Research

My research interests lie in the fields of topology, combinatorics and algebra. In particular, I study knot theory, graph theory and their applications in biology, physics and other sciences. I complete my Ph.D. in May 2018 under the direction of Yuanan Diao and Gábor Hetyei. At Simon Fraser University, I work with Caroline Colijn. We develop mathematical tools for phylogenetics and the study of infectious diseases.


Recently, I defined a polynomial for trees and proved that the polynomial is a complete invariant for unlabeled trees. This provides new methods for tree analysis.

Publications

Conference Talks

  • A tree distinguishing polynomial - an introduction to polynomial tree metrics
    SMB Annual Meeting, Université de Montréal, Montréal, QC.
    July 2019
  • A tree distinguishing polynomial - an introduction to polynomial tree metrics
    CAIMS Annual Meeting, Whistler, BC.
    Invited, June 2019
  • A tree distinguishing polynomial - an introduction to polynomial tree metrics
    CanaDAM 2019, Simon Fraser University, Vancouver, BC.
    May 2019

One of the projects I have been working on since graduate school is computing the braid index of links. We showed it is true for several classes of links that given an alternating diagram of a link, the braid index of the link equals the number of Seifert circles in the diagram minus the reduction number of the diagram and we conjectured it is true for all alternating links.

Publications

  • The braid index of reduced alternating links
    With Yuanan Diao and Gábor Hetyei
    Mathematical Proceedings of the Cambridge Philosophical Society
    DOI: 10.1017/S0305004118000907
    Preprint: arXiv:1701.07366
  • The HOMFLY polynomial of links in closed braid form
    With Yuanan Diao and Gábor Hetyei
    Discrete Mathematics
    DOI: 10.1016/j.disc.2018.09.027
    Preprint: arXiv:1604.06127
  • A diagrammatic approach for determining the braid index of alternating links
    With Yuanan Diao, Claus Ernst and Gábor Hetyei
    Preprint: arXiv:1901.09778

Conference Talks

  • A diagrammatic approach for determining the braid index of alternating links
    The Geometry and Topology of Knotting and Entanglement in Proteins, CMO-BIRS Workshop, Oaxaca, Mexico.
    Invited, November 2017
  • The braid index of reduced alternating links
    AMS Sectional Meeting, University of Saint Thomas, Minneapolis, MN.
    Invited, October 2016
  • The HOMFLY polynomial of links in closed braid form
    Workshop on Graphs and Knots, Xiamen University, Xiamen, China.
    Invited, June 2016

I have also been studying the kinetoplast DNA network. We develop mathematical models for the network and study its properties, especially topological properties

Publications

  • Estimating properties of kinetoplast DNA by fragmentation reactions
    With Lara Ibrahim, Yuanan Diao, Michele Klingbeil and Javier Arsuaga
    Journal of Physics A: Mathematical and Theoretical
    DOI: 10.1088/1751-8121/aaf15f

Conference Talks

  • Estimating properties of kinetoplast DNA by fragmentation reactions
    Workshop on Knotted Fields, Beijing University of Techonology, Beijing, China.
    September 2019

For more information about my research and my experience, see the curriculum vitae.

Curriculum Vitae

Events

5/28-5/31 SFU, Vancouver, BC

CanaDAM 2019

Canadian Discrete and Algorithmic Mathematics Conference


6/9-6/13 Whsitler, BC

CAIMS Annual Meeting 2019

The Annual Meeting of the Canadian Society of Applied and Industrial Mathematics


6/17-6/28 IMA, Minneapolis, MN

BAGEL 2019

Biology, Analysis, Geometry, Energies, Links:
A Program on Low-dimensional Topology, Geometry, and Applications


7/22-7/26 Montréal, QC

SMB Annual Meeting 2019

The Annual Meeting and Conference of the Society for Mathematical Biology


9/7-9/8 Beijing, China

Workshop on Knotted Fields

Knotted Field Theory with Applications in Physical and Biological Sciences

About

I am a postdoctoral fellow in the Department of Mathematics at Simon Fraser University. See the research page for more information. I also produce music and take photographs. To know more, read one of my random stories.

Contact

Pengyu Liu
Simon Fraser University
Department of Mathematics
8888 University Dr.
Burnaby, BC V5A 1S6.

Email
pengyuliu.math@gmail.com

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