Date/Time : 18 Jan 2019 10:00
Venue : S17 #04-04 SR3
Speaker : Tan Kai Meng, National University of Singapore

Despite its rich structure where combinatorics play an important role, the modular representation theory of the symmetric group is still not at all well understood. Many fundamental questions remain open to this day. Perhaps the most famous among them is the complete determination of its decomposition numbers. The advent and development of the Khovanov-Lauda-Rouquier algebras in the last decade shows that the symmetric group algebras can be non-trivially Z-graded, giving rise to graded decomposition numbers and providing new understanding to the old decomposition numbers. On the other hand, the announcement of counterexamples to James’s conjecture by Williamson ensures that the decomposition numbers remain as mysterious as ever, if not more. The talk will briefly survey the developments and describe my contributions to this elusive open problem.

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Date/Time : 23 Nov 2018 15:00
Venue : S17 #04-06 SR1
Speaker : Pang Chin How, Jeffrey, National University of Singapore

I will talk about my work on designing a distributed optimization algorithm based on dual ascent (or Dykstra’s splitting) that is asynchronous, decentralized, and has deterministic convergence. We also discuss the extension to the case of directed unreliable edges, and on using majorizations so that one can use subgradients approximations or outer approximations of constraint sets to simplify subproblems to be solved. We also studying convergence rates. I will then describe how I had started working on this area after noticing a heuristic for improving the convergence of the method of alternating projections.

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Date/Time : 12 Nov 2018 16:00
Venue : S17 #04-06 SR1
Speaker : Dilip Raghavan, National University of Singapore

I will summarize some of my work on three connected topics in set theory. The work on cardinal invariants covers both countable and uncountable cardinals, and it includes both ZFC theorems and consistency results. The work on special subsets of real numbers concentrates on techniques for constructing ultrafilters and almost disjoint families. The work on partition calculus includes results in both structural Ramsey theory and partition relations at uncountable ordinals. I will provide the necessary background to understand these results.

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