Research Interest

My research seeks to uncover and understand the geometrical and topological data that characterize manifolds. My current work has focused on developing some novel cohomologies of differential forms as new tools for analyzing symplectic manifolds. I am also interested in applications of geometrical structures in theoretical physics.

I welcome inquiries from excellent undergraduate and graduate students who are interested in doing research projects in geometry, topology and mathematical physics.

Teaching

Fall 2024
Math 218A: Introduction to Manifolds and Geometry

Outreach

I am the co-director of the UC Irvine Math CEO (Community Educational Outreach) program, a transformative afterschool program that promotes college education and STEM careers to underserved youth in Southern California. I co-founded the program with Alessandra Pantano in 2014.

Papers

• L.-S. Tseng and J. Zhou, "Mapping cone connections and their Yang-Mills functional," arXiv:2407.01508 (submitted). pdf
• D. Clausen, X. Tang, and L.-S. Tseng, "Mapping cone and Morse theory," arXiv:2405.02272 (submitted). pdf
• D. Clausen, X. Tang, and L.-S. Tseng, "Symplectic Morse theory and Witten deformation," arXiv:2211.11712 (submitted). pdf
• L.-S. Tseng and J. Zhou, "Symplectically flat connections and their functionals," arXiv:2210.03032. pdf
• L.-S. Tseng and J. Zhou, "Symplectic flatness and twisted primitive cohomology," J. Geom. Anal. 32, 282 (2022). pdf
• M. Gibson, L.-S. Tseng and S. Vidussi, "Symplectic structures with non-isomorphic primitive cohomology on open 4-manifolds," Trans. Amer. Math. Soc. 375 (2022), no. 12, 8399-8422. pdf
• L.-S. Tseng and L. Wang, "Symplectic boundary conditions and cohomology," J. Differential Geom. 122 (2022) 271-340. pdf
• L.-S. Tseng and L. Wang, "Symplectic analysis of differential forms," in Proceedings of the International Consortium of Chinese Mathematicians, 2018: Second Annual Meeting, 351-366, International Press, Boston (2020). pdf
• H. L. Tanaka and L.-S. Tseng, "Odd sphere bundles, symplectic manifolds, and their intersection theory," Camb. J. Math. 6, (2018) no. 3, 213-266. pdf
• L.-S. Tseng, "Cohomologies on symplectic manifolds," in Proceedings of the 6th International Congress of Chinese Mathematicians, 119--127, Advanced Lectures in Mathematics, 37, Higher Education Press and International Press, Beijing-Boston (2016). pdf
• C.-J. Tsai, L.-S. Tseng, and S.-T. Yau, "Cohomology and Hodge theory on symplectic manifolds: III," J. Differential Geom. 103 (2016) 83-143. pdf
• S.-C. Lau, L.-S. Tseng, and S.-T. Yau, "Non-Kaehler SYZ mirror symmetry," Comm. Math. Phys. 340 (2015) 145-170. pdf
• L.-S. Tseng and L. Wang, "Hodge theory and symplectic boundary conditions," arXiv:1409.8250. pdf
• L.-S. Tseng and S.-T. Yau, "Generalized cohomologies and supersymmetry," Comm. Math. Phys. 326 (2014) 875-885. pdf
• C.-J. Tsai, L.-S. Tseng, and S.-T. Yau, "Symplectic cohomologies on phase space," J. Math. Phys. 53 (2012) 095217. pdf
• L.-S. Tseng and S.-T. Yau, "Cohomology and Hodge theory on symplectic manifolds: II," J. Differential Geom. 91 (2012) 417-443. pdf
• L.-S. Tseng and S.-T. Yau, "Cohomology and Hodge theory on symplectic manifolds: I," J. Differential Geom. 91 (2012) 383-416. pdf
• L.-S. Tseng and S.-T. Yau, "Non-Kaehler Calabi-Yau manifolds," in Strings Math 2011, 241-254, Proceedings of Symposia in Pure Mathematics, 85, Amer. Math. Soc., Providence, RI (2012). pdf
• L.-S. Tseng, "Cohomologies and elliptic operators on symplectic manifolds," in Fifth International Congress of Chinese Mathematicians Part 1, 341-354, AMS/IP Stud. Adv. Math., 51, Amer. Math. Soc., Providence, RI (2012). pdf
• M. Becker, L.-S. Tseng, and S.-T. Yau, "New heterotic non-Kaehler geometries," Adv. Theor. Math. Phys. 13 (2009) no. 6, 1815-1845. pdf
• J.-X. Fu, L.-S. Tseng, and S.-T. Yau, "Local heterotic torsional models," Comm. Math. Phys. 289 (2009) no. 3, 1151-1169. pdf
• L.-S. Tseng, "Heterotic geometry and fluxes," in Advances in String Theory, 101-108, AMS/IP Stud. Adv. Math., 44, Amer. Math. Soc., Providence, RI (2008). pdf
• M. Becker, L.-S. Tseng, and S.-T. Yau, "Heterotic Kaehler/non-Kaehler transitions," Adv. Theor. Math. Phys. 12 (2008) no. 5, 1147-1162. pdf
• M. Becker, L.-S. Tseng, and S.-T. Yau, "Moduli space of torsional manifolds," Nucl. Phys. B786 (2007) no. 1-2, 119-134. pdf
• K. Becker, M. Becker, J.-X. Fu, L.-S. Tseng, and S.-T. Yau, "Anomaly cancellation and smooth non-Kaehler solutions in heterotic string theory," Nucl. Phys. B751 (2006) 108-128. pdf
• K. Becker and L.-S. Tseng, "Heterotic flux compactifications and their moduli," Nucl. Phys. B741 (2006) 162-179. pdf
• K. Becker and L.-S. Tseng, "A note on fluxes in six-dimensional string theory backgrounds," Nucl. Phys. B707 (2005) 43-55. pdf
• K. Okuyama and L.-S. Tseng, "Three-point functions in N=4 SYM theory at one-loop," J. High Energy Phys. 0408 (2004) 055. pdf
• L.-S. Tseng, Virasoro Branes and Asymmetric Orbifolds, Ph.D. Thesis, UMI-31-08121 (2003).
• L.-S. Tseng, "SL(2,Z) multiplets in N=4 SYM theory," J. High Energy Phys. 0301 (2003) 071. pdf
• L.-S. Tseng, "A note on c=1 Virasoro boundary states and asymmetric shift orbifolds," J. High Energy Phys. 0204 (2002) 051. pdf
• L.-S. Tseng, "Noncommutative solitons and intersecting D-branes," Phys. Rev. D64 (2001) 126004. pdf
• E. D. Carlson and L.-S. Tseng, "Pseudoscalar conversion and X-rays from the sun," Phys. Lett. B365 (1996) 193-201. pdf

Links

• 30th Southern California Geometric Analysis Seminar, February 8-9, 2025, at UC Irvine
• UC Irvine Math CEO (Community Educational Outreach)
• Department of Mathematics, UC Irvine
• University of California Irvine