應(yīng)yl7703永利官網(wǎng)耿俊教授和楊四輩教授邀請(qǐng),北京交通大學(xué)梁熠宇副教授將于2022年8月25日舉行線上專題學(xué)術(shù)報(bào)告.

報(bào)告題目：Fourier dimension and avoidance of linear patterns

時(shí) 間：2022年8月25日(星期四)14:30;

騰訊會(huì)議ID:485-441-989.

報(bào)告摘要：

The results in this talk are of two types. On one hand, we construct sets of large Fourier dimension that avoid nontrivial solutions of certain classes of linear equations. We find a Salem set of dimension 1 that contains no nontrivial solution of any of these equations. Variants of this construction can also be used to obtain Salem sets that avoid solutions of translation-invariant linear equations of other kinds, for instance, when the collection of linear equations to be avoided is uncountable or has irrational coefficients. While such constructions seem to suggest that Salem sets can avoid many configurations, our second type of results offers a counterpoint. We show that a set whose Fourier dimension exceeds 2/(v+1) cannot avoid nontrivial solutions of all equations of some particular form.

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梁熠宇教授簡介

梁熠宇,北京交通大學(xué)yl7703永利官網(wǎng)副教授,研究方向?yàn)榛A(chǔ)數(shù)學(xué)調(diào)和分析方向. 2015年6月在北京師范大學(xué)獲得博士學(xué)位. 2017-2018訪問加拿大英屬哥倫比亞大學(xué)一年.從事調(diào)和分析及其應(yīng)用相關(guān)的研究工作,至今在包括Adv. Math., Trans. Amer. Math. Soc., Proc. Amer. Math. Soc., J. Fourier Anal. Appl.等刊物上發(fā)表論文十余篇,并在Springer數(shù)學(xué)叢書Lecture Notes in Mathematics上出版專著Real-Variable Theory of Musielak-Orlicz Hardy Spaces.

甘肅應(yīng)用數(shù)學(xué)中心

甘肅省高校應(yīng)用數(shù)學(xué)與復(fù)雜系統(tǒng)省級(jí)重點(diǎn)實(shí)驗(yàn)室

yl7703永利官網(wǎng)

萃英學(xué)院

2022年8月22日