Pengyu Liu

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

• A tree distinguishing polynomial
  Preprint: arXiv:1904.03332
• Polynomial phylogenetic analysis of tree shapes
  With Matthew Gould and Caroline Colijn
  DOI: 10.1101/2020.02.10.942367
  Preprint: bioRxiv

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
• 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

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.

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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Elements

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