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 : 17 Jan 2019 15:00
Venue : S17 #04-05 SR2
Speaker : Lee Ching-pei, University of Wisconsin-Madison

Date/Time:17 Jan 2019 15:00 Venue: S17 #04-05 SR2 Speaker: Lee Ching-pei, University of Wisconsin-Madison Convergence Rates for some Fundamental Algorithms for Continuous Minimization of functions that are a sum of a smooth part and a convex but possibly nonsmooth part that promotes regularization is prevalent in many ap- plication areas, and proximal-type methods are the most eective algorithms for such regularized optimization problems. In this talk, I will present our re- cent advancements on the convergence analysis of rst-order and second-order proximal-type methods for regularized optimization in [1, 2]. I will rst show that the long-known O(1/k) convergence rate on convex problems of gradient descent and coordinate descent in the function value is not tight and can be improved to o(1/k), and extend this result to proximal gradient and proximal coordinate descent for regularized optimization. The second part of this talk will focus on a general framework of inexact successive quadratic approxima- tion that has second-order proximal methods including proximal Newton and proximal quasi-Newton as special cases. Global convergence rates for strongly convex, convex, and nonconvex problems will be discussed. References: [1] Ching-pei Lee and Stephen J. Wright. First-order algorithms converge faster than O(1=k) on convex problems. Technical report, December 2018. URL http://www.optimization-online.org/DB_HTML/2018/12/6993.html. [2] Ching-pei Lee and Stephen J. Wright. Inexact successive quadratic approx- imation for regularized optimization. Computational Optimization and Ap- plications, 2019+. URL http://www.optimization-online.org/DB_HTML/ 2018/03/6499.html. Accepted. Add to calendar: 

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Date/Time : 16 Jan 2019 14:00
Venue : S17 #04-06 SR1
Speaker : Frank den Hollander, Leiden University, The Netherlands

Search algorithms on networks are important tools for the organization of large data sets. A key example is Google PageRank, which assigns a numerical weight to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of measuring its relative importance within the set. The weighting is achieved by exploration. The mixing time of a random walk on a random graph is the time it needs to approach its stationary distribution (also called equilibrium distribution). The characterisation of the mixing time has been the subject of intensive study. Many real-world networks are dynamic in nature. It is therefore natural to study random walks on dynamic random graphs. In this talk we focus on a random graph with rescribed degrees. We investigate what happens to the mixing time of the random walk when at each unit of time a certain fraction of the edges is randomly rewired. We identify three regimes in the limit as the graph becomes large: fast, moderate, slow dynamics. These regimes exhibit surprising behaviour. The talk is aimed at a general mathematics audience. No prior knowledge of probability theory or graph theory is required.

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Date/Time : 15 Jan 2019 15:00
Venue : S17 #04-05 SR2
Speaker : Leonard Huang , University of Nevada, Reno, USA

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Date/Time : 14 Jan 2019 15:00
Venue : S17 #04-05 SR2
Speaker : Bao Huanchen , University of Maryland (College Park)

Date/Time:14 Jan 2019 15:00 Venue: S17 #04-05 SR2 Speaker: Bao Huanchen, University of Maryland (College Park) From Schur-Weyl duality to quantum symmetric pairs The classical Schur-Weyl duality relates the representation theory of general linear Lie algebras and symmetric groups. Drinfeld and Jimbo independently introduced quantum groups in their study of exactly solvable models, which leads to a quantization of the Schur duality relating quantum groups of general linear Lie algebras and Hecke algebras of symmetric groups. In this talk, I will explain the generalization of the (quantized) Schur-Weyl duality to other classical types. This new duality leads to a theory of canonical bases arising from quantum symmetric pairs generalizing Lusztig’s canonical bases on quantum groups. Add to calendar: 

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Date/Time : 09 Jan 2019 14:30
Venue : S17 #04-06 SR1
Speaker : Ngo Bao Chau, The University of Chicago and Vietnam Institute for Advanced Study in Mathematics

Back to 2000, Braverman and Kazhdan formulate a program aiming at generalizing the Godement-Jacquet construction of principal L-function. We will recall their program with more precision and some modest progress.

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Date/Time : 09 Jan 2019 15:50
Venue : S17 #04-06 SR1
Speaker : Zhang Lei, National University of Singapore

Applying Arthur’s endoscopic classification of discrete automorphic representations for classical groups, we extend Ginzburg-Rallis-Soudry’s automorphic descent from quasi-split classical groups setting to their pure inner forms. Combining with the multiplicity-free results of local Gan-Gross-Prasad conjecture, we not just provide a concrete module construction of cuspidal automorphic representations from the sauce representations of general linear groups, but also prove one direction of global Gan-Gross-Prasad conjecture. Moreover, our study leads us to many fundamental questions on the Fourier coefficients of automorphic forms, which connect to the existence of nonvanishing twist central value of L-functions for instance.

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Date/Time : 02 Jan 2019 14:00
Venue : S17 #04-06 SR1
Speaker : Xu Jinchao, Penn State University

In this talk, I will discuss some mathematical relationships between deep neural networks, finite element and multigrid methods.

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Date/Time : 12 Dec 2018 14:00
Venue : S17 #04-06 SR1
Speaker : Alan Reid, Rice University

A consequence of Mostow-Prasad rigidity is that the trace-field of an orientable finite volume hyperbolic 3-manifold M is a number field. In addition, there is a quaternion algebra over this number field that is a natural invariant associated to M. This talk will review this background, and survey recent advances in trying to understand the trace-field and this quaternion algebra, especially in the setting of Dehn surgery on a hyperbolic knot.

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