Research

I have broad research interests, including Algebraic Geometry, Arithmetic Geometry, Combinatorics, and Computational Mathematics. I am particularly interested in rational curves and the birational geometry of hypersurfaces.  I am a student of Joe Harris. 

Algebraic Geometry Publications:

Roya Beheshti, Brian Lehmann, Carl Lian, Eric Riedl, Jason Starr, Sho Tanimoto, On the asymptotic enumerativity property for Fano manifolds, arXiv:2310.15252 (submitted for publication)

Brian Lehmann, Eric Riedl, and Sho Tanimoto, Non-free curves on Fano varieties, arXiv:2304.05438 (submitted for publication)

Brian Lehmann, Eric Riedl, and Sho Tanimoto, Non-free sections of Fano fibrations, arXiv:2301.01695 (submitted for publication)

Anand Patel, Eric Riedl, Geoffrey Smith and Dennis Tseng, Lines highly tangent to a hypersurface arXiv:2208.04393 (submitted for publication)

Xi Chen, Eric Riedl and Wern Yeong, Algebraic hyperbolicity of complements of generic hypersurfaces in projective spaces, arXiv:2208.07401 (accepted to J. Reine Angew. Math.)

Roya Beheshti, Brian Lehmann, Eric Riedl and Sho Tanimoto, Rational curves on del Pezzo surfaces in positive characteristic, Trans. Amer. Math. Soc. Ser. B10(2023), 407–451. arXiv:2110.00596 

Beheshti, Roya and Riedl, Eric, Restrictions on rational surfaces lying in very general hypersurfaces, Restrictions on rational surfaces lying in very general hypersurfaces, Forum Math. Sigma 10 (2022), Paper No. e71, 11 pp.  arXiv:2107.13584 

Lehmann, Brian and Riedl, Eric, Restricted tangent bundles for general free rational curves International Mathematics Reserch Notices (2022) arXiv:2104.03345

Coskun, Izzet, and Riedl, Eric, Clustered families and applications to Lang-type conjectures Clustered families and applications to Lang-type conjectures, Proc. Lond. Math. Soc. (3) 125 (2022), no. 6, 1353--1376.  arXiv:2010.11301

Roya Beheshti, Brian Lehmann, Eric Riedl, and Sho Tanimoto, Moduli spaces of rational curves on Fano threefolds, Moduli spaces of rational curves on Fano threefolds, Adv. Math. {\bf 408} (2022), part A, Paper No. 108557, 60 pp. arXiv:2010.06795

Anand Patel, Eric Riedl, and Dennis Tseng, Moduli of linear slices of high degree smooth hypersurfaces (accepted to Algebra Number Theory) arXiv:2005.03689

Coskun, Izzet and Riedl, Eric, Algebraic hyperbolicity of very general surfaces Israel Journal of Mathematics (2022)  arXiv:1912.07689

Beheshti, Roya and Riedl, Eric, Linear subspaces of hypersurfaces, Duke Math. J. {\bf 170} (2021), no.~10, 2263--2288. arXiv:1903.02481

Coskun, Izzet and Riedl, Eric, Effective bounds on ampleness of cotangent bundles, Bull. Lond. Math. Soc. {\bf 52} (2020), no.~1, 237--243. arXiv:1810.07666

Riedl, Eric and Yang, David, Applications of a grassmannian technique to hyperbolicity, Chow equivalence, and Seshadri constants J. Algebraic Geom. {\bf 31} (2022), no.~1, 1--12. arXiv:1806.02364 

Coskun, Izzet and Riedl, Eric, Algebraic hyperbolicity of the very general quintic surface in P^3 Adv. Math. 350 (2019), 1314--1323. arXiv:1804.04107

Beheshti, Roya and Riedl, Eric, Positivity results for spaces of rational curves. Algebra Number Theory {\bf 14} (2020), no.~2, 485--500. arXiv:1801.05834

Coskun, Izzet and Riedl, Eric Normal bundles of rational curves on complete intersections Commun. Contemp. Math. 21 (2019), no. 2, 1850011, 29 pp. , with Macaulay2 calculations

Riedl, Eric and Woolf, Matthew Rational curves on complete intersections in positive characteristic, Journal of Algebra 494, 28-39. arXiv:1609.05958

Coskun, Izzet and Riedl, Eric Normal bundles of rational curves in projective space, Mathematische Zeitschrift 288 (2018), no. 3-4, 803-827. arXiv:1607.06149

Riedl, Eric and Yang, David Rational curves on general type hypersurfaces, J. Differential Geom. {\bf 116} (2020), no.~2, 393--403. arXiv:1605.01759

Riedl, Eric and Yang, David Kontsevich spaces of rational curves on Fano hypersurfaces, J. Reine Angew. Math. 748 (2019), 207--225. 

Barbara Bolognese, Jack Huizenga, Yinbang Lin, Eric Riedl, Benjamin Schmidt, Matthew Woolf and Xiaolei Zhao. Nef cones of Hilbert schemes of points on surfaces, Algebra Number Theory 10 (2016), no. 4, 907--930.

Jesus De Loera, Susan Margulies, Michael Pernpeintner, Eric Riedl, David Rolnick, Gwen Spencer, Despina Stasi, Jon Swenson Graph-coloring ideals: Nullstellensatz certificates, Gröbner bases for chordal graphs, and hardness of Gröbner bases Interntl. Symposium on Symbolic and Algebraic Computation 2015

Combinatorics Papers

Riedl, Eric. Largest minimal percolating sets in hypercubes under 2-bootstrap percolation. Electronic Journal of Combinatorics, Volume 17(1), 2010.

Riedl, Eric. Largest and Smallest Minimal Percolating Sets in Trees. Electronic Journal of Combinatorics, Volume 19(1), 2012.

Computer Science Papers

Riedl, John and Riedl, Eric. Crowd-sourcing medical research. IEEE Computer. January 2013. 46(1) 0089-92

Hang Zhang, Eric Riedl, Valery A Petrushin, Siddharth Pal, Jacob Spoelstra. Committee Based Prediction System for Recommendation: KDD Cup 2011, Track2. In: KDD Cup, 2012. 

Notes

Notes from ETH virtual seminar talk here.