Weng

Daping Weng (翁达平)

I am a KAP at UC Davis.

I am interested in cluster theory, representation theory, algebraic geometry, symplectic geometry, and mathematical physics.

My PhD thesis advisor is Professor Alexander Goncharov.

This is a copy of my CV.

This is a copy of my research statement.

Office: MSB 3151

Email: daping AT math DOT ucdavis DOT edu

Office Hours: Mondays and Wednesdays 2:00 - 3:00 p.m.

Research Interest

            

My main research focus has been on cluster theory and its application to other branches of mathematics such as combinatorics, algebraic geometry, symplectic geometry, and representation theory.

I have worked on the construction of the cluster Donaldson-Thomas transformation on various families of cluster varieties, including Grassmannians, double Bruhat cells, and double Bott-Samelson cells. I have also studied cluster duality of Grassmannian, cyclic sieving phenomenon, and Zamolodchikov's periodicity conjecture.

Recently, I have become interested in the cluster structures on various geometric invariants of Legendrian links and their interaction with other constructs on Legendrian links.

I am also interested in many applications of cluster theory in mathematical physics, including integrable systems, scattering amplitudes, and mirror symmetry.

Publications & Preprints

            
  • Donaldson-Thomas Transformation of Grassmannian (58 pages)
      published in Advances in Mathematics 383:107721, 2021. arXiv:1603.00972

  • Donaldson-Thomas Transformation of Double Bruhat Cells in General Linear Groups (36 pages)
      arXiv:1606.01948

  • Donaldson-Thomas Transformation of Double Bruhat Cells in Semisimple Lie Groups (84 pages)
      published in Annales Scientifiques de l'École Normale Supérieure 53:291-352, 2020. arXiv:1611.04186

  • Cyclic Sieving and Cluster Duality for Grassmannian, with Linhui Shen (41 pages)
      published in SIGMA, Special Issue on Cluster Algebras, 16, 2020. arXiv:1803.06901

  • Cluster Structures on Double Bott-Samelson Cells, with Linhui Shen (89 pages)
      published in Forum of Math. Sigma, 9, E66, 2021. arXiv:1904.07992

  • Augmentations, Fillings, and Clusters, with Honghao Gao and Linhui Shen (77 pages)
      accepted by Geometric and Functional Analysis. arXiv:2008.10793

  • Braid Links with Infinitely Many Fillings, with Honghao Gao and Linhui Shen (19 pages)
      arXiv:2009.00499

  • Microlocal Theory of Legendrian Links and Cluster Algebras, with Roger Casals (119 pages)
      accepted by Geometry & Topology. arXiv:2204.13244

  • F-Polynomials of Donaldson-Thomas Transformations (27 pages)
      arXiv:2303.03466

  • Demazure Weaves for Reduced Plabic Graphs (with a Proof that Muller-Speyer Twist is Donaldson-Thomas), with Roger Casals, Ian Le, Melissa Sherman-Bennett (79 pages)
      arXiv:2308.06184

  • Augmentations, Fillings, and Clusters for 2-Bridge Links, with Orsola Capovilla-Searle and James Hughes (39 pages)
      arXiv:2308.11858

  • Intersections of Dual SL3-Webs, with Linhui Shen and Zhe Sun (31 pages)
      arXiv:2311.15466

Javascript Programs

           
  • A javascript program to compute the Ekholm-Honda-Kálmán functorial homomorphism and the cluster seed for admissible cobordisms/fillings of rainbow closures of positive braids.
  • A javascript program to generate a reduced plabic graph together with Plücker labelings and quiver from a permutation.
  • A javascript program to compute the cluster associated with a type A Demazure weave (c.f. arXiv:2207.11607).
    Warning: due to the lack of an efficient algorithm to simplify multivariate rational functions, it may take a long time to compute the cluster for a complicated Demazure weave. If you know how to implement such simplifications in javascript, please let me know.

Yale University
  • Teaching Assistant of
    • Math 112, Calculus I (Spring 2013)
  • Coach of
    • Math 118, Multi-variable calculus and linear algebra (economics majors oriented) (Fall 2013)
  • Instructor of
    • Math 120, Multi-variable calculus (Fall 2014, Spring 2016, Spring and Summer 2018)
    • Math 112, Calculus I (Fall 2016, Fall 2017)
    • Math 115, Calculus II (Summer 2017)

Michigan State University
  • Instructor of
    • Mth 132, Calculus I (Fall 2018 and Spring 2019)
    • Mth 310, Abstract Algebra and Number Theory (Fall 2019, Summer 2020)
    • Mth 235, Applied Differential Equantions (Spring and Fall 2020, Spring 2021)

University of California, Davis
  • Instructor of
    • MAT 108, Introduction to Abstract Mathematics (Fall 2021)
    • MAT 21C, Calculus: Partial Derivatives and Series (Fall 2021)
    • MAT 17B, Calculus for Biology and Medicine (Winter 2022)
    • MAT 21A, Calculus: Limits and Derivatives (Winter 2023, Fall 2023)
    • MAT 150B, Abstract Algebra (Winter 2023)
    • MAT 150C, Abstract Algebra (Spring 2023)
    • MAT 127A, Real Analysis (Spring 2023)
    • MAT 280, Cluster Algebra (Fall 2023)
    • MAT 185B, Complex Analysis II (Spring 2024)

Other Teaching Experience
  • Young Scholar Program counselor @ University of Chicago (2009 - 2012)