3月11日学术报告
报告题目：On the factoriality and fullness of q-deformed Araki-Woods von Neumann algebras
报告人：王斯萌(Simeng Wang)哈尔滨工业大学（Harbin Institute of of Technology）
报告时间：2024年3月11日（March 11th, 2024）上午09：30 - 10：30
报告地点：数理楼235教室 （Room 235）
报告摘要:I will present a complete answer to the question of factoriality and fullness of the q-deformed Araki-Woods von Neumann algebras. Our new approach essentially takes advantage of the type III deformation, which does NOT apply to the tracial setting. The talk is based on joint work with Panchugopal Bikram, Kunal Mukherjee, Eric Ricard and Manish Kumar (Comm. Math. Phys. 398 (2023) and arXiv:2401.07504).
报告题目：Proper cocycles, measure equivalence and Lp-Fourier multipliers
报告人： 姚淦(Gan Yao)哈尔滨工业大学（Harbin Institute of of Technology）
报告时间：2024年3月11日（March 11th, 2024）上午10:40-11:40
报告地点：数理楼235教室 （Room 235）
报告摘要:In this talk, we establish a new transference method of completely bounded Lp-Fourier multipliers for proper cocycles for pmp group actions on standard probability spaces. This generalizes the previous results by Haagerup and Jolissaint which only deals with the case p =∞. In particular, this gives a natural transference method of Fourier multipliers between groups with measure equivalence, which directly implies and notably generalizes the main result of Hong-Wang-Wang on the pointwise convergence of noncommutative Fourier series on amenable groups. As a second application, this theory also yields a transference method of Lp-Fourier multipliers from lattices in a linear Lie group to the whole group, which strengthens the previous results for Schur multipliers obtained by Haagerup and Lafforgue-de la Salle. This is ongoing joint work with Simeng Wang.
报告题目：Finite de Finetti theorems for free easy quantum groups
报告人:王建权(Jianquan Wang)哈尔滨工业大学（Harbin Institute of of Technology）
报告时间：2024年3月11日（March 11th, 2024）下午15:00- 16:00
报告地点：数理楼235教室 （Room 235）
报告摘要:We prove various finite de Finetti theorems for noncommutative distribution which are invariant under the free easy quantum group actions. This complements the de Finetti theorem by Banica, Curran and Speicher; the latter only applies to infinite sequences. We also discuss some refined results for the infinite setting.
报告题目：Summability of two dimensional noncommutative Walsh Fourier series
报告人： 赵甜甜(TianTian Zhao)哈尔滨工业大学（Harbin Institute of of Technology）
报告时间：2024年3月11日（March 11th, 2024）下午16：15 - 17：15
报告地点：数理楼235教室 （Room 235）
报告摘要:This paper investigates the summability of two dimensional noncommutative Walsh Fourier series. We construct a family of general positive operators $(T_{\gamma})_{(\gamma)\in \Gamma}$, where $\Gamma$ is a index set. When the kernel functions of these operators satisfy some assumption, we can prove the noncommutative maximal inequalities of this family of operators $(T_{\gamma})_{(\gamma)\in \Gamma}$. Specifically, we demonstrate that the kernel functions of Ces\`{a}ro means, Marcinkiewicz means and triangular means of noncommutative Walsh Fourier series satisfy this assumption, and then we obtain the noncommutative maximal inequalities of these three means operators, which implies bilateral almost uniform convergence with initial data in $L_1(L_\infty(0,1)\bar{\otimes}\mathcal{M})$.
3月12日学术报告
报告题目：TBA
报告人：Dmitriy Zanin(The University of New South Wales )
报告时间：2024年3月12日（March 12th, 2024）下午14：30 - 15：30
报告地点：数理楼235教室 （Room 235）
报告题目：Diagonality of commuting self-adjoint $n$-tuples modulo normed ideals
报告人：赵红印（Hongyin Zhao）（The University of New South Wales)
报告时间：2024年3月12日（March 12th, 2024）下午15: 40 - 16:40
报告地点：数理楼235教室（Room 235）
报告摘要:The famous Weyl-von Neumann Theorem states that, for every self-adjoint operator $b$ on a separable Hilbert space and for every $\e>0,$ there exists a diagonal operator $d$ such that $\|b-d\|_{L_2(B(H))}<\e$, where $L_2(B(H))$ is the Hilbert-Schmidt class. Voiculescu proved that every normal operator is a Hilbert-Schmidt perturbation of a diagonal operator.
More generally, Voiculescu developed a systematic method for the treatment of the diagonality of a commuting self-adjoint $n$-tuple $\alpha\in (B(H))^n$ modulo a given normed ideal, based on his beautiful non-commutative Weyl-von Neumann theorem regarding the approximate equivalence between representations of separable $C^\ast$-algebras. He proved that the diagonality of $\alpha$ modulo $\mathcal{J}$ is equivalent to the existence of a quasicentral approximate unit of $\alpha$ relative to $\mathcal{J}$. In this talk, I will introduce our recent results on the extension of Voiculescu's results in the setting of von Neumann algebras. This is a joint work with Alexey Ber, Fedor Sukochev and Dmitriy Zanin.
报告题目：Fourier multipliers on HNN extensions
报告人：夏润莲(Runlian Xia)University of Glasgow
报告时间：2024年3月11日（March 11th, 2024）下午16:40 - 17: 40
报告地点：数理楼235教室 （Room 235）
报告摘要:Amalgamated free products and HNN extensions are the two fundamental objects in the Bass-Serre theory. In this talk, we will introduce some $L_p$-bounded ($1<p<\infty$) Fourier multipliers for HNN extensions, with the help of Khinchine type inequalities on these groups.
This work is a continuation of a recent work with Adri\'an Gonz\'alez and Javier Parcet. It is related to the results of Mei, Ricard and Xu who proved $L_p$-boundedness of the same type of Fourier multipliers on amalgamated free products of von Neumann algebras.
