中科院数学与系统科学研究院

数学研究所

中科院华罗庚数学重点实验室

华罗庚青年数学论坛

学术报告

 

报告人: 陈绿洲 博士(Purdue University
  目:Quasimorphisms and Bavard's duality
  间:2023.03.06(星期一),09:00-11:00
  点:腾讯会议:258-427-102
摘 要:Quasimorphisms are generalizations of homomorphisms to the real number. Groups with nice aciton on Gromov-hyperbolic spaces often have a large space of quasimorphisms, although such groups can have trivial abelianization. In this talk, I will give an introduction to quasimorphisms, including basic examples and constructions, their relation to bounded cohomology and group actions on certains spaces, and a duality theorem of Bavard that makes quasimorphisms a powerful tool to prove lower bounds of stable commutator length.


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报告人: 陈绿洲 博士(Purdue University
  目:Stable commutator length and linear programming
  间:2023.03.09(星期四),09:00-11:00
  点:腾讯会议:471-327-730
摘 要:Several topological optimization problems involving surfaces can be turned into linear programming problems. In the case of stable commutator length, this was first discovered by Danny Calegari in the case of free groups. I later generalized this to a much broader class of graphs of groups. In this talk, I will explain the idea of turning such topological optimization problems into linear programming problems, and how linear programming duality can be used to obtain sharp lower bounds of stable commutator length (or similar invariants) as a replacement of Bavard's duality.

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