If you are doing a geo problem and you can invert, do, because if you invert, now you have two problems, and if you can solve either of them, you're done, so you're twice as likely to succeed! (... Isn't that how probability works?)
About me
I am an assistant professor at Texas A&M University.
One of the areas I work in is the study of low dimensional topology via gauge theory. In particular, my research so far has related to monopole and instanton Floer homologies of links, and their relation (via spectral sequences) to the links' Khovanov homologies.
Another area I work in is operator theory and non-commutative geometry. In this area, I study certain properties of group C* algebras, looking, in particular, at the finite part of the K-theory of such groups.
You can find my CV here.
Papers
1. Families of metrics with positive scalar curvature on spectral sequence cobordisms, https://arxiv.org/abs/2310.02552, accepted, Journal of Topology and Analysis, 2023.2. Non-orientable link cobordisms and torsion order in Floer homologies (with Marco Marengon), Algebraic & Geometric Topology 23.6 (2023): 2627-2672.
3. On the Kronheimer-Mrowka concordance invariant, Journal of Topology, 2021 14(1):1- 28
4. The Novikov conjecture, the group of volume preserving diffeomorphisms and Hilbert- Hadamard spaces (with Jianchao Wu and Guoliang Yu), Geometric and Functional Analysis volume 31, pages206–267 (2021)
5. Khovanov homology and binary dihedral representations for marked links, Journal of Geometry and Physics (2019) Volume 140, Pages 214-245.
6. Property RD and the Classification of Traces on Reduced Group $C^*$-algebras of Hyperbolic Groups, Journal of Topology and Analysis, (2017) Volume 9, Issue 4, Pages 707-716.
7. Finite part of operator K-theory for groups with rapid decay, Journal of Noncommutative Geometry, (2015) Volume 9, Issue 3, Pages 697-706.
8. Computational approaches to Poisson traces associated to finite subgroups of Sp(2n,C) (with Pavel Etingof, Aldo Pacchiano, Qingchun Ren, and Travis Schedler), Experimental Mathematics, (2012) Volume 21, Issue 2, Pages 141-170.
9. On Congruence Conditions for Primality (with Scott Kominers), INTEGERS: The Electronic Journal of Combinatorial Number Theory, (2010) Volume 10, Issue 3, Pages 313-317.
10. On a problem regarding coefficients of cyclotomic polynomials, Journal of Number Theory, (2009) Volume 129, Issue 12, Pages 2883-3114.
Teaching and Outreach
Current teaching:I am currently only teaching reading courses with individual students.
Past teaching experience:
- TAMU Math 490, The Putnam Challenge, Fall 2023.
- TAMU Math 415, Modern Algebra, Fall 2023.
- TAMU Math 644, Algebraic Topology II, Spring 2023.
- TAMU Math 304, Linear Algebra, Fall 2021, Spring 2023.
- UCLA Math 182, Algorithms, Fall 2019.
- UCLA Math 110A, Abstract Algebra, Fall 2019.
- UCLA Math 32a, Real analysis, Winter 2019, Winter 2020.
- UCLA Math 31a, Single variable calculus, Fall 2018.
- UCLA Math 131a, Real analysis, Fall 2018, Spring 2019, Winter 2020.
- TA for MIT course 18.02, multivariable calculus.
Outreach:
- I am a co-founder and co-organizer of the PreMa high school research program.
- I am a co-founder and co-organizer of the G2 (Girls Together) Math Program.
- I am a co-organizer and instructor of the Texas A&M Math Circle.
- I am an on the editorial boards of the AIME and USA(J)MO.
Past Outreach:
- BEAM LA, a program to help low-income students from underserved communities learn advanced mathematics and enter a career in STEM fields. I have volunteered for this program to help run events, and am currently teaching an introductory programming class.
- Taught at Yau's Summer Camp for high school student at Tsinghua university, 2019.
- Taught multiple times at the Math Olympiad Program, a training program for the United States team to the International Mathematical Olympiad.
- Was the leader or deputy leader for the United States team to the European Girls' Math Olympiad 2012-2017.
- Have coached several Puerto Rican mathematical olympiad teams.
- Was leader of the Puerto Rican team to the Olimpiada Iberoamericana de Matematicas.
Contact
Office: Blocker Building, Room 342BA.E-mail: sgongli at, like, tamu.edu
Inversion