BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Oleg German DTSTART:20260211T190000Z DTEND:20260211T195000Z DTSTAMP:20260424T113931Z UID:FGC-IPM/65 DESCRIPTION:Title: On the transference principle in Diophantine approximation\nby Oleg G erman as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nIn 1842 \, Dirichlet published his famous theorem which became\nthe foundation of Diophantine approximation. The phenomenon he found\ninspired Liouville to study how well algebraic numbers can be\napproximated by rationals\, and t hus\, to come up with a method of\nconstructing transcendental numbers exp licitly. The development of these\nideas led to the concepts of irrational ity measure and transcendence\nmeasure. Thanks to Minkowski\, it became cl ear that many problems arising\nin the theory of Diophantine approximation could be addressed quite\neffectively using the tools of geometry of numb ers. In particular\, the\ngeometric approach naturally offers a wide varie ty of multidimensional\nanalogues of the concept of irrationality measure — so called\nDiophantine exponents. In the talk\, we will discuss variou s Diophantine\nexponents and the geometry that arises when studying them. We will pay\nspecial attention to the phenomenon discovered by Khintchine\ , which he\ncalled the transference principle.\n LOCATION:https://researchseminars.org/talk/FGC-IPM/65/ END:VEVENT END:VCALENDAR