MenuEvents for 03/03/2025 from all calendars
Geometry Seminar
Time: 3:00PM - 4:00PM
Location: BLOC 302
Speaker: R. Oliveira, U. Waterloo
Title: Primes via Zeros: interactive proofs for testing primality of natural classes of ideals
Abstract: A central question in mathematics and computer science is the question of determining whether a given ideal I is prime, which geometrically corresponds to the zero set of $I$, denoted $Z(I)$, being irreducible. The current best algorithms for the ideal primality testing problem require, in the worst-case, exponential space (i.e., in EXPSPACE). This state of affairs has prompted intense research on the computational complexity of this problem even for special and natural classes of ideals. Notable classes of ideals are the class of radical ideals, complete intersections (and more generally Cohen-Macaulay ideals). For radical ideals, the current best upper bounds are given by (Buergisser & Scheiblechner, 2009), putting the problem in PSPACE. For complete intersections, the primary decomposition algorithm of (Eisenbud, Huneke, Vasconcelos 1992) coupled with the degree bounds of (Dickenstein et al 1991), puts the ideal primality testing problem in exponential time (EXP). In these situations, the only known complexity-theoretic lower bound for the ideal primality testing problem is that it is coNP-hard for the classes of radical ideals, and equidimensional Cohen-Macaulay ideals. In this work, we significantly reduce the complexity-theoretic gap for the ideal primality testing problem for the important families of ideals (namely, *radical ideals* and *equidimensional Cohen-Macaulay ideals*). For these classes of ideals, assuming the Generalized Riemann Hypothesis, we show that primality testing can be efficiently verified (also by randomized algorithms). This significantly improves the upper bound for these classes, approaching their lower bound, as the primality testing problem is coNP-hard for these classes of ideals. This talked is based on joint work with Abhibhav Garg and Nitin Saxena.
Applied Math Seminar
Time: 4:00PM - 5:00PM
Location: Zoom
Speaker: Michael Siegel, New Jersey Institute of Technology, Newark
Title: A fast mesh-free boundary integral method for two-phase flow with soluble surfactant
Abstract: We present an accurate and efficient boundary integral (BI) method to simulate the deformation of drops and bubbles in Stokes flow with soluble surfactant. Soluble surfactant advects and diffuses in bulk fluids while adsorbing and desorbing from interfaces. Since the fluid velocity depends on the bulk surfactant concentration C, the advection-diffusion equation governing C is nonlinear, which precludes the Green’s function formulation necessary for a BI method. However, in the physically representative large Peclet number limit an analytical reduction of the surfactant dynamics surprisingly permits a Green’s function formulation. Despite this, existing fast algorithms for similar BI formulations, such as those developed for the heat equation, do not readily apply. To address this challenge, we present a new fast algorithm for our formulation which gives a mesh-free solution to the fully coupled moving interface problem, including soluble surfactant effects. The method extends to other problems involving advection-diffusion in the large Peclet number limit. This is joint work with Michael Booty (NJIT), Samantha Evans (NJIT), and Johannes Tausch (SMU). Zoom: https://tamu.zoom.us/j/94220070032
Student/Postdoc Working Geometry Seminar
Time: 4:00PM - 5:00PM
Location: BLOC 302
Speaker: Derek Wu, Texas A&M
Title: Hypercohomology II
Math Club Meeting- Tomography - seeing invisible. An engineering, mathematics, and physics miracle.
Time: 7:00PM - 8:00PM
Location: BLOC 150
Speaker: Peter Kuchment
Description: Tomography is an area of imaging techniques prominent in medical imaging, industrial non-destructive testing, geology/seismology, and homeland security. It has been around for about 60 years (with some earlier predecessors), but it is still not only alive and kicking, but virtually exploding, bringing all the time new fascinating engineering, mathematics, and physics problems. In this talk I will try to wet your interest without diving too deep into many technicalities.
