Department of Mathematics & Statistics
Hamilton Hall, Room 218
1280 Main Street West
Hamilton, Ontario, L8S 4K1, Canada
- Online seminars, workshops, and conferences
- About me
- Fall 2020. MATH 3U03, Combinatorics. Students can find the course on Avenue to Learn.
- Winter 2021. MATH 2XX3, Advanced Calculus II.
- Fall 2019. MATH 3V03, Graph Theory.
- Fall 2019. MATH 1A03, Calculus.
I really like integrable systems, group actions, and symplectic/Poisson manifolds.
Hoffman, Lane. Canonical bases and collective integrable systems. 59 pages. arXiv.
Alekseev, Hoffman, Lane, Li. Action-angle coordinates on coadjoint orbits and multiplicity free spaces from partial tropicalization. Submitted, 66 pages. arXiv.
Lane. Local normal forms for multiplicity free U(n) actions on coadjoint orbits. Submitted, 16 pages. arXiv.
Alekseev, Hoffman, Lane, Li. Concentration of symplectic volumes on Poisson homogeneous spaces. To appear in J. Symplectic Geom., 14 pages. arXiv.
- Alekseev, Lane, Li. The U(n) Gelfand-Zeitlin system as a tropical limit of Ginzburg-Weinstein diffeomorphisms. Philos. Trans. Roy. Soc. A., 376, 21 pages, 2018. arXiv. doi:10.1098/rsta.2017.0428.
- Lane. The geometric structure of symplectic contraction. Int. Math. Res. Not. IMRN, 19 pages, 2018. arXiv. doi:10.1093/imrn/rny122.
- Lane. Convexity and Thimm's trick. Transform. Groups, 23:963-987, 2018. arXiv. doi:10.1007/s00031-017-9436-7.
- Lane. Topological monodromy of an integrable Heisenberg spin chain. SIGMA Symmetry Integrability Geom. Methods Appl., 11, 18 pages, 2015. arXiv. doi:10.3842/SIGMA.2015.062.
- Lambrechts, Lane, Stanley. An example using improved Lefschetz duality. Chin. Ann. Math. Ser. B., 38:1269-1274, 2017. doi:10.1007/s11401-017-1035-3. (undergraduate work)
3. Online seminars, workshops, and conferences
Peter Crooks and I recently organized an online workshop at the Fields Institute. Video recordings of the presentations are now available on the Fields webpage by following the link to the individual talk.
The following is a list of currently running online seminars related to integrable systems and symplectic/Poisson geometry.
A more comprehensive list of online seminars can now be found at mathseminars.org!
4. About Me
I am a postdoctoral fellow at McMaster University. My advisors at McMaster are Megumi Harada and Adam Van Tuyl. Before coming to McMaster I was a postdoc for two years at the University of Geneva, Switzerland, working with Anton Alekseev. I graduated with my Ph.D. from the University of Toronto in 2017, where my advisor was Yael Karshon.
From January to June I am a visiting postdoctoral fellow at the Fields Institute's 2020 thematic program on Toric Topology and Polyhedal Products.