Sylvester Eriksson-Bique

I am a NSF Postdoctoral Fellow at University of California, Los Angeles. I grew up in Finland and graduated with a M.Sc. from University of Helsinki, and a Ph.D from Courant Institute, New York University. I am facinated by many types of geometric problems in mathematics and computer science. Specifically about how analytic properties and the geometry of the space interact - in a smooth and fractal context. Also, I love teaching and finding new ways of explaining things. I pursue volunteer tutoring opportunities where I can support students from disadvantaged backgrounds to realize their full potential. Currently I tutor at HOLA -- Hear of Los Angeles in their LEAL program. On my free time I love to go on spontaneous road trips, or walk in a pine forest.

Currently, with the lead of Mario Bonk, and jointly with Annina Iseli and Mikhail Hlushchanka, we are organizing a virtual and international Research seminar "Quasiworld". To see more details, consult the website Quasiworld. We have an email list, which you can join through the website, or contact one of the organizers for assistance. This seminar is on quasiconformal analysis, complex dynamics and analysis on metric spaces.

For videos to my current class Math 131B, Real analysis, consult my youtube playlist for the class here.

Together with Alex Austin we organized a special session at the AMS Western and Central sectional meeting at the University of Manoa in Hawaii with the title "Special Session on Topics at the Interface of Analysis and Geometry", whose website is here.

I am available to tutor most topics in mathematics from high-school level to graduate level and research mathematics. Contact me by email if you are interested. Sometimes I may be able to do it pro bono.

Quick links

Links to my most recent papers. See also The up to date arxiv list or the google scholar page, which include more up to date information.

  1. Classifying Poincare inequalities and the local geometry of RNP-differentiability spaces, GAFA, 2019
  2. Regular mappings and non-existence of bi-Lipschitz embeddings for slit carpets, joint with Guy C David, Advances in Mathematics, 2019
  3. Self-improvement of weighted pointwise inequalities on open sets, joint with Juha Lehrbäck and Antti V. Vähäkangas, submitted 2019
  4. Pointwise inequalities for Sobolev functions on outward cuspidal domains, joint with Pekka Koskela, Jan Maly and Zheng Zhu, submitted 2019.
  5. Thin Loewner carpets and their quasisymmetric embeddings in S2, Joint with Jeff Cheeger, submitted, 2020.
  6. Almost uniform domains and Poincaré inequalities, joint with Jasun Gong, 2020.
  7. Self-improvement of pointwise Hardy inequality, joint with Antti V. Vähäkangas, Trans. Amer. Math. Soc.(2019)
  8. Asymptotic behavior of BV functions and sets of finite perimeter in metric measure spaces. Joint with James T. Gill, Panu Lahti, Nageswari Shanmugalingam. submitted, 2018
  9. Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a 1-Poincaré inequality, joint with Estibalitz Durand-Cartagena, Riikka Korte, Nageswari Shanmugalingam, Advances in Calculus of Variations 2019.
  10. Alternative proof of Keith-Zhong self-improvement and Conenctivity. Ann. Acad. Sci. Fenn. Alternative version with a different argument may be of interest, see here
  11. Quantitative Bi-Lipschitz embeddings of bounded curvature manifolds and orbifolds, Geometry and Topology 2018.
  12. Geometric k shortest paths, joint with J. Hershberger, V. Polishchuk, B. Speckmann, S. Suri, T. Talvitie, K. Verbeek, H. Yıldız. Soda 2015.
  13. Optimal geometric flows via dual programs, joint with V. Polishchuk, M. Sysikaski. SoCG 2014
  14. Optimization schemes for protective jamming, (minor contribution) joint with S. Sankararaman, K. Abu-Affash, A. Efrat, V. Polishchuk, S. Ramasubramanian, M. Segal. MobiHoc 2012.
  15. On Polygonal Paths with Bounded Discrete-Curvature: The Inflection-Free Case, joint with D. Kirkpatrick, V. Polishchuk. JCDCGG 2014.
  16. Optimizing Geometric Flows, coauthored with Mikko Sysikaski and Valentin Polishchuk.
  17. Disseration: Quantitative Embeddability and Connectivity in Metric spaces
  18. Importance Sampling for a Monte Carlo Matrix Multiplication Algorithm, with Application to Information Retrieval , coauthored with Mary Solbrig, Michael Stefanelli, Sarah Warkentin, Ralph Abbey and Ilse Ipsen.

Below is a small list of more expository notes and my CV.


  • "Γίνεσθε οὖν φρόνιμοι ὡς οἱ ὄφεις καὶ ἀκέραιοι ὡς αἱ περιστεραί."

Some Links