Photo of Lei Chen

Lei Chen

Research

Papers

3. Surjective homomorphisms between surface braid groups Arxiv Notes
Classify surjective homomorphisms from PB_n(S_g,p) to PB_m(S_g,p), n-strand braid group to m-strand braid group.
Then we compute the automorphism group of PB_n(S_g,p)
Surprisingly, in contrast to the n=1 case, any automorphism of PB_n(S_g,p), n>1 is geometric.(2017)
2. The number of fiberings of a surface bundle over a surface Arxiv
Compute the number of ways Atiyah Kodaira example can fiber over a surface.
We also compute the fibering number of some other examples. (2017)
1. The universal n-pointed surface bundle only has n sections Arxiv
Classify homomorphisms from PB_n(S_g) to Pi_1(S_g), n-strand braid group to 1-strand braid group.
Using this, we compute the number of homotopically different sections of universal bundles on M_g,n. (2016)

Not for publication

In Winter 2014 I passed my topic exam, on Characteristic Classes of Surface Bundles, under the supervision of Benson Farb. The proposal is here.

Videos

Talks

2. ICMS Edinburgh
Slides: Surjective homomorphisms between surface braid groups.
1. Oberwalfach surface bundle
Youtube video: The section problems.
Notes: The section problems

Teaching

Mathematical journals

  • 2017.7.7: Birman-Hilden Theorem PDF
  • 2017.7.9: counting short geodesics on flat torus PDF
  • Notes

    Mapping Class Groups

  • Burau Representation PDF
  • Describe Johnson homomorphism using Massay Product PDF
  • Homology 3-sphere and Casson Invariant PDF
  • Torsions in mapping class group PDF
  • Random Topics

  • Finite generated residually finite group is Hopfian PDF
  • Grothendieck Riemann Roch PDF
  • polynomial growth--nilpotent group PDF
  • Reeb Stability Thurston PDF
  • Reading Groups

  • Reading group on moduli space Spring 2017 Website
  • About me

    I'm a graduate student in at The University of Chicago, interested in Mapping Class Group and topology in general.

    Postal address
    5734 S. University Avenue
    Chicago, IL 60637-1514
    USA
    E-mail chenlei1991919@gmail.com
    Office E105 in Eckhart
    Advisor Benson Farb
    Here is my CV