


Commutative algebra seminar
Tuesday, 30 August 2022, 4.00 pm5.30 pm
Venue: Ramanujan Hall
Speaker: J. K. Verma
Title: Fibers of blowing ups, symbolic Rees algebras, and settheoretic complete intersections
Abstract: In this series of three talks, I will present classical results of CowsikNori about fibers of blowing ups, criteria for Noetherian property of symbolic Rees algebras, due to Huneke, GotoNishida, and its relation with settheoretic complete intersections. If time permits, I will show some concrete examples of settheoretic complete intersection ideals in polynomial rings such as monomial space curves, Fermat ideals, and certain ideals of hyperplane arrangements.
Mathematics Colloquium
Venue: Ramanujan Hall, Mathematics Department, Room 214
Date and time: Wednesday, 7 September 2022 at 4 pm
Speaker: Dr. Akashdeep Dey, Princeton University
Title: A comparison of the AlmgrenPitts and the AllenCahn minmax theory
Abstract: Minmax theory for the area functional was developed by Almgren
and Pitts to construct closed minimal hypersurfaces in arbitrary closed
Riemannian manifolds. There is an alternate PDEbased approach to the
construction of minimal hypersurfaces. This approach is based on the study
of the limiting behavior of solutions to the AllenCahn equation. In my
talk, I will briefly describe the AlmgrenPitts minmax theory and the
AllenCahn's minmax theory and discuss the question of to what extent these
two theories agree.
Note: The Mathematics Colloquia are accessible to the general audience.
Mathematics Colloquium Speaker: Prof. Ravi Raghunathan Date: Friday, 9 September 2022 Duration: 4.005.00 pm Venue: Ramanujan Hall, Mathematics Department, Room 214 Title: Sphere packing, the Uncertainty Principle, $E_8$ and Fourier interpolation on the real line Abstract: The talk will focus on two theorems of M. Viazovska who was awarded the Fields medal in Helsinki earlier this year. The first theorem resolved the problem of sphere packing in eight dimensions, while the closely related second theorem (proved jointly with D. Radchenko) establishes a new "Fourier interpolation" result for even Schwartz functions on the real line. The first half of the talk should be completely accessible to anyone with a first course in linear algebra and multivariable calculus (MA 109, MA 111, MA 106), and thus to most undergraduate students at IIT. The second half will require some familiarity with basic complex analysis (MA 205).