# Carl Lian

## About

I am a Norbert Wiener Fellow (postdoc) at Tufts University. I was previously an NSF Postdoctoral Fellow at Humboldt-Universität zu Berlin.

I completed my PhD in mathematics in May 2020 at Columbia University, advised by Aise Johan de Jong. My thesis may be found here. Previously, I was an undergraduate at MIT.

Pronouns: he/him (English), er/ihm (Deutsch)

Information on recommendation letters

Research activities:

Tufts Algebra, Geometry, and Number Theory Seminar (AGeNTS) (Thursdays 4:30-5:30, Joyce Cummings Center 502)

Boston Algebraic Geometry Day on Moduli of Curves (20 April 2024, Tufts)

VERSEIM-REU (3 June-9 August 2024, Tufts)

Summer School on Algebraic Curves (8-19 July 2024, Berkeley)

## Contact

E-Mail: Carl.Lian (usual symbol) tufts (usual symbol) edu

Joyce Cummings Center, Room 584

177 College Ave

Medford, MA 02155

## Papers

I work in algebraic geometry, with an emphasis on moduli spaces of curves and related objects, e.g. branched covers of curves (Hurwitz spaces), [limit] linear series on curves (Brill-Noether theory), stable maps (Gromov-Witten theory), and abelian varieties. I'm especially interested in the intersection theory (enumerative geometry) of such moduli spaces and various combinatorial problems that emerge in related calculations.

Research articles (listed in reverse order of publication, not necessarily in order of writing):

(with François Greer) d-elliptic loci and the Torelli map (arXiv), submitted

Degenerations of complete collineations and geometric Tevelev degrees of P^r (arXiv), submitted

The HHMP decomposition of the permutohedron and degenerations of torus orbits on flag varieties (arXiv), submitted

(with Alessio Cela) Fixed-domain curve counts for blow-ups of projective space (arXiv), submitted

(with Roya Beheshti, Brian Lehmann, Eric Riedl, Jason Starr, and Sho Tanimoto) On the asymptotic enumerativity property for Fano manifolds (arXiv), to appear in Forum Math. Sigma

Torus orbit closures and 1-strip-less tableaux (arXiv), to appear in Algebraic Combinatorics

(with Rahul Pandharipande) Enumerativity of virtual Tevelev degrees (arXiv, journal), to appear in Ann. Sc. Norm. Super. Pisa Cl. Sci.

Asymptotic geometric Tevelev degrees of hypersurfaces (arXiv, journal), to appear in Michigan Math. J.

(with Gavril Farkas) Linear series on general curves with prescribed incidence conditions (arXiv, journal), J. Inst. Math. Jussieu 22 (2023), 2857-2877.

(with Alessio Cela) Generalized Tevelev degrees of P^1 (arXiv, journal), J. Pure Appl. Algebra 227 (2023), 107324.

(with Riccardo Moschetti) Z/rZ-equivariant covers of P^1 with moving ramification (arXiv, journal), Israel J. Math. 253 (2023), 487-500.

Enumerating pencils with moving ramification on curves (arXiv, journal), J. Algebraic Geom. 32 (2023), 143-182.

Non-tautological Hurwitz cycles (arXiv, journal), Math. Z. 301 (2022), 173-198.

d-elliptic loci in genus 2 and 3 (arXiv, journal), Int. Math. Res. Not. IMRN (2021), no. 20, 15959-16007. The published version of this paper contains some errors in some formulas stemming from a mistake in Proposition 5.1, see this erratum. The errors have been fixed in the version linked here and in the arXiv version.

The H-tautological ring (arXiv, journal), Selecta Math. (N.S.) 27 (2021), Article Nr. 96.

(with Joshua Alman and Brandon Tran) Circular Planar Electrical Networks: Posets and Positivity (arXiv1, arXiv2, journal). J. Comb. Theory Ser. A 132 (2015), 58-101.

Other writing:

Counting linear series on curves: old and new results, Oberwolfach report for Classical Algebraic Geometry, June 2021

(with Raymond Cheng and Takumi Murayama, in collaboration with Yordanka Kovacheva and Monica Marinescu, mentored by Davesh Maulik) Projectivity of the Moduli of Curves, exposition of Kollár's Projectivity of complete moduli, initiated at the Stacks Project Workshop in Ann Arbor, August 2017

## Teaching

In Fall 2024, I am teaching Math 145: Abstract Algebra 1.

Previous courses:

Algebraic Geometry Spring 2024 (Tufts)

Abstract Algebra 1 Fall 2023 (Tufts)

Linear Algebra Spring 2024 (Tufts), Summer 2020 (Columbia)

Calculus 1 Fall 2023 (Tufts), Summer 2019, Fall 2018 (Columbia)

Other programs I have taught in: MathROOTS, PRIMES-USA, PRIMES Circle, CMUSR