Jeremy Lane

Curriculum Vitae

Experience

• Applied Scientist II, Amazon, New York, NY. Aug 2022 – Current
• Postdoctoral Fellow: Geometry and Topology, McMaster University, Department of Mathematics and Statistics, Hamilton, ON. Sept 2019 – Aug 2022
  • Advisor: Prof. Megumi Harada.
• Postdoctoral Fellow, The Fields Institute for Research in Mathematical Sciences, Toronto, ON. Jan 2020 – June 2020
  • Cross-appointed with McMaster for the Thematic Program on Toric Topology and Polyhedral Products.
• Postdoctoral Fellow, University of Geneva, Section of Mathematics, Geneva, Switzerland. Sept 2017 – Aug 2019
  • Advisor: Prof. Anton Alekseev.
• Course Instructor and Course Coordinator, University of Toronto, Department of Mathematics. Summer 2016 – Spring 2017

Education

• PhD, Mathematics University of Toronto, Toronto, ON. Spring 2017
  • Advisor: Prof. Yael Karshon.
  • Thesis title: On the topology of collective integrable systems.
  • NSERC Postgraduate Scholarship and Ontario Graduate Scholarships totalling $78,000 CAD.
  • 4.0 GPA
• MSc, Mathematics University of Toronto, Toronto, ON. Summer 2013
  • NSERC Postgraduate Scholarship, $17,500 CAD.
  • 3.96 GPA
• BSc Hons, Mathematics University of Regina, SK. Summer 2012
  • Published research paper on homological algebra.
  • NSERC Undergraduate Student Research Award recipient. Wrote monograph on hyperelliptic surfaces.
  • TRIUMF particle accelerator student researcher. Developed Monte Carlo simulations of photon detectors with C++ and ROOT.
  • 4.0 GPA

Selected Research Papers

Note: All co-authorships are in alphebetical order, representing equal contributions from co-authors.

[1] Alekseev, Hoffman, Lane, Li. Action-angle coordinates on coadjoint orbits and multiplicity free spaces from partial tropicalization. Advances in Mathematics. 2023.

[2] Lane. Local normal forms for multiplicity free U(n) actions on coadjoint orbits. Pacific Journal of Mathematics. 2021.

[3] Carlson, Lane. The topology of Gelfand-Zeitlin fibers. In submission. 2021.

[4] Alekseev, Hoffman, Lane, Li. Concentration of symplectic volumnes on Poisson homogeneous spaces. Journal of Symplectic Geometry. 2020.

[5] Hoffman, Lane. Stratified Gradient Hamiltonian Vector Fields and Collective Integrable Systems. In submission. 2020.

[7] Lane. The geometric structure of symplectic contraction. International Mathematics Research Notices. 2020.

[8] Alekseev, Lane, Li. The U(n) Gelfand–Zeitlin system as a tropical limit of Ginzburg–Weinstein diffeomorphisms. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2018.

[9] Lane. Convexity and Thimm’s trick. Transformation Groups. 2018.

[10] Lane. Topological monodromy of an integrable Heisenberg spin chain. SIGMA Symmetry, Integrability and Geometry: Methods and Applications. 2015.

Google Scholar, ArXiv

Selected Invited Presentations

• Minicourse on Gelfand-Tsetlin systems and Poisson-Lie groups, NRU HSE Moscow. 2021.
• Canadian Mathematical Society Summer Meeting. 2021.
• Edinburgh Geometry (EDGE) seminar, Edinburgh Hodge Institute. 2021.
• Topology and Geometry seminar, Imperial College London. 2020.
• Symplectic and Poisson geometry Seminar, University of Illinois at Urbana-Champaign. 2020.
• Symplectic Joint Seminar in Rio, IMPA, UFRJ, UFF and PUC-Rio. 2020.
• Algebraic Topology Seminar, Princeton. 2020.
• Workshop on Torus Actions in Topology, The Fields Institute. 2020.
• Gone Fishing Meeting on Poisson Geometry, Georgia Southern University. 2020.
• Lie Groups Seminar, Cornell University. 2020.
• Geometry, Physics, and Representation Theory Seminar, Northeastern University. 2020.
• Geometry and Physics Seminar, Center Of Mathematical Sciences And Applications, Harvard.
• Toric Topology Research Seminar, The Fields Institute. 2020.
• Finite dimensional systems in geometry and mathematical physics, Shanghai Jiao Tong University. 2019.
• Canadian Mathematical Society Summer Meeting. 2019.
• Workshop on cluster algebras, crystal bases, and Poisson geometry, University of Hong Kong. 2018.
• Geometric aspects of momentum maps and integrability, Ascona, Switzerland. 2018.
• Algebraic Structures in Topology and Geometry (conference), Riederalp, Switzerland. 2018.
• Symplectic Seminar. Centre Interuniversitaire de Recherches Géométrie et Topologie, Montreal. 2018.
• Symplectic Geometry Seminar, University of Toronto. 2018.
• Interactions between symplectic geometry, combinatorics, and number theory (seminar), University of Cologne. 2018.
• Canadian Mathematical Society Winter Meeting. 2016.
• Integrable Systems, Ascona, Switzerland. 2016.
• Topology seminar, Cornell University. 2016.
• Canadian Mathematical Society Winter Meeting. 2015.
• Workshop on Recent Developments in the Geometry and Combinatorics of Hessenberg Varieties, The Fields Institute. 2015.
• Canadian Mathematical Society Winter Meeting. 2014.

Leadership and Volunteer Work

• 2020 - 2021 Supervised an undergraduate Summer research project resulting in a publication.
• 2020 Organized an online international research workshop with 25 speakers and more than 200 registered participants in 2 months in response to conference cancellations at the beginning of the covid-19 pandemic. Secured support from the Fields Institute.
• 2015 - 2020 Chaired and organized research seminars at the University of Toronto, University of Geneva, and the Fields Institute.
• 2015, 2016 Lead learning sessions at Canada Math Camp, University of Toronto.
• 2009 - 2012 Volunteer and executive of the University of Regina chapter of Engineers Without Borders Canada.

Teaching

• 2022 Calculus II.
• 2021 Introduction to Mathematical Reasoning, Advanced Calculus II.
• 2020 Undergraduate Combinatorics.
• 2019 Calculus I, Undergraduate Graph Theory.
• 2017 - 2019 Complex analysis, general mathematics, programming labs in MATLAB, Maple, and R.
• 2017 Linear Algebra I, Calculus I.
• 2016 Linear Algebra I.

A sample teaching materials is available on github. A sample of teaching feedback is available on RateMyProf.

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Github, ArXiv, Google Scholar, LinkedIn