Weng

* I am on the right

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 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
      arXiv:1603.00972
  • Donaldson-Thomas Transformation of Double Bruhat Cells in General Linear Groups
      to appear in Adv. Math. arXiv:1606.01948
  • Donaldson-Thomas Transformation of Double Bruhat Cells in Semisimple Lie Groups
      Ann. Sci. Éc. Norm. Supér. 53:291-352, 2020. arXiv:1611.04186
  • Cyclic Sieving and Cluster Duality for Grassmannian, with Linhui Shen
      SIGMA, Special Issue on Cluster Algebras, 16, 2020. arXiv:1803.06901
  • Cluster Structures on Double Bott-Samelson Cells, with Linhui Shen
      to appear in Forum of Math. Sigma arXiv:1904.07992
  • Augmentations, Fillings, and Clusters, with Honghao Gao and Linhui Shen
      arXiv:2008.10793
  • Braid Links with Infinitely Many Fillings, with Honghao Gao and Linhui Shen
      arXiv:2009.00499

Some Computer Programs

           
  • A javascript program to compute the EHK functorial homomorphism and the cluster seed for admissible cobordisms/fillings. Please let me know if you find any bugs.

Yale University

  • Teaching Assistant
    • Math 112, Calculus I (Spring 2013)
  • Coach
    • Math 118, Multi-variable calculus and linear algebra (economics majors oriented) (Fall 2013)
  • Instructor
    • 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
    • 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
    • MAT 108, Introduction to Abstract Mathematics (Fall 2021)
    • MAT 21C, Calculus: Partial Derivatives and Series (Fall 2021)

Other Teaching Experience

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