報(bào)告題目：Cyclicity in Polynomial Systems via Algebraic Methods

報(bào)告人：Brigita Fer?ec（研究員博導(dǎo)），University of Maribor

報(bào)告時(shí)間：2025年9月23日（周二）16:00-18:00

報(bào)告地點(diǎn)：明理樓C302

報(bào)告人簡(jiǎn)介：

Brigita Fer?ec 是馬里博爾大學(xué)能源技術(shù)學(xué)院以及自然科學(xué)與數(shù)學(xué)學(xué)院和應(yīng)用數(shù)學(xué)與理論物理研究中心的研究員。她于2009年在馬里博爾大學(xué)獲得碩士學(xué)位，并于2013年獲得博士學(xué)位。她的博士生導(dǎo)師是Valery Romanovskij教授，博士論文主題是常微分方程組的定性分析。她的研究領(lǐng)域包括微分方程和動(dòng)力系統(tǒng)。

報(bào)告內(nèi)容簡(jiǎn)介：

We investigate the cyclicity of planar polynomial systems, with emphasis on the bifurcation of limit cycles from singular points. Building on computational tools from commutative algebra, we analyze the structure of Bautin ideals and their role in bounding the number of bifurcating cycles. To overcome difficulties arising from non-radical ideals, we employ polynomial subalgebras adapted to the symmetry of time-reversible systems. Our approach further clarifies the relationship between center conditions and cyclicity, and allows us to distinguish the behavior across irreducible components of the center variety.

主辦單位：理學(xué)院、科學(xué)技術(shù)發(fā)展研究院、人工智能研究院