August, 2024

Thursday
August 1
11:00 am
SE 215

Analysis and Algebra Seminar

Speaker:  Parker Edwards, Assistant Professor 

Title: On computing local monodromy (part IV)

Abstract: A fundamental fact about zero sets of systems of polynomial equations over the complex numbers is that they decompose into a finite number of irreducible algebraic subsets. Knowing a thorough description of the irreducible components of an algebraic variety tells you quite a bit about it, and computing one is an essential preprocessing step to many numerical algorithms.  Standard algorithms for computing this numerical irreducible decomposition combine some relatively sophisticated machinery. This week's talk will cover some background on monodromy actions and how they're used to detect irreducible components of algebraic varieties.  A main component is computing the monodromy action of certain linear projection maps using numerical continuation.

What if one is instead interested in studying the geometric properties of an algebraic variety localized at a point? This puts you into the realm of singularity theory in complex analytic geometry, which is a rich and ongoing area of theoretical development. Every zero set of a system of complex-valued analytic functions has a local irreducible decomposition at each point. Computing a corresponding numerical local irreducible decomposition is similarly essential to developing a local approach to numerical algebraic geometry.

I will discuss some recent work with Jon Hauenstein which culminates in an algorithm for doing so. My aim for these seminars is to give a thorough enough overview of the background to understand what the algorithm is doing. If there's interest, we can discuss enough to get at the main ideas of the proof that it works. Here's the breakdown:

• Background: Algebraic varieties, reducibility, and hyperplane sections
• Background: Covering maps, branched covers, and monodromy
• Local monodromy, statement of algorithm, and example results

August, 5-9
9 am-5 pm
Sandbox
(Wimberly Library)

Young CryptograpHers Cybersecurity Summer Camp

Young CryptograpHers is a Cybersecurity summer camp specially designed for high school girls. Participants will be introduced to the fundamental principles of cybersecurity and learn how to apply conceptual knowledge to real-world situations. The camp will focus on Post-Quantum Cryptography, the area of math that is in charge of protecting our information in the era of quantum technology. The program includes lectures and activities by FAU faculty, alumni and speakers from industry and government. Our goal is to motivate and inspire talented students who are interested in a cybersecurity career.    ( flyer )

Regsiter Here!

Thursday
August 22
11:00 am
SE 215

Analysis and Applications

Speaker:  Turgay Bayraktar, Sabanci University (Istanbul)

Title:  Random Real Algebraic Geometry and Random Ameobas

Abstract: Click here