Woonam Lim

I moved to Utrecht University. Here is my new website.

Email: woonam.lim at math.ethz.ch
Office: HG J 43, Rämistrasse 101, 8092 Zürich, Switzerland

I work in algebraic geometry with a focus on moduli spaces of sheaf-theoretic objects (e.g. stable sheaves, quotients, framed sheaves, quiver representations). Specifically, I study enumerative properties of these moduli spaces by means of partition functions, wall-crossing formulas, geometric representation theory.

Papers and Preprints

• Cohomological $\chi$-dependence of ring structure for the moduli of one-dimensional sheaves on ${\mathbb{P}}^2$ (with Miguel Moreira, Weite Pi), arXiv:2305.14193 (2023) -- preprint
  
• Virasoro constraints on moduli of sheaves and vertex algebras (with Arkadij Bojko, Miguel Moreira), arXiv:2210.05266 (2022) -- preprint
  
• The virtual K-theory of Quot schemes of surfaces (with Noah Arbesfeld, Drew Johnson, Dragos Oprea and Rahul Pandharipande), J. Geom. Phys. 164 (2021) -- preprint
  
• Virtual ${\chi }_{-y}$-genera of Quot schemes on surfaces, J. Lond. Math. Soc. 104 (2021) -- preprint
  
• Virtual invariants of Quot schemes of surfaces, Ph.D. thesis -- Open Access
  
• Lecture note on Moduli of Stable Bundles on Curves, 102pp (2022)
  

Teaching

• Moduli of Stable Bundles on Curves, SP 2022 at ETH
  

Invited Talks (with notes)

• Virasoro constraints, vertex operator algebras, and wall-crossing, Derived Categories, Moduli Spaces, and Counting Invariants, Imperial College London, S23 -- notes
  
• Virasoro constraints, vertex operator algebras, and wall-crossing, Workshop on moduli spaces, virtual invariants and shifted symplectic structures, KIAS, S23
  
• Moduli spaces of sheaves: an overview, curves, and surfaces, School on moduli spaces, virtual invariants and shifted symplectic structures, KIAS, S23 -- notes
  
• Virasoro constraints; history and moduli of sheaves, Simons collaboration meeting, Oxford, WI22 -- notes
  
• Quot scheme theory of surfaces, Utrecht Geometry Seminar, FA22 -- notes
  
• Virasoro constraints and wall-crossing via vertex algebras, Edinburgh Geometry Seminar, FA22 -- notes
  
• Virasoro constraints on moduli of sheaves and vertex algebras, Arithmetic and Algebraic Geometry Seminar, EPFL, FA22
  
• Virasoro constraints in sheaf theory and vertex algebras, Intercontinental Moduli and Algebraic Geometry Zoominar, FA22 -- notes
  
• Virasoro constraints in sheaf theory and vertex algebras, UCSD Algebraic Geometry Seminar, FA22 -- notes for a main talk and a pre-talk
  
• Virasoro constraints for moduli of sheaves, Seminar Algebraic Geometry at Bonn, SP22 -- notes
  
• Virasoro constraints for sheaves and pairs via wall-crossing in vertex algebra, ETH moduli seminar, SP22
  
• Virasoro constraints for stable pairs on Calabi-Yau 4-folds, KIAS algebraic geometry seminar, FA21
  
• Wall-crossing formula for pairs on Calabi-Yau 4-folds, ETH moduli seminar, FA21
  
• Virtual invariants of Quot schemes of surfaces, FRAGMENT seminar, SP21 -- notes
  
• Lecture series on virtual invariants of Quot schemes of surfaces, ETH moduli seminar, SP21 -- notes 1, 2, 3. (See here for details of the lectures.)
  
• Virtual χ−y-genera of Quot schemes on surfaces, ETH moduli seminar, WI20 -- notes
  
• Rationality of the virtual invariant series of Quot schemes on surfaces, UCSD Algebraic Geometry Seminar, WI20
  

Conferences

• Derived Categories, Moduli Spaces, and Counting Invariants, Imperial College London, 3-7 July 2023.
• School and Workshop on moduli spaces, virtual invariants and shifted symplectic structures, KIAS, 20-30 June 2023.
• Helvetic Algebraic Geometry Seminar, Les Diablerets, 4-9 June 2023.
• Algebraic Geometry, Gauge Theory and the Swampland Conjectures (Simons collaboration), Oxford, 9-13 January 2023.
• Donaldson-Thomas invariants in Aussois, Paul-Langevin Center, 9-14 October 2022.
• Derived Categories, Moduli Spaces, and Hyperkähler Varieties, University of Michigan, 30 July - 5 August 2022.
• Vector Bundles on Algebraic Curves, Warwick, 25-29 July 2022.
• School on Mirror Symmetry and Moduli Spaces, Lisbon, 27 June - 1 July 2022.
• Helvetic Algebraic Geometry Seminar, SwissMAP Research Station, 5-10 June 2022.
• Curves and K3 surfaces, University of Bonn, 9-12 May 2022.
• Helvetic Algebraic Geometry Seminar, Geneva, August 2021.
• Summer school on Enumerative Geometry, Physics and Representation Theory, IHES, July 2021.
• BPS states, mirror symmetry and exact WKB, Sheffield Algebraic Geometry and Mathematical Physics Group, June 2021.
• Perverse Sheaves in Enumerative Geometry, HCM, February 2020.
• School and Workshop on Gauge Theories and Differential Invariants, ICTP, September 2019.
• Winter School on Enumerative Geometry and Modular Forms, Goethe University Frankfurt, February 2019.
• Complex Algebraic Geometry II, University of California, San Diego, January 2018.
• FRG Workshop on Moduli Spaces of sheaves and Bridgeland Stability, University of Illinois Chicago,December 2018.
• Western Algebraic Geometry Symposium, University of Oregon, October 2018.
• MSRI Summer School: Derived Categories, MSRI, June 2018.
• Arizona Winter School: Iwasawa Theory, University of Arizona, Mar 2018.
• Summer School on Algebra and Geometry of Spheres and Tori, KIAS, June 2017.

Seminars

Fall 2020: Donaldson-Thomas theory of 3-fold and CY 4-fold. See here.

Spring 2020: Enumerative geometry of K3 surfaces. See here.

Winter 2020: Hilbert scheme of points on surfaces and Beauville-Voisin conjecture for HyperKahler varieties. See here.

Fall 2019: Vafa-Witten invariants of surfaces. See here.