2022 Research Experience for Undergraduates at the University of Alabama

Topology: Knots, 3- and 4 manifolds

Dates: June 6-July 18, 2022
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Our Team

Mentors:
​The program was managed by UA mathematics professors Bülent Tosun and Subhankar Dey. 

Student participants:
Veronica King (UT Austin)
Colby Shaw (Georgia Tech)
Audrick Pyronneau (University of West Alabama)
Nicolas Fontova (University of Georgia Athens)​

Activities​

Week 1: June 8 Peter Jackson (University of Virginia/Michigan State University).
Professional Development Talk on “A tutorial on Latex and Drawing Programs”

Week 2: June 15 Lisa Traynor (Bryn Mawr).
Professional Development Talk on “TAing and Teaching”
Research Talk on “Legendrian knot theory”

Week 3: June 22 John Etnyre (Georgia Institute of Technology).
Professional Development Talk on “Preparing and Applying for Graduate Schools”
Research Talk on “Exotic world of 4-manifolds”

Week 4: June 29 Graduate Student Panel: Lawford Hatcher (Indiana University, Bloomington), Blake Jackson (University of Alabama), Marie Neubrander (Duke University)

Week 6: July 13 Swatee Naik (National Science Foundation)
Professional Development Activity on “Fellowship opportunities at NSF”
Research Talk on “Knot concordance and periodicity”

More pictures​

From left to right:

  • Veronica and Colby: A proud moment. They found Fibonacci numbers as a key ingredient for their work. These numbers are really everywhere!
  • A group discussion
  • Audrick and Nico: formulating the right question
  • A group photo in front of the math building

Projects/Results

  • Veronica King and Colby Shaw: Unknotted curves on Seifert surfaces.

A poster was prepared and presented at a poster session at Georgia Tech (July 20, 2022).
A paper is in preparation. 

UPDATE: A resulting paper, “Unknotted curves on genus one Seifert surfaces of Whitehead doubles” is available on arxiv:2307. 04313, and the paper is accepted to appear in Pacific Journal of Mathematics.

  • ​​Audrick Pyronneau and Nicolas Fontova: On Fox’s conjecture and quasi-alternating knots

A poster was prepared and presented at a poster session at Georgia Tech (July 20, 2022).
A paper is in preparation. 

More Updates
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  • Audrick started his PhD studies at UT at Austin in Fall 2023.
  • Nico started his PhD studies at NC State in Fall 2023.
  • Veronica is spending 2023-2024 in Germany as a Fulbright fellow. 
  • Colby is in the process of applying to graduate schools.
  • Dr. Dey started a postdoctoral fellowship at Durham University in Fall 2023.