Fri, April 19, 2019
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10:00am [10:30am] Kirill Cherednichenko, University of Bath
Lecture Series on Partial Differential Equations. Speaker: Kirill Cherednichenko. Affiliation: University of Bath. Title: Periodic PDEs with micro-resonators: unified approach to homogenisation and time-dispersive media. Venue: Ramanujan Hall, Department of Mathematics. Friday 19 April, 10.30 am - 12.30 pm. Lecture IV. Schur-Frobenius inversion formula the generalised resolvent on the resonant inclusion. An effective description of the original family of transmission problems. A time-dispersive effective formulation in the whole space. An example of the effective formulae for a specific cell geometry. Band gaps and “metamaterial” properties.

2:00pm [2:30pm] Ananthnarayan Hariharan
Commutative algebra: Date, Time, Venue: Friday, 19th Apr, 2:30 - 3:30 p.m.,Commutative algebra Room 113. Title: Pure modules and Cohen-Macaulay rings Abstract: This is a talk in Boij-Soderberg theory, which involves the study of Betti cones over quotients of polynomial rings. These were introduced by Boij-Soderberg in 2008, and explored further by Eisenbud-Schreyer in 2009. I will give a quick introduction to this theory and the main problems. Finally, I will point out how of a result of mine (joint with Rajiv Kumar) on the construction of pure modules over Cohen-Macaulay rings follows immediately from the work of Eisenbud-Schreyer using Noether Normalization, and the Auslander-Buchsbaum Formula (which are two important results the students proved in the reading course). I will try to make the talk as self-contained as possible. All are welcome.