The goal of the meeting is for people at nearby universities to get to know each other. We will have eight 30 minute talks, with ample time remaining for discussions and exchanging ideas. Registration is now closed. List of SpeakersMichael Burr (Clemson) Dustin Cartwright (UT Knoxville) Noah Giansiracusa (University of Georgia) Robert Krone (Georgia Tech) Luke Oeding (Auburn) Rainer Sinn (Georgia Tech) Mark van Hoeij (Florida State University) Cynthia Vinzant (NCSU) Schedule9-10 registration, coffee 10-10:30 Noah Giansiracusa 10:30-11 Cynthia Vinzant 11-11:30 break 11:30-12 Mark van Hoeij 12-12:30 Dustin Cartwright 12:30-2:30 lunch 2:30-3 Michael Burr 3-3:30 Robert Krone 3:30-4 break 4-4:30 Rainer Sinn 4:30-5 Luke Oeding Dinner DirectionsThe School of Mathematics is located at Skiles Classroom Building, 686 Cherry St, Atlanta GA 30332 The talks will take place in room Skiles 005 on the ground floor. Please enter from the southwest corner of the building. ParkingStreet parking is available on weekends on Ferst Drive, Tech Parkway, and in the streets south of campus (e.g. near Luckie St and Merritts Ave). You can also park in any visitor parking lot: Visitor Area 1 (North Ave) 33°46'16.1"N 84°23'41.7"W Visitor Area 2 (Student Center, Ferst Drive) map Please take a ticket when you enter and and keep it. We can give you a validation. If the gate is up, then you can park for free. Abstracts**Michael Burr.****Continuous Amortization: Intrinsic Complexity for Subdivision-based Algorithms.**
**Dustin Cartwright. A quantitative version of Mnev's theorem**
**Noah Giansiracusa. A persistent homology approach to fingerprint classification and comparison**
**Robert Krone. Equivariant Gröbner bases and syzygies**
Given a polynomial ring with an action of the infinite symmetric group on its set of variables, an equivariant Gröbner basis of an ideal is a set of polynomials whose orbits under the action form a Gröbner basis. Equivariant Gröbner bases offer a concise way to describe ideals in high dimension with symmetry and (under some conditions) can be effectively computed. We look to adapt signature based Gröbner basis algorithms to the equivariant setup, and in doing so confront the notion of equivariant syzygies. We prove that an ideal that is finitely generated up to symmetry has finitely generated equivariant syzygies when considered in the correct module. This is work in progress with Jan Draisma and Anton Leykin. **Luke Oeding. Homotopy techniques for tensor decomposition and perfect identifiability**
We propose a new method to find tensor decompositions via homotopy continuation. This technique allows us to find all decompositions of a given tensor (at least for relatively small tensors). Our experiments yielded a surprise - we found two new tensor formats, (3,4,5) and (2,2,2,3), where the generic tensor has a unique decomposition. Using techniques from algebraic geometry, we prove that these cases are indeed "generically identifiable".
**Rainer Sinn.****Generic Spectrahedral Shadows**
**Mark van Hoeij. Computing an Integral Basis for an Algebraic Function Field.**
**Cynthia Vinzant. An algebraic view on phase retrieval***The problem of phase retrieval is to reconstruct a signal from certain magnitude measurements. This problem is closely related to low-rank matrix completion and has many imaging-related applications: microscopy, optics, and diffraction imaging, among others. In purely mathematical terms, phase retrieval means recovering a complex vector from the modulus of its inner product with certain measurement vectors. One can ask how many measurements are necessary for this recovery to be possible. I’ll discuss recent progress made on this problem by translating it into real algebraic language and using tools from computational algebraic geometry.*
We thank the support from School of Mathematics at Georgia Tech. |