Date/Time : 30 Jan 2019 14:00
Venue : S17 #04-06 SR1
Speaker : Peter Forrester , University of Melbourne

Date/Time:30 Jan 2019 14:00 Venue: S17 #04-06 SR1 Speaker: Peter Forrester, University of Melbourne Decomposition of measure in random matrix theory and integral geometry Fundamental to random matrix theory is various factorisations of Lebesgue product measure implied by matrix change of variables. Factorisation of measure is also fundamental to integral geometry, with one of the most important results due to Blaschke and Petkantschin. Following recent work of Moghadasi, we show how the latter is related to matrix polar decomposition, and can be applied to the calculation of the moments of the volume content of the convex hull of random points in higher dimensional spaces. Applications to the computation of Lyapunov exponents will also be discussed. Add to calendar: 

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Date/Time : 28 Jan 2019 15:00
Venue : S17 #04-06 SR1
Speaker : Zhang Zhiyuan, Institute for Advanced Study

Date/Time:28 Jan 2019 15:00 Venue: S17 #04-06 SR1 Speaker: Zhang Zhiyuan, Institute for Advanced Study Zimmer’s conjecture for simple complex Lie groups We will discuss Zimmer’s conjecture on the actions of lattices in higher rank Lie groups on manifolds of small dimension. This conjecture is recently proved by Aaron Brown, David Fisher and Sebastian Hurtado for real split simple Lie groups. We discuss the proof of this conjecture for simple complex Lie groups. We also give significant improvements for the dimensional bounds for many other non-split Lie groups. This is a joint work with Jinpeng An and Aaron Brown. Add to calendar: 

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Date/Time : 26 Jan 2019 15:00
Venue : S17 #04-04 SR3
Speaker : Hsin-Ku Chen , National Taiwan University

Date/Time:26 Jun 2019 15:00 Venue: S17 #04-04 SR3 Speaker: Hsin-Ku Chen, National Taiwan University Threefolds of Kodaira dimension one We prove that for any smooth complex projective threefold of Kodaira dimension one, the m-th pluricanonical map is birational to the Iitaka fibration for every m >= 5868 and divisible by 12. Add to calendar: 

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Date/Time : 24 Jan 2019 16:00
Venue : S17 #05-12 SR4
Speaker : Xia Chao, Xiamen University

Date/Time:24 Jan 2019 16:00 Venue: S17 #05-12 SR4 Speaker: Xia Chao, Xiamen University Stability on two types of partitioning problems In this talk, two geometric variational problems, so-called partitioning problems for convex domains will be discussed. Type-I is on area minimizing hypersurfaces with volume constraint and Type-II is on area minimizing ones with wetting area constraint. The stationary points for Type-I are free boundary CMC hypersurfaces while the ones for Type-II are minimal hypersurfaces with constant contact angle. We study the stability problem, namely, the second variation for area functional is nonnegative under two types of admissible deformations. We show the uniqueness result for stable type-I or type-II stationary hypersurfaces in a Euclidean ball. This talk is based on joint works with Guofang Wang and Jinyu Guo. Add to calendar: 

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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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