Preprint

• Avik Charavarty, Positivity of coinvariant divisors on $\overline{\mathrm{M}}_{0,n}$ and the parafermions. (ArXiv, Journal)

International Mathematics Research Notices, Volume 2026, Issue 9, May 2026.

Abstract: We give criteria for determining the positivity of line bundles coming from vertex operator algebras (VOAs) on the moduli space $\overline{\mathrm{M}}_{0,n}$ of rational curves with $n$ marked points. The criteria use the multiplicative structure of VOA representations encoded in the fusion ring. Using them, we construct positive line bundles on $\overline{\mathrm{M}}_{0,n}$ from certain parafermion VOAs. These give the first examples of commutant VOAs producing positive line bundles.

See a poster on this paper I presented in the Richmond Geometry meeting 2025 [link]

Seminars organized

Fall 2025 | Basic notions seminar

Summer 2025| Reading Group - Fukaya categories and Mirror symmetry

Spring 2025 | Mirror symmetry and math/physics

Fall 2024 & Spring 2025 | UPenn Graduate Algebraic Geometry seminar

Selected Talks

Nov. 2025 | Positive line bundles on moduli of curves from VOA representations
VT Geometry&Topology seminar, Virginia Tech.

Sep. 2025 | Positivity of coinvariant divisors on \bar{M}_{0,n} and the parafermions [Link]
Math/Phys joint seminar, University of Pennsylvania.

May 2025 | Positivity of coinvariant divisors
VOA Day, University of Pennsylvania.

Feb. 2025 | Intrinsic mirror symmetry: I and II
Mirror symmetry and math/physics seminar, University of Pennsylvania.

Oct. 2024 | Moduli $\mathcal{A}_g$, its compactifications and tautological rings [Link]
Graduate algebraic geometry seminar, University of Pennsylvania.

Aug. 2024 | Virtual fundamental classes [Link]
eCHT seminar, Wayne State University.

Nov. 2023 | Moduli of stable curves [Link]
Algebraic geometry student research seminar, University of Pennsylvania.

Travel

Forthcoming

Recent

Jun. 2026 | ICM 2026. [Link]
Philadelphia, PA.

Jun. 2026 | Summer school: Geometry of Instantons and quivers. [Link]
Lille, France.

Jun. 2026 | RGAS Summer school: Mirror symmetry and homological methods in algebraic geometry. [Link]
Zaragoza, Spain.

Apr. 2026 | Hot topics: Geometric langlands conjecture. [Link]
SLMath, CA.

Feb. 2026 | the Richmond Geometry day Spring 2026  [Link]
Virginia Commonwealth University, Richmond, VA.

Jan. 2026 | Homological Mirror Symmetry 2026 [Link]
IMSA, Miami, FL.

Nov. 2025 | AGNES Fall 2025  [Link]
University of Massachusetts, Amherst, MA.

Nov. 2025 | Geometry & Topology seminar  [Link]
Virginia Tech, Blacksburg, VA.

Sep. 2025 | the Richmond Geometry Meeting 2025  [Link] [POSTER LINK]
Virginia Commonwealth University, Richmond, VA.

Sep. 2025 | FRG Fall school on Quantizations and Lagrangians  [Link]
University of Illinois, Chicago, IL.

Jul. 2025 | Bootcamp & 2025 Summer research institute in Algebraic geometry [Link]
Colorado State University, Fort Collins, CO.

Jun. 2025 | Summer school: Enumerative geometry and Geometric rep. theory  [Link]
Università di Pisa, Italy.

May  2025 | Derived categories and Mirror symmetry [Link]
UW, Madison, WI.

Mar. 2025 | Lefschetz centennial [Link]
IMSA, Miami, FL.

Mar. 2025 | Georgia Algebraic Geometry Symposium 2025 [Link]
University of Georgia, Athens, GA.

Jan. 2025 | Homological Mirror Symmetry 2025 [Link]
IMSA, Miami, FL.

Jan. 2025 | Winter school on Enumerative geometry and Mirror symmetry [Link]
Caltech, Pasadena, CA.

Jul. 2024 | Logs and stacks in birational geometry and moduli [Link]
LMS Invited Lecture Series 2024, London, UK.

Jun. 2024 | Workshop on Computational and Applied Enumerative Geometry [Link]
Fields Institute, Toronto, Canada.

Feb. 2024 | A panorama of moduli spaces [Link]
Goethe University Frankfurt am Main, Frankfurt, Germany.

Jun. 2023 | Arithmetic, birational geometry, and moduli spaces [Link]
Brown University, Providence, RI.

Teaching Experience

-- at the University of Pennsylvania

• Summer 2026 | Instructor for Math 2400: Calculus III

• Summer 2022 | Instructor for Math 3120: Linear algebra

• Fall 2021 | Teaching Assistant for Math 1400: Multivariable calculus

• Spring 2024 | Teaching Assistant for Math 2030: Proofs in Algebra

• Fall 2024, Fall 2023, Spring 2022 | Teaching Assistant for Math 3140: Adv. Linear algebra

• Spring 2025 | Teaching Assistant for Math 6030: Graduate algebra 2

• Summer 2024, Summer 2023 | Teaching Assistant for Pre-First Year Program

Service

• Jan. 2025 - May 2025 | Organizer for the Mirror symmetry and math/physics seminar at the University of Pennsylvania.

• Sep. 2024 - May 2025 | Co-organizer for the Upen Graduate Algebraic Geometry Student seminar (GAGS).

• May 2024 | Technical help for AGNES at UPenn. 

• Mentored undergraduate students via the Directed Reading Program at the University of Pennsylvania on the following topics:

Algebraic topology, Hilbert schemes, Toric geometry,  Complex algebraic geometry, Scheme theory, Tropical Riemann-Roch,  Abstract varieties

Fellowships and Awards

Mentored undergraduate students via the Directed Reading Program at University of Pennsylvania on the following topics:

• 2022-2027 | Benjamin Franklin & Fontaine Fellowship, University of Pennsylvania

• 2020-2022 |Bridge-to-PhD program Fellowship, University of Pennsylvania.

• 2013-2017 | Undergraduate Dean's list-College of Engineering, Wayne State University.

• May 2015 | Undergraduate Research Opportunity Program (UROP) Creative Project Award, Wayne State University

• Feb. 2015 | Engineering Dean Discretionary Fund for a creative project, Wayne State University

• 2015-2020 | Tau beta Pi Michigan Epsilon Membership, Wayne State University

Links

• Physics: http://www.damtp.cam.ac.uk/user/tong/teaching.html

• Calculus: https://tutorial.math.lamar.edu/classes/calci/calci.aspx