Research

My research projects lie in the fields of mathematics, biology and data science. I am interested in introducing and developing new mathematical methods for biology and medicine. Specifically, my current projects include developing methods based on discrete mathematics, topology and geometry for phylogenetics, genomics and molecular biology, aiming to help solve problems in epidemiology, public health and medicine.


Polynomial phylogenetic analysis

In this project, we introduce graph polynomials for phylogenetic analysis. We define a polynomial that uniquely represents trees and use the polynomial with statistical and machine learning tools to solve problems in phylogenetics and evolutionary biology, which shows that graph polynomials are promising methods for phylogenetic analysis and for other related tasks.

Publications

Invited 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.
    June 2019
  • A tree distinguishing polynomial - an introduction to polynomial tree metrics
    CanaDAM 2019, Simon Fraser University, Vancouver, BC.
    May 2019

Monte-Carlo kDNA Model

Kinetoplast DNA or kDNA is a network of circular DNA in a mitochondrion of the organisms kinetoplastids, which include parasites that cause serious diseases like African sleeping sickness and Chagas disease. We develop a Monte-Carlo based model for the kDNA network using tools based on topology and discrete mathematics, aiming to study the structures and the mechanisms of the mitochondrial DNA.

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
  • Characterizing the topology of kinetoplast DNA using random knotting
    With Ryan Polischuk, Yuanan Diao and Javier Arsuaga
    Topology and Geometry of Biopolymers, Contemporary Mathematics
    DOI: 10.1090/conm/746

Invited Conference Talks

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

Braid indices of alternating links

In this project, we solved a long-standing problem in knot theory. We fully characterized the alternating links whose braid indices equal the number of Seifert circles in their reduced diagrams. We also conjectured that for any alternating link, its braid index equals the difference of the number of Seifert circles in its reduced diagram and its reduction number. We proved the conjecture is true for a large class of alternating links including Montesinos 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
  • 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
  • A diagrammatic approach for determining the braid index of alternating links
    With Yuanan Diao, Claus Ernst and Gábor Hetyei
    To appear in Journal of Knot Theory and Its Ramifications
    Preprint, arXiv:1901.09778

Invited 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.
    November 2017
  • The braid index of reduced alternating links
    AMS Sectional Meeting, University of Saint Thomas, Minneapolis, MN.
    October 2016
  • The HOMFLY polynomial of links in closed braid form
    Workshop on Graphs and Knots, Xiamen University, Xiamen, China.
    June 2016

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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