F-S indicator: I am working on the Frobenius-Schur indicator of representations of division algebras over local field. This mainly depends on Prof. D. Prasad and Prof. D. Ramakrishnan's work "Self-dual representations of division algebras and Weil groups: a contrast".
Geometric trace formula: I am very interested in Prof. E. Frenkel and Prof. B. C. Ngo's work "geometrization of trace formulas" and hope to work on it in the near future.
Free probability and Hecke operator: Back earlier, I have worked on connecting the free probability and Hecke algebra, my math Master thesis was a baby step on that and I still like to think about it.
Tachyon, dark matter and dark energy: Earlier and earlier, I finished a physics Master degree with a research on the effect of tachyons on the early universe. I may explore more about this in the future.