I am an Assistant Professor in the mathematics department at the University of Massachusetts Boston. I study symplectic and contact geometry, using techniques from geometric topology, category theory, homotopy theory, and dynamical systems. My research focuses on unifying symplectic flexibility and h-principles with rigidity and 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.
- Resolutions of toric subvarieties by line bundles and applications (with A. Hanlon, J. Hicks). Preprint. p. 1-63.
- 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. 1-105.
- Localization and flexibilization in symplectic geometry (with Z. Sylvan and H. Tanaka). Preprint. p. 1-53.
- Prime-localized Weinstein subdomains (with Z. Sylvan). To appear in Geometry and Topology. p. 1-29.
- 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.
- 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.
Teaching notes.
- Spring 2020, Introduction to algebraic topology.
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.
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.