Caleb McFarland, TBA
- Series
- Graph Theory Seminar
- Time
- Tuesday, October 20, 2026 - 15:45 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Caleb McFarland – Georgia Tech
TBA
TBA
TBA
TBA
TBA by Xilu Zhu
TBA
The dual Garside left canonical form is used to solve the conjugacy problem in braid theory, introduced by Xu (3-braids), Kang-Ko-Lee (4-braids) and Birman-Ko-Lee (n-braids). The fractional Dehn twist coefficient (FDTC) is a measurement of the boundary twist of a surface homeomorphism, introduced by Honda-Kazez-Matic. In contact geometry, it is a powerful tool to detect tightness/overtwistedness of a given contact structure. In this talk, I will give applications of the left canonical form to the computation of the FDTC of 4-braids.
Motivated by applications and the classical theory of A-discriminants of Gel'fand, Kapranov, and Zelevinsky, we develop the basic theory of discriminants of multivariate reciprocal polynomials. These reciprocal discriminants parameterize reciprocal polynomials that define a singular hypersurface. We show that a reciprocal discriminant has a rich combinatorial structure. It is a reducible hypersurface whose components are dual varieties to Chebyshev subvarieties which correspond to certain layers in a toric arrangement associated to the exponents of the reciprocal polynomials. The layers which contribute correspond to certain matroidal decompositions of the exponents.
This is joint work with Trevor Karn and Simon Telen.