About me

I am a postdoctoral researcher at UCLA. I got my PhD at MIT, advised by Tom Mrowka.

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. On the Kronheimer-Mrowka concordance invariant, https://arxiv.org/abs/1908.05018

2. The Novikov conjecture, the group of volume preserving diffeomorphisms and Hilbert-Hadamard spaces (with Jianchao Wu and Guoliang Yu), https://arxiv.org/abs/1811.02086

3. Khovanov homology and binary dihedral representations for marked links, accepted, Journal of Geometry and Physics.

4. 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.

5. Finite part of operator K-theory for groups with rapid decay, Journal of Noncommutative Geometry, (2015) Volume 9, Issue 3, Pages 697-706.

6. 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.

7. On Congruence Conditions for Primality (with Scott Kominers), INTEGERS: The Electronic Journal of Combinatorial Number Theory, (2010) Volume 10, Issue 3, Pages 313-317.

8. 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:
- UCLA Math 182, Algorithms
- UCLA Math 110A, Abstract Algebra

Past teaching experience:
- UCLA Math 32a, Real analysis, Winter 2019.
- UCLA Math 31a, Single variable calculus, Fall 2018.
- UCLA Math 131a, Real analysis, Fall 2018, Spring 2019.
- TA for MIT course 18.02, multivariable calculus.


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: Math Sciences Building Room 6617A.
E-mail: sgongli at, like, math.ucla.edu
(Tips to help find Math Sciences offices: The first digit of an office number is the floor number. The second digit is the hallway number. On all floors, even hallways (meaning the 2nd digit of the office number is even) run north-south, odd ones run east-west. On the sixth floor, hallway numbers that are a multiple of three are in the western half of the building, non-multiples of three are in the eastern half. Within a hallway, numbers trend up as you go east or south, but this is just a general trend; it does not hold locally near my office.)