Oleg Lazarev

I am an Assistant Professor in the mathematics department at the University of Massachusetts Boston. Previously I was an NSF postdoctoral research fellow at Columbia during 2017-2020. My work is partially supported by NSF grant DMS-2305392 from 2023-2026.

I study symplectic geometry, using techniques from category theory, geometric topology, and dynamical systems, and conversely use symplectic geometry to study these areas. My research focuses on unifying symplectic flexibility (h-principles) with symplectic rigidity (Floer theory), leading to new structural results for the Fukaya category and connections to algebraic K-theory, Anosov dynamical systems, and rational homotopy theory.

Curriculum Vitae.

Email: oleg.lazarev -at- umb.edu

Recent Papers and preprints.

• Relating categorical dimensions in topology and symplectic geometry (with A. Hanlon, J. Hicks). Preprint. p. 1-38.


• The Floer theory of Anosov flows in dimension three (with K. Cieliebak, T. Massoni, A. Moreno). Preprint. p. 1-60.


• The infinity-category of stable Liouville sectors (with Z. Sylvan and H. Tanaka). Preprint. p. 1-135.


• Localization and flexibilization in symplectic geometry (with Z. Sylvan and H. Tanaka). Preprint. p. 1-63.


• Resolutions of toric subvarieties by line bundles and applications (with A. Hanlon, J. Hicks). To appear in Forum of Mathematics, Pi. p. 1-63.


• Weinstein presentations for high-dimensional antisurgery (with I. Datta, C. Mohanakumar, A. Wu). To appear in Algebraic and Geometry Topology. p. 1-28.


• Prime-localized Weinstein subdomains (with Z. Sylvan). Geometry and Topology. 27(2) 699–737 (2023).


• Symplectic flexibility and the Grothendieck group of the Fukaya category. Journal of Topology. 15(1) 204-237 (2022). (previously called Geometric and algebraic presentations of Weinstein domains).


• Maximal contact and symplectic structures. Journal of Topology, 13(3), 1058-1083 (2020).


• H-principles for regular Lagrangians. Journal of Symplectic Geometry, 18(4), 1071–1090 (2020).


• Simplifying Weinstein Morse functions. Geometry and Topology, 24, 2603-2646 (2020).


• Contact manifolds with flexible fillings. Geometric and Functional Analysis, 30, 188–254 (2020).


• Flexible Lagrangians (with Y. Eliashberg and S. Ganatra). International Mathematics Research Notices, 8, 2408 - 2435 (2020).

Older Papers (mostly number theory).

• A smooth, complex generalization of the Hobby-Rice theorem (with E. Lieb). Indiana University Mathematics Journal, 62(4): 1133--1141, (2013).
• An extension of a proof of the Ramanujan congruences for multipartitions (with M. Mizuhara, B. Reid, and H. Swisher). Ramanujan Journal, 45(1): 1--20, (2018).
• Maass waveforms and low-lying zeros (with L. Alpoge, N. Amersi, G. Iyer, S. Miller, and L. Zhang). Analytic number theory, 19--55, (2015).
• Distribution of missing sums in sumsets (with S. Miller and K. O'Bryant). Experimental Mathematics, 22(2): 132--156, (2013).
• Generalized more sums than differences sets (with G. Iyer, S. Miller, and L. Zhang). Journal of Number Theory, 132(5): 1054--1073, (2012).
• Finding and counting MSTD sets (with G. Iyer, S. Miller, and L. Zhang). Combinatorial and Additive Number Theory: CANT 2011 and 2012, 79--98, (2014).
• A combinatorial proof of a recursive formula for multipartitions, (with H. Swisher). Integers 12(1): 113--127, (2012).

Videos and slides.

• A symplectic geometric view on syzygies. Syzygies and Mirror symmetry seminar. October 2024.
• Flexibility and rigidity in contact and symplectic geometry (general audience talk). The Haitian Scientific Society. April 2023.
• Floer invariants of Anosov flows on 3-manifolds. Montreal symplectic seminar, December 2022.
• Localization and flexibilization in symplectic geometry. IAS workshop "H-principles and beyond," November 2021.
• Inverting primes in Weinstein geometry. Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry. Slides.
• Weinstein geometry of cotangent bundles. Western Hemisphere Virtual Symplectic Geometry Seminar, May 2020. Slides.
• Simplifying Weinstein Morse functions. Low-dimensional topology and its interactions with symplectic geometry conference, Princeton.
• Constructions in symplectic and contact topology via h-principles. Princeton/IAS symplectic geometry seminar.
• Flexibility in contact and symplectic geometry. Columbia Graduate Student Colloquium.
• Euler characteristic (and the unity of mathematics). Stanford SPLASH, talk for high school students.

Research with undergraduates.

• In summer 2016, I co-advised (with Ben Dozier) three Stanford undergraduates, as part of the Stanford Undergraduate Research Institute in Mathematics (SURIM). Their project was on Mapping Class Groups and Lefschetz Fibrations.
• In 2023, I advised Jack Pierce in his honors thesis at UMass Boston. His project was on Constrained Motion Spaces of Robotic Arms.

Seminars and conferences.

• I co-organize the UMass Boston Math Department seminar.
• Early-career workshop for symplectic geometers.
• From 2017-2020, I co-organized the Columbia symplectic geometry, gauge theory, and categorification seminar.
• In June 2017, I co-organized the Kylerec graduate student workshop.