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Mathematicians Solve Longstanding Four-Strand Braid Question
Joan Birman was a mathematician who wanted to keep doing maths after she retired.
In 2019, a 15-year-old student named Vasudha Bharathram contacted her for help.
Birman introduced her to braids, which are strands that cross over and under one another.
The two began studying a difficult question about how braids can be represented using algebra.
Later, mathematician Tara Brendle joined them.
The question concerned braids with four strands, a case that had remained unresolved.
Instead of checking many examples one by one, the team found a way to use a method involving five-strand braids.
They posted a paper about their work in July.
Joan Birman began mentoring 15-year-old Vasudha Bharathram in 2019 after the teenager asked for help with mathematics.
Bharathram and Birman later worked with mathematician Tara Brendle on a question about the Burau representation of braids.
The representation was known to be faithful for braids with three or fewer strands and unfaithful for those with five or more.
The team adapted a method from the three-strand case to study four-strand braids, avoiding an extensive case-by-case approach.
The collaborators posted a paper describing their work in July; the article does not specify the year.
- Who
- Mathematicians Joan Birman, Vasudha Bharathram, and Tara Brendle.
- What
- They developed a proof concerning the faithfulness of the Burau representation for four-strand braids.
- Where
- Their work included meetings at Birman's apartment in New York and online meetings over Zoom.
- When
- Birman and Bharathram began working together in 2019; the paper was posted in July, with no year specified.
- Why
- They investigated whether the Burau representation preserves enough information to distinguish four-strand braids.
Key facts
- Mentorship began
- Summer 2019, when Bharathram was 15.
- Mathematicians
- Joan Birman, Vasudha Bharathram, and Tara Brendle.
- Research topic
- The faithfulness of the Burau representation.
- Three-strand case
- Known to be faithful.
- Five-or-more-strand cases
- Known to be unfaithful.
- Previously unresolved case
- Four-strand braids.
- Paper
- The collaborators posted their paper in July; the article does not give the year.
Quotes
Tara Brendle
Mathematician and former graduate student of Joan Birman who collaborated with Birman and Vasudha Bharathram
“the most satisfying moment of my mathematical career”
telegraphindia.com




