisconsin. 2015 Math 222: Calculus 2, University of Wisconsin, (750 students in 3 lectures). Math 542: Modern algebra II, University of Wisconsin. 2014 Math 863: Toric varieties, University of Wisconsin (designed course). Math 541: Modern algebra, University of Wisconsin. Math 746: Commutative rings, University of Wisconsin (designed course). 2013 Math 222: Calculus 2, University of Wisconsin, (500 students in 2 lectures).

Organizational Activities: Conferences and Workshops 2021 CA+ Meeting, (with C. Berkesch and J. McCullough), University of Minnesota. Special session on commutative algebra, Omaha, NE, AMS regional meeting, (with C. Raicu). Daniel Erman 7

2020 CA+ Meeting, (with C. Berkesch and J. McCullough), Iowa State University.2 2019 Special session on combinatorial commutative algebra, University of Wisconsin-Madison, AMS regional meeting, (with J. Bruce, C. Eur, L. Silverstein). Geometry and Arithmetic of Surfaces, (with J. Bruce, W. Li), University of Wisconsin-Madison. 2018 Macaulay2 at Wisconsin, (with J. Bruce, S. Sam, and J. Yang), University of Wisconsin. 2017 CA+ Meeting, (with C. Berkesch and S. Sam), University of Minnesota. A view towards algebraic geometry, (with M. Mustata, C. Raicu, and G. Smith, in honor of David Eisenbud’s 70th birthday), Edgartown, MA. 2016 CA+ Meeting, (with C. Berkesch and S. Sam), University of Wisconsin. Asymptotic Algebra, Syzygies, and Representation Theory, (with Gregory G. Smith), Banﬀ In- stitute Research Station. 2014 Special session on toric varieties, AMS regional meeting, (with C. Berkesch and H. Schenck), University of Wisconsin-Eau Claire. 2012 Boij–Söderberg Theory Focus Period, (with D. Eisenbud and F.O. Schreyer), MSRI. RTG Learning Workshop on Derived Algebraic Geometry (with B. Bhatt), University of Michi- gan. 2011 MSRI Summer School on Commutative Algebra (with I. Swanson and A. Taylor). Western Algebraic Geometry Symposium, (with J. Hall, J. Li, C. Liedtke, and R. Vakil), Stanford University. 2010 Co-organizer, Special Session on Commutative Algebra and Representation Theory, Joint AMS- SMM meeting, (with D. Eisenbud, J. de la Peña, and R. Villareal), UC Berkeley. 2009 SAGE Days 14 Conference, (with D. Eisenbud, D. Grayson, M. Hansen, W. Stein, and M. Still- man), MSRI.

Outreach Activities since 2013 2020 Panelist, Grad Panel on Work-life balance. 2013–20 Faculty organizer, Madison Math Circle Total number of students reached per year has expanded from 25 to 250. In addition to weekly meetings, the Math Circle visits several local high schools. 2017 Faculty Organizer, Math Careers: Beyond academia. Half-day workshop involving speakers from Google, Epic, Milwaukee Brewers, and more. 50 graduate student participants. 2018-19 Co-Organizer, Professional Development Lunches, University of Wisconsin. 2016–18 Panelist on Mathematics for College Readiness, University of Wisconsin. Each meeting involves about 150 teachers from around the state. 2016 Presenter at meeting of the Dane County Advanced Learning Network. 2015–17 Faculty organizer, professional development panels for math PhD students. 2015 Invited Lecturer, University of Wisconsin Talent Search Honors Day. 2014 Trained LGBTQ Ally, LGBT Center, University of Wisconsin. 2010–17 Mentor, Association for Women in Mathematics Mentoring Program.

2Cancelled due to COVID-19. Daniel Erman 8

Service Activities since 2013 2021– TA Supervisor: oversee all TA matters for 150 TA’s. 2019–20 Member, Hiring Committee. 2019–20 Member, Ad Hoc Committee on library space. 2018–20 Chair of Committee on TA Policies and Procedures.. 2019 Member, Ad Hoc Expansion Plan Committee. 2017–18 Contributor to REACH redesign of Math 222. 2016–18 Ad Hoc Committee on Diversity and Inclusion. 2014– Committee on TA Pay and Performance: Led redesign of TA evaluations and feedback process. 2013– Outreach Committee. 2013–14 Graduate Student Committee 2013–14 Conferences and Distinguished Lecturers Committeee

Postdoc Mentoring at University of Wisconsin, Madison 2020– Aleksandra Sobieska. 2019– Robert Walker, awarded NSF postdoc with me as sponsoring scientist. 2017–20 Michael Brown. Co-mentored with Andrei Caldararu. Now faculty at Auburn. 2016–18 Sasha Pavlov. Co-mentored with Andrei Caldararu and Steven Sam. Now faculty at HSE University.

Graduate Student Mentoring at University of Wisconsin, Madison

PhD Students 2018 Jay Yang (currently an NSF RTG postdoc at Minnesota). 2019 Amy Hang Huang. (Main advisor was Steven Sam; currently a postdoc at Texas A&M.) 2020 Juliette Bruce. (Awarded NSF fellowship at UC-Berkeley.) Robert Laudone. (Awarded NSF fellowship at Michigan. Main advisor was Steven Sam.) Current Caitlyn Booms. (Exp 2023.) Maya Banks. (Exp 2023.) John Cobb. (Exp 2024.)

Editorial Work 2020– Communications in Algebra, Associate Editor.

Referee Work Daniel Erman 9

Algebra and Number Theory; Algebraic Geometry; Central European Journal of Mathemat- ics; Communications in Algebra; Compositio Mathematica; EMS Surveys; Illinois Journal of Mathematics; International Mathematics Research Notices; International Journal of Algebra and Computation; Inventiones; Journal de Théorie des Nombres de Bordeaux; Journal für die reine und angewandte Mathematik (Crelle’s Journal); Journal of Algebra; Journal of Algebraic Combinatorics; Journal of Algebraic Geometry; Journal of the American Mathematical Society (JAMS); Journal of Combinatorial Theory, Series A; Journal of Commutative Algebra; Journal of the London Mathematical Society; Journal of Pure and Applied Algebra; Journal of Software for Algebra and Geometry; Journal of Symbolic Computation; Mathematical Research Letters; Math Reviews; Mathematische Nachrichten; Mathematisches Zeitschrift; Michigan Mathemati- cal Journal; Proceedings of the AMS.

Contributions to K-12 Mathematics Education

2007–12, 2017–18 Consultant, Instructional Research Group (non-proﬁt education research group). - Edited professional development standards for mathematics teachers grades 3-5. - Provided input on Texas Education Agency revisions of knowledge standards for K-12 mathematics education. 2009 Speaker, Project DATA “Mathematician Series”, University of Oregon. - Designed and taught a two-day workshop for 50 middle school teachers to help teachers improve their content knowledge for teaching algebra. 2003–05 Author, Education Development Center, CME Project. - Co-wrote and edited Algebra 1 textbook for an NSF-funded high school textbook curriculum.